you can follow along with this presentation using printed slides from the nano hub visit www.nano hub dot org and download the PDF file containing the slides for this presentation print them out and turn each page when you hear the following sound enjoy the show okay so this is lecture 22 and non-ideal effects and in this by this non-ideal effect I mean there are some additional complexity that we want to look into for the IV characteristics the first one is junction recombination because we haven't been sort of putting the recombination away but you know you cannot do it forever and we'll talk a little bit of impact ionization before concluding we are still talking about the DC characteristics of a diode and at various bias conditions and today we are going to talk about this six region six this is trap assisted recombination generation so it's almost it happens at a only at a very low bias that is where you can see it happens at high bias also but I'll show you in a second why you will not see that effect in a high bias case I'll show you in a second and then we'll talk about this other other aspect of it now it's a little bit mathematically complex I cannot explain every step I can explain every step but I shouldn't go through them all you should be able to follow the math once you go home and trace through the argument one argument we had been making that in if you have the device in equilibrium the Fermi level is flat there is a built-in potential of q vbi and the carrier concentration has a certain profile as shown here on the right-hand side you can see the blue remains a majority carrier on the left-hand side becomes a minority carrier on the right-hand side and falls off in between similarly the red large on the right-hand side very small on the left-hand side and falls in between but the idea is that in equilibrium if you take any two points at a given location multiply them what is that value so always equal to ni square so therefore there's no recombination generation because the numerator of the recombination generation is NP minus ns square in equilibrium no net generation or recombination however as soon as you apply a forward bias let's say by the amount of v then the carrier concentration will not remain equal to equal to ni squared anymore right so that is what I have shown on the bottom right figure that the carrier concentration is no longer the same and in the junction region especially it has been modified quite a bit you can see the linearly drooping region on the blue car that's the diffusion remember the triangular region so that's I'm trying to show it there but now I want to just focus on the junction because junction is where recombination generation plays a important role now why in the junction it is because when you diffuse a dopant in in a let's say in a p-type material you diffuse a dopant in in the junction region many times they do not find their chair meaning they did not find the spot they should sit in and therefore junction is always prone to a lot of defects and right processing is very important so you primarily focus on the junction region where recombination generation might play an important role so let's let's try to work it out I just want to calculate the current due to recombination alone assuming I have calculated all other currents previously now what happens that the electron and hole comes in and you can see that the red and the blue they will come and they can come halfway in the junction and they can recombine right why don't they recombine on the right and the left hand side because on the right and left hand side carrier concentrations are close to equilibrium I'll show here that this is a huge amount of carrier concentration in the junction and that causes a significant recombination this expression you know and fear and this is a complicated expression but this is what expression is this this is Shockley Reed Hall expression right but this time I have written it as a function of nx and px because carrier concentrations are not constant everywhere you have solved this problem also in your homework now let's try to calculate this nx and px and we'll insert it in and see see what happens now if I assume tau n is equal to tau p for a particular case it simply means that their velocities are approximately the same okay e i is equal to e t that all the traps are mid-gaps sort of so that n1 and p1 you know this right becomes equal to n i okay it's my simplifies my life doesn't change the physics so I have a very simple expression where np is given by n i squared and exponential of the voltage and then in the denominator tau have been taken out n and p together and n1 and p1 has been written as 2n i okay this is no rocket science yet hopefully you remember the homework now this is I have mentioned this already that in non-equilibrium case the splitting of the quasi Fermi level at low current levels low current levels right otherwise they'll be drooping the Fermi level and in the junction the separation will have a delta fn and delta fp that I am not writing low current level so the carrier concentration goes like this but first let me convince you that the carrier concentration will be given by this red line do you agree n i exponential of fn minus e i that you agree right that's the traditional expression now fn at low current is flat up to the other side of the junction so I shouldn't really have to touch fn so I keep it keep it the same but e i well as the junction as the potential is varying e i you should follow along so e i will have a reference e i sub l which is whatever the i is on the left hand contact and the potential whatever potential does e i does the same thing so you put it in there and that's the second expression so only x dependence is coming through the potential vx okay so what about px do you agree because n and p is equal to ni squared the exponential that's on the numerator on the denominator I have simply written an expression borrowed the expression for n sub x and just put it in the right hand side denominator and if you divide you can see that ni squared and ni will take you take care of one ni here this is a constant that comes here and the whole thing gets flipped so you have a minus sign but other than that I haven't done anything here see okay now let's see so we'll redefine this term I'll go through the next two things because difficult to explain in a board like this all the steps but I'm just renormalizing things and calling variables various names so that I can write it a little simply don't have to carry around all the kts and all other things and I can emphasize on the shape of the function now do you see on the denominator why it will become a cosine hyperbolic do you see that what is the expression for cosine hyperbolic e to the power x plus e to the power minus x divided by 2 right so you can see why there should be a cosine hyperbolic do you see why should there should be a sine hyperbolic because if you pull out e exponential of ua over 2 pull it out then the remaining piece will become a sine hyperbolic because it has a exponential 2 exponential subtractive now the applied voltage is a constant it doesn't depend on a position so I should be able to pull it out of the integral that's what I have done and only place where the x dependence remains is in u right u is the new v here normalized v so there's the only place it remains and then if I want to integrate this out you know I have just written that if I want to integrate it out I just provide the two steps that is behind that step I just made that why there's an exponential of cosine and there's a sine hyperbolic in here this is just go back do your in your room for a few minutes that should be simple so once you have that you can integrate this and that requires the integration table and I will not do that but only point I will point out is that u at x at a given point generally one can find out the from this triangular electric field what the potential is at various points but in general that's difficult so I will replace it with a constant electric field and call that e max and then e max multiplied by x is what that u is this is an approximation but now I can do the integration and that's it that's the integration and this one has two features that I want to emphasize one is the effective width do you agree kt over q what is that that's a dimension of a voltage if you divide with e max which is electric field what do you get you get a dimension of a space or the distance so that is of sort of the effective distance over which recombination is occurring the right hand side do you agree that that's essentially the extra carrier concentration that you have in the junction region exponential of q va over kt now why is that to because it's middle of the junction because the whole thing is separated by va in the middle of the junction is separated by va over 2 so therefore you have that and this feature that it goes half of the slope of the classical diffusion that is an indicator that you have a huge amount of traps in your system you better take care of it otherwise your diode is not going anywhere that's signature of that to in the low current part in the high current part what is the signature of that's the ambipolar part right ambipolar has lots of electrons and holes together that's where the 2 comes off that's high current but a low current if you see also you have half the slope then you know that that's because there's a lot of traps in your system and where is the trap hiding by the way do you see what the trap is in the tau right because tau is inversely proportional to the number of traps if you have a huge amount of traps then they recombine very quickly tau is small if you have no traps tau is infinity no recombination current so that makes us and this is a very important problem by the way because we had been thinking about just one-dimensional cut most of the time it doesn't look too bad but you see the problem is that many times most of the time diodes are two-dimensional you cover it up with the oxide so that dark doesn't go through from the top it doesn't go through the junction is protected but do you realize that any time you have a curvature on the corners the electric field will be concentrated on the curvatures right when do you know that that generally if you have a sphere then you have a certain electric field but they the lightening rod on many of the top of the homes has a very asymmetrical shape right it's very long and very sharp because sharp points have