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Electric circuit analogies

The rope loop
The band saw
Water flowing in a pipe 'The water circuit'
Uneven ground
A ring of people each holding a ball
The number of buses on a bus route
Hot water system
Horse and sugar lump
Train and coal trucks
Rough sea
Crowded room

The rope loop

In this analogy a circuit is modelled as a big loop of rope.  One person is the battery and pulls the loop through their hands.  Another person is the resistance and squeezes the