high electric field so what's going to happen that although you did your design on one-dimensional thing that I just showed you in the previous one in the real device you will have these corners where the electric field will be very high and in that case you can have a significant amount of recombination on those points so one has to be very careful about designing junctions for practical devices now that was all about forward bias side that's fine on the reverse bias side the answer is very simple fortunately because in the reverse bias side again you have done it in a homework have you in the reverse bias side you do not have any carriers n and p are both zero and so therefore the generation current is ni divided by tau you have done this in last homework so you can integrate it out now this time even I can do this integration because ni divided by tau that's a constant so I can pull it out I will have a w and what is that w said to a saying and telling us this is the width of the depletion do you remember that the depletion with as you apply reverse bias that becomes larger and larger and goes as square root of the voltage right applied voltage va has a negative sign here so that overall thing is positive and so therefore this current in region 4 increases with the square root of voltage and that's why this current keeps increasing otherwise ideally it should have been flat the diffusion kind should have been flat because the recombination generation generation in the depletion region you will have a square root dependency on the voltage again that's another signature to know that you have too much too much defects okay I will start doing this non-ideal effect associated with impact ionization a little bit let me just show you one slide and then we'll continue so the final point one is to discuss is this breakdown due to impact ionization and this is how it occurs now you are in reverse bias right hand side is grounded left hand side you have applied a huge positive bias right positive on an n side is a bad thing means it's in reverse bias what happens that think about an electron coming from the top from the top side it's like a one skier is sort of standing on the top of a mountain now that electron comes in if it is not scattered by the phonons which is lattice vibration then it can have a certain amount of energy right if it has enough energy larger than the band gap then and in fact it turns out three halves band gap yeah it's a 50% more than the band gap if it can somehow gain that amount of energy then it can kick a way it can scatter with an electron from the valence band and kick that electron up in the conduction band right now it has two electrons one hole this two electrons keep going it's like a second skier has joined two electrons starts going let's say phonons done doesn't steal its energy it gets three halves kt a three halves the band gap approximately then this two scatters with two more electrons from the valence band gets his friends up in the conduction band now I have four electron going and how many holes I had one from before this time I have generated two I have three electrons three holes going and you can very quickly see that 1 to 2 2 to 4 4 to 8 8 to 16 what is this progression this is an exponential progression geometric progression so therefore eventually in exponential progression and therefore huge amount of current will start flowing through such a system and this is called an impact ionization and impact ionization is also maybe called as a inverse oj process because oj force them to combine and go down here electrons are being generated why doesn't it happen and his bias is low well if the bias is low no matter how much bias you put in or how much what you do it never has enough energy larger than the band gap and if it doesn't have any better larger than the band gap no hope of impact ionization so therefore in a forward bias case right or in the small reverse bias case impact ionization doesn't occur and so this is this is it keeps going down like this and somebody helped me to do this animation let's see how it works not too bad what you say so but you get the idea right how many electrons and how it will rapidly multiply now the math part of it I will take up in the next slide okay alright so what you just saw in the previous slide was this idea that if you have an electron from the top of the conduction band shown here in single red circle then when it gains enough energy from the electric field this is a reverse bias p-n junction you remember then it is going to gain enough energy larger than the band gap and most of the time almost 50% larger than the band gap in that case if it can survive that far without scattering then it is going to excite an electron from the valence band which is shown here in blue it will leave behind a hole and correspondingly an electron will go up and then there are two electrons and in this process one electron generates two electrons two electrons generates four four to eight and this process continues like an avalanche and the same thing is going to happen for the holes because if you consider the holes that have been generated in this process when they the world is upside down for the holes and so holes would like to go from left to right and this electric field assist them and when in a high electric field it has enough energy the holes can scatter and it can generate among themselves and it can also pump an electron up to the conduction band so both this avalanche goes out in goes in parallel and as a result there's a huge flux of electrons flowing through so let's see how if you take a small chunk between 0 and w a small grid delta x let's say 100 you divide it and you take one small chunk in that case if you look at the electron number then I will say that the electron number at x plus delta x out of that little box is whatever electron came in in x and then the electron multiplied by its impact ionization probability because not all electrons had energy or were able to gain energy equal to the band gap or more than the band gap in only a fraction did and that fraction is let's say alpha n that were able to ionize the electrons and therefore put them in the conduction band so this impact ionization would be alpha n multiplied by i n that's the contribution from the electron side but the holes are also doing their own multiplication and every time a new hole is generated a new electron is generated as well as a result the term in blue that in is the whole contribution to this impact ionization process remember all this top line is all electrons actually this is just contribution from various places now one thing I would like you to notice is the x axis I have drawn here is in a typical in the form right to left so that the signs will remain consistent okay so this is a very simple equation that we know how to solve because if I just bring the right hand i n x to the left hand side divide throughout by delta x then you realize that this becomes a simple first order differential equation of how the electron current grows as a function of distance right because of the impact ionization and you can see this equation you may have seen before if there were no impact ionization in that case alpha n and alpha p is 0 and you see what this equation is this is simply divergence of j is equal to 0 so this right hand side is like a generation term you see previously have seen divergence of j is equal to generation minus recombination so this whole thing that I'm seeing showing you here is actually nothing new it is just the generation term but this time we can solve it so for example the electron current remember this is steady state there is no derivative term for time in steady state the current must be continuous that whether you look at in the right hand side in the middle or in the left hand side the total current some of the electron and hole current that must be continuous and that total current if I call that total current i sub t whatever that current is I don't know yet if I call that current i sub t I shouldn't carry around a x around it because it is independent of position and the hole current since the current must be conserved must be written as it minus i sub n now this is only in steady state of course if you are doing a transient problem you cannot write it this way because then it will be depending on both time and position okay so if you have this then you realize that immediately this becomes a differential equation with the only unknown is i n and it whatever it is that one can calculate in magenta that will become that's a constant now this is a first order differential equation that you have solved many times in your life you may not recognize it here so people use it something called an integrating factor do you remember first order differential equation of this sort that has both the first derivative and a linear term so if you do not remember just open up a book or search it in google called integrating factor and you will immediately see that the answer you get is look something horrendous like this but it's not too bad because you know as electrical engineers will actually begin to throw away most of the terms and only keep the one that are most interesting but thing is that you can sort of see how why the solution has to be like this right you can see there are lots of exponentials floating around and when you have exponentials floating around that's sort of saying that if you put a small amount of current on the one side that is going to multiply geometrically you know one two four eight and eventually when it goes out from w by the time it goes out to the w a huge amount of current will go out so therefore there are lots of exponentials floating around and you can also see i n of zero i n of zero is the amount of injected current on the right hand side of the junction what is that coming current coming from do you remember that in reverse bias in the minority carrier side one side of the carrier concentration was suppressed to zero right in the reverse side as a result there was a diffusion flux is constant diffusion flux coming out from the right hand side so that minuscule amount of current that will be the seed of this avalanche and then it will proceed so that's the right hand side the one at red i n zero is the diffusion reverse diffusion current flowing through the diode right and this is something we have already calculated in our previous class and and then of course i n w is the total amount that is getting out from the left hand side after all this avalanche multiplication immediately you realize i n is very small i w is huge right because of this all this impact ionization process going on okay and alpha and alpha p you remember these are what are these these are impact ionization coefficients how many electrons does one electron generate as a result of impact ionization per unit length so this number can be 1000 electrons new electrons generated per injected electron per centimeter to a million that means so you can see it's a very efficient process at high voltages this i have already told you that the whole current and the electron current is constant at any point and if it's constant at any point obviously it's constant at w so i am writing it i sub t now look at what i did next what i said that i can drop i pe of w right the whole current and then at beginning of w is this correct this may be correct because you see current is constant and the electron current has drawn huge amount by the time it has reached w after all this impact ionization if the current has to be constant and this one component has grown exponentially the other piece must be negligible right so therefore i drop that term which is ip at w of course i couldn't drop ip at zero because ip at zero is a huge number so therefore you have to be careful how you drop it and also let me write this quantity that i enough zero as a fraction of it is some number i sub p it could be a million so that is the total current that is getting out at the point w relative to the current that was injected on the initial seed point that's really i will be calling a global multiplication factor m sub p so this number by the time it is done it could be you may inject one electron and you can get 10 000 out from the w point so that's what this number is a very large number okay so if i have these two relationships then do you see i can simplify it in this way do you see this on the right and look at the first equation on the top side i n zero i'm dropping it that's small do you see the magenta the show one shown in magenta that i'm cross multiplying and i n at w and it is that equal to one almost equal to one do you see that why because most of the current which is getting out at w is the electron current i do not have any whole current so therefore i n at w divided by it is very close to one so i have one i cross multiply the whole thing and just exchange sides and that will give me this very simple relationship of course it's not simple enough for me i need to simplify further so let's see what we do but you do you see what term next term you should drop one over mp this m sub p is 10 000 let's say so compared to one well that can go also so if that can go one over mp then i'm carrying around just one and if i'm carrying around just one then it's already simple enough but not really now i'm going to further assume that the number of electrons extra electron generated by an electron and number of extra electron generated by a hole they are the same now of course they cannot be the same right because electrons can gain energy they have a different effective mass so they can gain energy a little bit faster let's say then the holes holes are heavy and sluggish they don't get energy from the field as easily and phonons can steal its energy very easily so in general if you look at your book reference books and other things you will see that alpha n and alpha p are not the same but you know for the time being let me assume they are the same if you want you can put the right values in and you can do the integral but if i set alpha n and alpha p equal to each other then what should be the fate of the exponential well that will be gone because that's e to the power zero now that's getting simple enough further further i'm going to assume that alpha doesn't really depend on position because if the electric field is constant in this starting from zero to w if it's so constant then i can say alpha is a constant but of course it's not a constant you can see the electric field shown here in the bottom is like a triangle right it's not a constant but what is going to happen that most i'm going to show you a little bit later that most of the impact ionization occurs at the maximum electric field point so actually we are talking about a very small region close to the peak of that triangle and so i will be taking alpha p out of the integral as well now that's simple enough for me because if i take alpha p out if i set the exponential top of that zero then i have nothing left i have alpha p multiplied by w equals one and this is when you know this happens when significant avalanching is going on because without significant avalanching one over mp that i couldn't neglect compared to one right so this is this condition only happens when i have a significant avalanche current flowing then i will have this now this alpha p what is this alpha p is number of extra electron generated per injected electron and it depends on the electric field because the more electric field you have it is easier for the electrons to gain energy right as a result this has typically if you look at the experimental data people have done a lot of beautiful theory many famous professors have spent probably a significant part of their life looking into this type of impact ionization process especially in the 60s and 70s and one simple form that sort of looks correct in terms of electric field is this now do you realize why this equation might be right you see if the electric field is very small then the exponent is very large and e to the power a very large quantity is zero so you don't have much impact ionization when the field is small but if the field is very large then you can see the gradually the magnitude of this quantity will keep rising and as a result you will have a huge amount of impact ionization if the electric field is high okay now if that is the case what electric field should i put in well if i solve the diode equation correctly then you can see the blue and the red the triangles depending on various bias reverse biases i can always calculate that do you remember depletion approximation the charges and the triangles that we created so i can always create that and i realize that the maximum electric field will be essentially i can put the e max in place of e the electric field e and calculate alpha now if i are on the other way if i know w the depletion width then the point where the avalanche will begin is one is given by one over alpha but that electric field from that i can also calculate the electric field a not is known a not and b unknown material parameters so only unknown in that case is the electric field e and from that i can calculate the voltage right if i know the electric field i also know the voltage voltage at which this diode will break down by avalanche right you by just using this relationship do you see this electric field as i have already told you that this is a formula that we have derived already right do you remember that vbi minus va and it's reverse bias so this should be a plus sign vbi plus magnitude of va and then from this if we insert back in the equation for alpha p and require that condition alpha p multiplied by w that be satisfied i only thing unknown in that equation is the applied voltage and as a result i can immediately tell you at what point is this diode going to break down by avalanche multiplication now this is a very important problem of course in technology there's a very important problem there are places where this effect is actually used in great advantage and sometimes it is bad you know there's always good and bad on the top side where i say good these are could be imagers where you reverse bias a diode just before impact ionization point so it hasn't really impact ionizing a lot now a single photon comes in that's the seed the single photon comes in generate an electron hole pair and now you have an electron which is falling down this huge potential and similarly a hole falling down the potential potential well or not potential well that's a from the mountain top of a mountain going down sort of down the hill and in that case you can have a single photon detectors based on this avalanche process but sometimes it's bad for example there are places where you do not want impact ionization and the corners i have already mentioned the corners are very high electric field like a lightning rod and in that case let's say you have done a one-dimensional analysis everything is fine you put your diode in the product all in a sudden you see it's breaking down all the time and your diodes are burning right feel there is customers are returning your product that is because you haven't designed the junction properly junction electric field was too much so when you're applying a reverse bias this is breaking down from the corner an avalanche is occurring from the corner and then the diode cannot function so depending on the application this is different things might happen how would you avoid that it's a very nice trick how you can avoid this type of problem and the trick is this instead of having an abrupt junction between n and p all you need to do is to insert a little i region little i region in between so put a little bit lighter dope region now i'll see whether you understood the previous concepts now do you agree that the electric field on the left hand side for the abrupt junction is a triangle but that of a region which has a i in between is really like a trapezoid why is it because by the time you come to the intrinsic region whatever electric field you came with that electric field must continue right because there is no charges to capture the field so that is the base of the trapezoid and of course once you come to the other side the electric field is going to go down and go to the zero value because it must start at zero and ended zero now do you remember i have applied a given bias across this if i have applied a given external bias then the area under these two triangles at two cars must be the same because voltage is simply area under the integral of the electric field and electric field means the area under the two cars must be the same now if the area under the two cars is the same which one would have higher electric field do you think obviously the abrupt junction because this one will have significantly lower electric field so therefore just by inserting a thin insulating or intrinsic region in between the abrupt junction you can lower the electric field significantly and in fact this is what you you will hear the term as we go on the term called lightly doped drain this is a this was a huge problem in 1980s for MOSFET design because MOSFETs were failing by hot electron injection and one person essentially came up with idea that you just put a lightly doped region in between the heavily doped region i will come back to this point again but the point is that actually allowed the scaling MOSFET scaling in your computer that to continue for many years in 1980 just based on the concept that i just showed you so none of them are just you know just to torture you these have actual and practical relevance so this is the point i wanted to make that if you insert an intrinsic region that can be excellent now one thing i must explain to you that this analysis that i showed you this date back to 1960s when the diodes were really big the junctions were huge and doping was one side 10 to the power 16 another side 10 to the power 17 this centimeter cube this type of doping low doping these days however in modern MOSFETs in many junctions the doping on one side could be 10 to the power 20 and another side it could be 10 to the power 18 huge doping if you have huge doping the junction is going to be very tiny right very small as a result when the electron comes in from one side it may be able to go from one side to the other side without ever scattering that's ballistic transport if you don't scatter of course you cannot really do an impact ionization right you need to scatter with other electrons so in case of ballistic transport in a highly doped junction everything that i told you might not be correct in this case an electron and that's called a dead space the space you need before an electron can impact ionize you know the first one it has to start now if it is many a huge junction you can impact ionize many times you can start with one get out of 10,000 if on the other hand it's extremely small let's say on the tens of nanometer in that case electron can get out without impact ionizing so you shouldn't any time you see this form situation you shouldn't immediately try to apply the classical formula you should see whether it is relevant or not now one final thing is how do you differentiate between zener tunneling and impact ionization do you remember both in the reverse side gives huge current one by tunneling another by impact ionization now generally one rule of thumb which is not a very good way of differentiating is that zener tunneling always occurs at a much lower voltage compared to impact ionization i'll ask you to verify this statement this is an interesting statement that zener tunneling would occur about a volt generally impact ionization occurs much later you should convince yourself why this should be the case but more importantly you see the interesting thing is zener tunneling is a tunneling process electrons slowly going to the other side and it doesn't have too much noise if you see it's a regular pattern of electrons sort of swimming through the band gap region and getting to the other side very calm current very not very very quiet current on the other hand impact ionization is a horrendous thing going on you know electrons holes are being generated so on the output side even if you have the same amount of current you will see impact ionization has significantly more noise and as a result that tells you that this is impact ionization versus zener tunneling and also impact ionization is not is a highly temperature sensitive function remember because phonons are taking away its energy band gap is changing because of this temperature on the other hand zener tunneling is much less temperature sensitive so by looking at this you know you have to find out why it's breaking down before you prescribe a fix fix to this problem and this is what you should be looking for the signatures a doctor like a doctor you should be looking for before you prescribe a medicine for the patient so that's it i explained the region five and two physics of region five in terms of zener tunneling or it could be impact ionization whichever occurs first so we have actually gone through all these dc characteristics region one purely diffusion region two what is that half the slope ambipolar transport because electron and hole where so much they essentially become equal to each other so the ni square divided by na it picked up a square root similarly region three where what is a huge injection so that there was a huge resistance drop in the bulk region itself delta p n and delta p region four what is this this is generation square root of the voltage as the depletion width is getting up then the thermal generation process increasing with a square root of delta v applied voltage region five either zener tunneling or impact ionization and you know the physics how to calculate that six and seven well six is trap assisted recombination in the forward side and again just like number two six has half the slope of the diffusion regime because the electron and hole must be equal to each other before they recombine so if you see a half slope region in our low voltage then you know your junction is horrible lots of trap sitting there you'll have to fix it right and seven well seven was again a tunneling process and that's the isaki tunneling you remember that how under heavy bias heavy doping condition electrons can flow from the conduction band to the valence band of the other side the extra current component wouldn't happen in low dope samples okay so i just try to describe the physics of various pieces and junction recombination is very important that's a process maturity tool that one can use it as a process maturity tool to see how many defects you have if you have very low this region six that you have sorry very high region six in low voltage regime you better go back and fix your process otherwise this product isn't going out of the door now as i said impact ionization is very important and wide variety of devices use this and these are commercial products that you can buy in various places go to radio shack you may be able to find some of this and now let's move on to ac response we are done with dc this is gone let's talk about ac now ac is i'll apply a small bias and small signal and see how it proceeds how the same thing proceeds okay


Okay, if you can I was going to pause that right there I just want you to watch your hand if you can I call it seesaw and don't see saw back and forth as much Try to have your hand a little lower and then I Want to point something else out right here. So see this toe right there? Look at that toe. It's pointing straight towards the horse. You want to turn that toe out Where it opens up? that knee Okay, and then you're able to balance your horse By using your feet not happen to see saw your reins if that makes sense Okay, and if it don't then we can go over it later But that's that's what I see. I want you to turn those toes out to maneuver the body of the horse To take your rain hand and make it more quiet See right there. See that's what I was talking about right there You could have controlled that right there. I hadn't got to that point right there, but you could let me let me rewind this just a minute Okay So look what happens right here.  I really like your horse See right there. Just I can see you using your foot turn the toe out I don't care if you have to sit on the in the Living room on watching TV put a put a saddle rack up there and turn your toes out if you're if you're serious about it So I can see So right there. I'm gonna stop right there.  You're pushing that cow to go that way Okay, so you need to be I got a lot of lines. I want you here I want you to hear that because you're pushing that cow right there. So you're you're you're getting it I'm gonna push play here. Okay, and you're you're getting no credit earning cut right there Like you're going down 69 right now or 68 right now because you're cut so right there you dictate


Check. Welcome back after the break. We look at the last lesson in fulfilling God's purpose for our life. Okay. The last lesson is finishing your course. So can some of you just tell me what we were learning from chapter, you know, from the very beginning. Just a few points. Okay, Anand. Yes. Okay. Anand says fulfilling God's purpose for our life is not going to be easy. Okay. We can have even our online students contribute. Okay. We're looking at the last chapter. So we are just reviewing what we have learned throughout. So can you share what are some of the points that you learned? You have to bear the cost. Okay. Okay. You have to make sacrifices. Yes, Nina. Okay. The sacrifices, daily sacrifices, life sacrifices, what else? Okay. You have to, it can be freshly led sacrifices or spirit led sacrifices. What did we study in the previous lessons? Sorry.  Okay. We are called to partner with God. Thank you. To fulfill our purpose or his purpose, his purpose for our lives. Okay. What is the basic thing we learned? The first, the nine guidepost, we basically first learned that God has a plan and purpose for our lives.   Nations he wants us to shake. Okay. So he has great big plans for us. Does he reveal his plans for us? Yes. And so we saw that, you know, the nine guideposts to how God communicates his plan and purpose. And so he knows one or more of the nine guideposts to lead us, to guide us. Okay. Now, if you have discovered God's plan and purpose for your life. Yeah. We have some answers from our online students. Sacrifice and surrender to God. Sacrifice our, surrender our life to God. Jason says, spirit let sacrifices to please God. Okay. Anything else you'll learn online students? Yes, Sean. Very good. Very important to fulfill God's purpose for our lives. We need to position ourselves rightly at the right time, the right place, doing the right things so that we can receive God's provision, his blessing. And we can fulfill God's assignment for our lives. Surya says being transformed. Okay. Thank you. So these are some of the things that we learned. We're looking at the last chapter now. Okay.  You know, and somewhere along the line, you can give up, right? In give up saying it's not good. It's difficult. But it can be difficult. It will not be easy. I told you all the days of your life will not be very exciting, happy. You will not feel, you know, the joy, she will not feel the excitement. Some days you will not feel the anointing.  All of those things, but irrespective of, we don't depend on our feelings. We just go on what God has called us, what he's asking us to do. You know, God will help us with our failures. He will correct us and he will guide us. But we need to finish our race and not give up. Yes, Sean. I think we're all in the same boat with you. All of us don't understand the entirety of scripture. You know, we're all struggling. I know we all are struggling, but just to, you know, to encourage you. Yeah, so, you know, that will get us to go deeper into. What if we read everything and we just know? Oh, we know everything. Then sometimes they say, why don't we even read the word? But, you know, when we read God's Word, we're like, okay, what does it say? Where else? So we go to other scripture passages we're trying to find out. And we know it takes us deeper into meditation, into reading God's Word. And also it takes us, depends more on the Holy Spirit to inspire us to help us understand. And when we receive some revelation, like, wow, we receive this revelation. We're so excited about it. Yeah, so it's a good thing to, yeah, not like, you know, you said, not stop there. Oh, I didn't understand it. Okay, there's something in scripture. Don't understand. That's a totally different attitude. But have your attitude is so important. You search scripture to find the answer. Okay. So we don't give up and we finish our race. Luke chapter 14, 27 to 35. So can somebody read, please? Luke chapter 14, 27, 28, 29 and 30. Nina says we need to recognize the stirring within the spirit of man as a lamp of the Lord. Yes, we learned the nine guideposts. So one of the guideposts you're mentioning here is recognize the stirring within. Thank you, Nina. And also, yes, we need to depend on the spirit of God, because the spirit of God reveals things in the spirit of man because the spirit of man is a lamp of the Lord in which she enlightens us, reveals things to us. Thank you, Nina. Okay. So can somebody read Luke chapter 14, verse 27? Yeah, that's enough, Anand. Yeah. So here, you know, Jesus is saying that we need to count the cost before we jump into or begin the journey of what God is calling us to do. So these verses very clearly tell us that. Okay. So if somebody is building a tower, really not sit down and think about the cost, how much money I need. You know, how much I need for foundation, how many flows, you know, what all of the things that we need. Okay. Whether he has enough to finish it. He won't start and then keep thinking how to get the money. Okay. So he says that, you know, if he does not do, then he will just lay the foundation and he will not be able to finish and all who see it will make fun of him. This is somebody who started building but did not count the cost. The same thing goes in our spiritual lives as well.   That's great. You're very excited about it. You're happy. It's wonderful. You tell everybody about that, but it's important for you to sit down. You know, you found God's purpose for your life, but it's important for you to sit down and count the cost. Meaning, what does it take for me to become a pastor? What does it take for me to become who God has called me to be? So what am I going to do? You plan the future. Okay. You plan five years down the line. You plan 10 years down the line. You just don't rush into it, but you plan. You say, okay, I don't have enough theological knowledge, so I will go to a theological college. How many years I'll invest in the theological college? There is the finances I'm going to get for it. You know, okay, I also want to get married. You know, how am I going to get married and study? What am I going to do? Or am I going to get to finish my studies first and get married?  The same with, even in the world, you know, you're starting a business. You just don't say, okay, I got a dream. I saw myself sitting in, you know, a restaurant, a bakery, so I'm going to start a bakery. Just don't go to the next day, look for a shop and start a bakery.  You're going to study other bakery businesses or hotel businesses, and then it will take time for you to see the right place to venture in, what kind of cuisine, what kind of food, all of that needs planning. The same way, even if they're calling in life. So don't rush into it, okay? When we plan, it can help us to successfully finish our race, okay? Planning is actually having four sites. What does it mean, your four site? That means thinking about things that will come in the future, okay? Thinking of things that will come up in the future. So for example, you're planning to have, you're trying to open a restaurant here in this area. Then if you say, I'm going to open a restaurant here. You cannot, you know, you can say, okay, this area is okay, but why don't I open it somewhere near Christa Genti College? You know, so I'm opening a Christa Genti College. Now if I have sambar and idli and rice, the students obviously don't like sambar, rasam and idli and dosa and all that.  It's not something that's... So you're thinking about all of these strategies before you get into your business, okay? And how you can be different from other businesses around you so that your business can prosper, okay? So you need to have foresight before. What if some other person comes and starts a restaurant? They also have something like this. How is mine going to be very unique compared to theirs? How can I keep my customers to my... So it's not just about, you know, the products that you have, but you have quality products, tasty products.   You know, they open at 6.30 till about one o'clock in the night. Why? Because they have that many customers. And if you look around, there are so many restaurants serving idli, dosa and pongal and all of those things, but these people, it's selling like hotcakes.  But why? And I went and checked it out because there's some unique innovative ideas they have from the rest of them who are making idli and dosa and chutney and sambar. You know, but everybody's running to their shop and meeting idli dosa for so many years. So these people have become very unique and that is why they are just bringing in customers and they're having from 6.30, I've gone to 7 o'clock in the morning, there's rush. You go at 11 o'clock, 11, 30, 12, 1 o'clock there is rush in that shop, okay? So how can you be very, very innovative? So you need to think and plan and anticipate upcoming events and then decide on the course of action. Now there's a Bible teachers that we need to plan. Does the Bible teachers that we need to plan? Yes, no. Some people say, you know, the Bible does not teach us to plan because God Jesus tells us, don't worry about tomorrow. Don't worry about tomorrow. The Bible is telling us, don't worry about tomorrow but it's not telling us don't plan about tomorrow. Some of us are so worried about tomorrow that we fail to plan and that becomes an extra worry burden for us, okay? So the Bible teaches us to plan. Let's look at some scripture passages. It's all given in your notes. Proverbs 4 verse 26 says, ponder the path of your feet and let all your ways be established, okay? Ponder the path of your feet. That means ponder means what?  Proverbs 6 verse 6 to 8. Can somebody read that please? Proverbs 6 verse 6 to 8. So God is telling, learn from whom? And the smallest creature. You know, we don't even sometimes see and stamp it. You know, saying learn from that and what do you learn from that ant? What are we learning? Suppose you learn from the ant. How to to work hard, okay? Unity How to plan? How to plan? Okay, what does the ant do? It has no overseer, has no leader telling them what to do, what not to do. But what does the ant do? During summer it is storing up food for the winter because it knows during winter it cannot gather food, okay? So the ant is teaching us to plan. So God can even use the smallest thing to teach us sometimes, some things. Okay, so next time we look at the ant, think about planning. Maybe God is reminding you about planning. Okay, can somebody please read Proverbs what is the meaning of go to the ant you sluggered? Who's a slugger? lazy, slow, moving, dull, moving person, okay? Proverbs 7 to 14 verse 8 and 15 can somebody read that? Proverbs 14 8 and 15. Yeah, so here it's talking about a prudent man or a prudent woman. Man is very general. Don't think women are left out, okay? Anthropos is a Greek word. Anthropos means human being, okay? But when it's translated they use men but it's also women here. So women don't think that we are left out, okay? So prudent here means be a prudent person is somebody who is wise, careful, cautious and practical. So here it says a prudent man, a wise man understands his way, knows where he's going, knows what he's doing. He considers well his steps, what he is doing. So ask yourself the way I'm going, the path I'm going, the way I'm preparing myself is it to fulfill God's purpose for your life? If you find some path or something that you're doing which is not going on this helping you fulfill God's plan or purpose for your life, you need to stop going on that path. You need to take the right path, walk on the right path. So you need to be prudent, okay? Proverbs chapter 22 verse 3, can somebody read that please? Yes, a prudent man, a wise man, a careful man, a smart man has four sides, is able to see things in the future, things coming in the future, is able to plan, to prepare you know, so here we see that, you know, he sees the dangers coming ahead and he's able to take precautionary action which will preserve his life. Okay, so we need to be like the prudent man. So Bible really clearly says that we need to plan, prepare and have foresight, plan, think about the future, plan for the future, see things that will come up in the future and prepare in advance.     I'll just test it out the first year and if it's good then I will do all the three years but got three years for the sun and after that I plan to get, you know, plan to go back to my place and then I plan to work under my pastor or you know, I plan to work under pastor Rashi because I can learn so much from him or I plan to learn from some other pastor in the city learn from him and then God in that meantime as I'm, you know, preparing and equipping myself how to be a pastor I'm going to get married and then, you know, maybe five years I would have prepared myself and after that, you know, God, I'm going to go to the place that you have called me to go back to Chattisgarh or to UP or Deradun or wherever and I'm going to plant a church. Okay but then after you have planned it, you can say God, this is my plan.  Have your way in my life show me what you want me to do and I will just do that. So when we do that, you know we need to be ready for uninterrupted changes, okay? Or you can, you need to be open to heavenly interventions that God will bring in. God may step in and change things in your plan that you have planned, okay? And we need to be willing to accommodate that and I'll say God, no, this is my plan, I decided this, I'm going to go by this, okay?  Then you can say, yes God, I'm willing to give this up, I'm willing to step into what you want me to do change this around maybe not five years, being with this pastor two years or maybe you want me to go straight away to Deradun and be under this pastor, I'll do that God whatever, you know, be willing to change because the Bible says the steps of a good man are ordered by the Lord, okay? So when we plan also we don't plan according to our own will but we plan according to God's own will so we submit and surrender ourselves to God's own will. Let's look at an example in 1 Corinthians 1 verses 15 to 17 1 Corinthians 1 verses 15 to 17 yes, read on 16 and 16 also, thank you. Okay, so here we see that Paul is planning his travel itinerary. Okay, what where and all he plans to go and then he answer question, do I plan this according to the according to the what does he say? Look at verse 17 the things I plan, do I plan according to the flesh? What is the answer? Does he plan according to the flesh? No, he plans according to the spirit, you know we see that Paul is constantly led by the spirit, he does what the spirit asks him to do. So we can plan according to the spirit or we can plan according to the flesh. Okay, in John chapter 16 verse 13 Jesus said the Holy Spirit will show you things to come. Okay, so you and I as believers we have the privilege. You know what is a privilege? We have heavily forecast. You know whether forecast will tell us what is going to happen, business forecast. You know that stock market forecast will tell you how the stock market is going to happen. Like that we have heavenly forecast. Okay, so you and I are very privileged because we have heavenly forecast. The Holy Spirit forecast or warns us or tells us things that are going to come and the things that we need to get prepared for. But the Holy Spirit is willing to give you the heavenly forecast and willing to listen. You need to be tuned into the Holy Spirit. Only when you go and tune into the weather forecast you will know what's the weather for today. Others you can just assume now the sun is shining but suddenly it can change. The weather can change. And you know the weather changes very drastically in some places. Okay, so you see that the Holy Spirit will tell you beforehand you need to get ready and you need to begin to plan according what is leading you to. So when the Holy Spirit will give you the warning he will also give you the strategies and he will also help you. So in your plan you need to take the Holy Spirit as your senior partner. All of us in fulfilling God's plan and purpose for your life. Who is your senior partner? Holy Spirit needs your senior partner. We need to develop Spirit inspired plans. The Holy Spirit will inspire us, tell us what to do. I always depend on the Holy Spirit for everything. I'm not a very I have some sense of creativity but I'm not a very creative person. But doing children's ministry everything I get download from heaven. The Holy Spirit will tell me. Even for you know when you have to have BBS or kids conference or do something in children's church some activity something is the Holy Spirit will give me the download. Just tell me what to do I'll just go do it. But I just have to work hard to prepare to think and everything but Holy Spirit will give the download. You know even what is the title, what is the you know theme what topics to be taught in children's church all heavenly download. You don't have to worry. See so once you are totally inspired but then it's so it's so exciting. You know even when I joined APC I was thinking of I joined in for the school outreach ministry and I was asking God what is I was looking at all the possible topics you know names that we can call the school outreach ministry of APC and I had a long list and then I was I remember I went back home and I was just lying on my bed and say God what would you want to call the school outreach ministry pop the answer came catalyst you know I never thought of catalyst and I put on all the names I thought of and I put catalyst and I send it to all the pastors and everyone chose catalyst see so you know everything all the programs that I have done for children's church I know it's it has children have enjoyed it they're very happy but everything is a download of from God even when I'm just walking and thinking you know go for my evening walks and thinking God how to decorate this whole theme children's church for kids conference he was suddenly show me somewhere I remember I was thinking once God how to do decorations for the kids conference this year and suddenly I was walking and I saw one a play school and they had you know they had how things in in a circle and they had written all those things in the you know in this in that printed circle wow this is a nice idea God thank you and you know we we just did that and the children and thoroughly enjoyed it after the kids conference everybody all the children said they wanted that auntie we want this they all took it and they went and hang it in their home so you know everything is just spirit led so you know the spirit can give you inspire ideas you can give you amazing ideas and you can when you just depend on him but the important thing to know is you know sometimes what we do is you know we we take two extremes we just take you know we just waiting what the spirit is telling us to do and we just do that and sometimes we are just going with what our mind is telling us to do okay but both need to operate to gather okay yes the spirit will give us the ideas but the God also uses our mind he's given us our mind he's given us our thinking he's given us a logical thinking reasoning faculties of the mind and we need to use it okay so don't leave out your brain okay you need to use your brain to create those innovative ideas which the Holy Spirit is giving you and don't always you know just say okay I'm waiting for the spirit to be to be led and the spirit is not telling me anything so I'm not going to do anything for kids conference this year because Holy Spirit is not giving me any ideas no I mean we can't do that okay so we we need to have a balance sometimes we are so spirit led you know that we can we can make a mess of it sometimes we are so led by this flesh that we use latest techniques modern techniques tools and all of that and we failed to hear what the spirit is telling us and then we think why did this whole thing become a failure I use modern techniques use the latest things I thought the youth will like it the children will like it nothing happened because it was not spirit led as well so you have to have your spirit led also use your brains your mind your logical reasoning and your thinking okay there's some comments here about spirit inspired planning by Pastor Jack Hayford that didn't hear basically this is the same thing that you know when we need to when we take on anything it has to be we have to have a clear sense of direction from the Holy Spirit can look at your notes the bullet points when they're doing things to promote our ministry you know it needs to be dependent on the Holy Spirit not on the human you know mind thinking logical understanding reasoning and we also need to pursue the things of God that is worship relationship with people unity maintaining unity discipleship and ministry when you're planning all these things are important and prayer is very very important okay most important thing is prayer we do everything else leave our prayer no it doesn't really work pray much often and always okay and wait for the Holy Spirit to give you clarity and conviction and lead you and guide you and also the he says you know it's important to have faith because without faith it's impossible to please God okay then we look at the ending but we have to run till the finish line okay Hebrews chapter 12 verses 1 and 2 very important can somebody read that please Hebrews chapter 12 verses 1 and 2 thank you so here this verse clearly these two verses tell us clearly what we need to do to ensure that we run our race and finish it we get to the finish line the first thing can anyone tell me what we need to do to ensure to run our race from this lay aside every weight thank you Rin lay aside every weight that means what you know when an athlete runs he does not run with all his backpack and you know with gear and all that you know he doesn't run with all of those things and gear and feet and all that he runs as light as possible okay so even when we are running our race we need to lay aside every weight means what yes so what is a weight back thoughts your distractions what else your burdens the past some of us are still holding on to our past it's such a burden on us you know when you're carrying something heavy you are you know you faint you will be faint hearted you will be so heavy hearted you will be so tired exhausted leave everything about the past there's nothing you can do about your past you can't go back there you can't rectify things you can't change things just continue looking in the present okay running your race can we can we run 100 meters race looking at the back no it cuts our speed you know I did that once when I was in bible college I took part in the in the race I qualified for the finals of the 100 meters race and it was all you know none of the students qualified I was only student who qualified among the ladies and all of them with you know our faculty children all small children I was like already thinking I'm going to lose the race because I'm thinking all of these children are so much faster and there was one girl called jamaima just from money put no she was the fastest runner in her school and I already had assumed that she's going to be first and I'm going to be last and all these days I was actually the 75 meter mark I was leading suddenly you know this whole thing hit me said I can't lead I can't come first I can't be first because these other children are faster than me and I turned around and jamaima was just behind me I thought I had done a false start and I'm just running the race and look at all these thoughts it taught me a big lesson in life and then I just look back I cut my speed and look back and just in the little distance everybody was shouting at me and don't you know when you're running the race you have to look in front why did you stop why did you look back and I didn't tell anybody what was going through my mind so don't look back there's no point you know the devil will always remind you of your past but you remind him of his future some of us are still living in the past so when you're living when you're turning back you can never move leave the past walk in the the future that God has for you yes Sean true thank you Sean for that example Sean is giving us an example of the horse when they go for the horse race you know they they cover the horse's eyes so that their horse doesn't see and just focused in the front okay what a second thing we need to do to ensure to run our race first one is lay aside every weight second one before on with endurance look at your the son Hebrew chapter 12 verse 1 look into Jesus before looking into Jesus what is given there lay aside every weight and then the sin that's so easily and tangles don't forget that sin can stop you or hinder you from running your race you can just get so caught up in it you know sometimes you know Satan is so smart you can just put things in our life that will just totally divert our attention rather than focusing on what Christ wants us to do it can even be people now people can come you can say people are gossiping about me talking about me okay let me let me find out what they're saying let me you know get back to them let me do this you know all that is a waste of time that is going to create disunity that's going to create division that's going to eat up your peace of mind so I don't focus on what people are saying besides me okay I know that people are saying this and that I can hear this and that but I'm saying God you deal with them I have no time no energy I'm just going to do what you want and God deals with all of those people he just moves what who he has to move he removes who he has to remove he keeps who he has to keep and who he has to keep even shows them what is that attitude they come in line we just work but I just try to maintain the unity the whole project that God has entrusted to me and keep people under me in unity in oneness just love them be nice to them so lay aside every sin that ensnares us sin, pride, jealousy, hatred competition you want to be there up in the front you don't allow anybody else you pull down everybody else it's Aimee myself ministry nobody else all of those things since secret sins God knows we need to deal with it others that will stop us from running our race what is the third thing run with endurance yes like I said sometimes we don't feel very happy doing what God called us to do we don't feel very excited what God has called us to do we don't feel heavenly or anointing for what God has called us to do we don't feel sometimes special excitement but you know we just have to endure to fulfill God's purpose all we need to do at those times is just fulfill our responsibility and steward the gospel that God has entrusted to us there can be high points, low points but we don't go on our feelings we don't let our feelings stop us from doing what God has called us to do we run the race with endurance okay so you know people around you might be doing things you know but you know God has called you here he has placed you here you be you continue you focus on Jesus you continue running your race and it's a tough people who are willing to continue going on even when the going gets tough you know when I joined full-time ministry you know when I went to Bible college you know you all know that it was not something that I really wanted to be because it's not that I didn't want to you know do God's call I love God I was already teaching in Sunday school but it was I felt I was not worthy enough to be in full-time ministry I didn't feel I was worthy enough my life was not worthy enough or holy enough like other men and women of God to be in full-time ministry that's why I said no God you know I can even serve you but not be in full-time ministry but when I went to Bible college the first year there was strike in our college it was one of the best colleges there was strike there was division there was two groups but I didn't join into any group that there was another price that I had to pay it was daily sacrifices you know and you know there was there was a whole thing about the Bible college being shut down you know there was a fear and everybody were asked to go back home in December but I did not go back home because I was scared because if I go back home you know my father says he told you that's why I didn't want you to go to Bible college you know and I couldn't face my father and I just stayed in Bible college and said God you wanted me to go to Bible college you wanted me to be in full-time ministry this is where you want me to be you have to take care of me I'm not going to quit this place I'm gonna be here you know you have to make things work and of course the Bible college started January we continued continued things are not easy things were difficult but I always spent time you know I never ran away I never gave up I stayed there even though things were difficult things were not easy and I finished my six years and that taught me endurance that taught me that you know in ministry people are not angels you know they're not all perfect people come on all of us are perfect God handles us God deals with us in our church we're not perfect people we're all imperfect but we're here to help each other correct each other you know build each other up so we don't just quit and just don't leave I didn't see perfect people and because I didn't see perfect people in Bible college I didn't leave I didn't run away I didn't think God this is not where you wanted me to be I'll go to some other Bible college no I stayed there because I know that is where God called me to be this is where he wanted me to be and you know I you know I stayed on and I continued there God gave me the grace he gave me the strength he taught me precious lessons that is why after that I faced many challenges but I was still stuck in the ministry for the last 22 years because I learned valuable lessons in my six years on campus in Bible college so don't think you know everybody's perfect nobody's perfect we're not angels here we're not we're not God here we're not Jesus here we're all imperfect people we're all here to continue to build each other up and to help each other continue to run our race so tough people who are willing to continue going on even when the going gets tough and then the last thing is look on to Jesus we don't look to people people will fall so because of people fall I can't keep moving Bible colleges I can't keep moving churches I can't keep moving machine organizations if God tells me to move to move you know and God taught me something once I wanted to move from an organization Christian organization God says no you stay there and continue and I stayed there and continued for one week and again after one week I said God I can't it's not a place where I can and you know what God told me very strictly ministry is not a matter of convenience it's a command ministry is not a matter of convenience it's convenient for me food is convenient lifestyle is convenient the hostel is convenient people are convenient I'll stay ministry is not a matter of convenience it is a command you know it's a command you stay there you do what God is asking you to do and how do you get through your race looking on to Jesus you look on to Jesus because he's the perfect person he will help you to see and love others and accept others and love yourself and move on okay the apostle Paul says in chapter 20 verse 24 he says oh you can read chapter 20 verses 22 and 24 please somebody can read that yeah read read somebody who's not read who wants to read can read we can hear some nice new voices thank you and so here it says we need to finish our race we need to lay down our life see what Paul says but none of these things move me nor do I count my life dear to my self so he knows he's going to go to Jerusalem the spirit is telling him and the Holy Spirit is telling you go to Jerusalem you will face imprisonment chains is you'll be imprisoned you'll face many tribulations and difficulties but Paul is saying nothing is going to move me he's saying I'm willing to give up my life I'm going to give up my life for the sake of the gospel okay I'm willing to count my not count my life dear to my self I know persecutions chains prison imprisonment tribulations are there everywhere but I'm willing to lay down my life look at what he says in Acts chapter 21 verse 13 so you know all of them all the people who love Paul the ministry companions saying please don't go to Jerusalem Holy Spirit is always telling you're going to be imprisoned and you're going to go to tribulations and they're all weeping and moaning because he says no I have to go you know and then he says you know why are you crying because I'm ready to lay down my life for the sake of the gospel okay second Timothy chapter 4 verse 6 to 8 Paul very beautifully says is writing to Timothy you know where he's where he's writing to Timothy from he's writing from prison he's imprisoned in Rome and he knows that he is going to die soon okay he's not going to his first Roman imprisonment he was set free the second time he knows he's not going to be set free he's going to surely die he's going to be martyred it's going to be a terrible death he knows that but what is he saying he's saying I've been a drink offering my time of departure has come that means my end is coming near is drawing very near is very close you know but he said what does he say I have fought the good fight I have finished the race I have kept the faith so wonderful you know we need to be also able to say that you know fought the good fight finished the race I kept the faith and then he says there's laid up for me a crown of righteousness with the righteous judge the Lord will give me on that day not only from to all those who have loved his appearing so even as you pursue God's plan and purpose for your life it's something that's wonderful big you know great he'll reveal it to you but enjoy the journey as you pursue God's dream for your life and you know be sure to endure and to finish it so that you can receive your crown any questions hi Krisha I remember your question I actually wanted to start the the morning the first hour by answering your question but you had not joined class so that's why I told the rest of them that we'll answer the question when you come when you join so I I do remember your question now you know when we we interpret something in scripture we always need to interpret it in the light of other scripture because one scripture always helps in interpreting other scripture if we take one scripture and interpret it out of context in isolation that can cause a lot of wrong doctrines and wrong teachings so when we look at some scripture we're trying to interpret something some way of living some lifestyle something that is being said there we always had to interpret it in the light of what was spoken earlier or what is also said in other passages of scripture so we keep them all together and then you have to interpret that scripture that you're trying to discern in the light of what other scriptures say so if you look at people saying that women have to cover their heads while praying or worshipping it's actually they're taking it from 1 Corinthians chapter 11 verses 3 to 16 where Paul is talking there about you know headships spiritual headship and head covering he's talking about spiritual headship and head covering and the context is writing this it's not in a context often that he wants women to cover the head but he's talking about spiritual headship he's talking about God's spiritual authority of God's government in the local church so he's talking about God's government through which he establishes or he brings about his exerts his influence or his blessing in the local church so all of us are placed under God's spiritual government or his spiritual headship in these areas of our life it can be in the family it can be in the local church it can be in the body of Christ it can be at the workplace and we all need to know what is God's spiritual headship in the area that he has planted and placed us so that we can recognize God's government and when we recognize and submit to God's government in that specific place you know we can experience God's influence blessing so here he's actually talking about in chapter 11 verses 3 to 16 he's basically talking about the spiritual headship in the body of Christ so he says in the body of Christ he's talking about the government in the body of Christ he says in the local church in the body of Christ he's saying man is the head of the woman and Christ is the head of man and he says and God is head of Christ now when we look at it we know that Christ and God are equal but here in God's government God the Father is the head over Christ just as Christ is the head of man and as man is the head of the woman so God even Jesus Christ willingly submitted to God's government or headship in the body of Christ and then he says in that context he's talking about a woman ought to cover her head I think it's in verse 10 and here it's a cultural context it's not a biblical context because we don't see it anywhere in the Bible where a woman has to cover her head so here is after pointing out that man and woman are co-equal we are the heads of God both men and women have the same Bible experience the same best things the same spiritual gifts we are called to different offices there is no division in that and then he goes on to talk about the cultural context and in the current cultural context was such that women typically had long hair but married women would cover their head and the prostitutes had short hair or bald head if you see a woman you know she's a prostitute because she had short hair or bald head and she was a good character woman because she had long hair and you know she was a married woman because she covered her head so it was actually the cultural context so here in this cultural context in the church at current he's talking about the headship and Paul is instructing all women to cover their heads by praying or prophesying in the local church but he does not mention this to the church at Galatians or Galatia or Ephesus or any other place okay and we also see in I think in verse 16 you know Paul clearly mentions there if anyone seems to be contentious we have no such custom nor do the churches of God okay so he's saying this is not a custom that other churches of God follow it's only a custom for the church at current so you know we can't take this and you know interpreted out of context and say all women have to cover their heads in all churches it's mandatory it's no it's the cultural context that Paul is writing and he's using that in the cultural context to explain to the church at current and he's not saying that it has to happen in other churches because he says we have no such customs nor do the other churches of God you know follow this okay it's time up thank you all for joining class I hope I answered your question Prisha


We know that the origin of this is arson. We do not know other information. There is no reason to assume that the origin of this fire or the reason this fire happened was because there were unhoused individuals nearby. Legally afforded this lessee and recall they have an unlawful attainer for a reason was the storage open storage broadly defined of non-flammable materials, non-explosive materials and vehicles operating vehicles. We saw those vehicles and we certainly saw a lot of pallets and a lot of open storage. Reroute my whole route I mean you have to consider like the 10 is a lot of people go on the 10 so we're all having to make adjustments pack the 101 that's already packed and then maybe even going to a 210 just it's just a headache but trying to get to Ontario airport our flight leaves out at eight but hopefully we make it all together they all collect. You got to you know leave early or try to you know use other routes you know try to you know just be hit and just be creative.


Hi everyone this is Alice Gao. In this video, let's start looking at our second normal form game. By analyzing this game, I will introduce another solution concept called the Nash equilibrium. In this game Alice and Bob are choosing between signing up for one of two activities, dancing or running. They both prefer dancing over running. You can see from the utility matrix that their utility for dancing are both higher, but they also prefer signing up for the same activity over signing up for two different activities, because everything is more fun when you do it together. Now from the first game, you should already know my passion and interest in swing dancing. Now this game might not accurately reflect my attitude towards running. As a child, I really, really hate running and that's still the case right now.  You have to get tested on the normal subjects like math, English, Mandarin, other things, but there is also a physical education exam. There's a PE exam with three subjects. One is doing crunches, which I was really good at. The other one is standing long jump. I was really terrible at it. But after a few months of practice, I can do it. And then the third one is running 800 meters. And then there is a time limit. So I think you can get perfect mark if it's a little bit less than four minutes. And you can pass if you can finish running 800 meters in almost five minutes. And I think I actually never really knew the perfect mark line very well, because I never got anywhere close to that. I was always barely passing and struggling with it. So ever since that, I hate any form of running whatsoever. Short distance, long distance. Yeah, just don't make me run. Anyway, enough about the rent about running. Let's come back to this game and let's figure out how Alice and Bob would like to play this game. As usual, first of all, let's think about what the players will do because our goal here is to predict how they would behave. So take some time and think about this yourself and then keep watching. I can't really ask you this question and show you the distribution of answers. But based on historical data, this is what I would predict. The the distribution we get will be a bimodal distribution. Most of you would say that Alice and Bob were both trues to go dancing. And some of you, a significant fraction of you would say that they would both go running. And both of you would be correct. These are two plausible, plausible outcomes of this game. And why is that? Well, because in some sense, these are the two stable outcomes of this game. And by stable here, I mean that if Alice sticks to dancing, then Bob does not want to go running instead. And similarly, if Bob sticks to running, then Alice does not want to go dancing instead, because deviating in that way will cause you to cause either player to get smaller lower utility. Now we've gotten this conclusion based on our intuition. Let's now see if solution concepts from game theory can help us to formalize this intuition. So far, the only solution concept we've talked about is the dominant strategy equilibrium. Let's try to apply the solution concept first and see what happens. So based on this game, dancing or running, is there a dominant strategy equilibrium of this game? If there is one, which of the four outcomes is a dominant strategy equilibrium? Think about this yourself, and then keep watching for the answer. The correct answer is the last one. This game has no dominant strategy equilibrium. And the short explanation is that first of all, the game is symmetric, so we can consider either player. If we consider Alice, then it turns out Alice does not have a dominant strategy. If Bob chooses a different action, then Alice would prefer a different action depending on Bob's choice. Therefore, there's no one action that's always the best for Alice. This means there's no dominant strategy. If there's no dominant strategy for a player, then there's no dominant strategy equilibrium. Unfortunately, this means that the dominant strategy equilibrium solution concept is not sufficient to capture our intuition about this game. Intuitively, we believe that dancing dancing or running running are both reasonable outcomes of this game. But based on dominant strategy equilibrium, it doesn't give us a prediction of how the players will behave. So we need to look at another solution concept and turns out Nash equilibrium would be a useful solution concept we can use to predict the player's behavior. In the next video, I'm going to introduce the concept of Nash equilibrium in more detail, and then use that to analyze this game. Thank you very much for watching. I will see you in the next video. Bye for now.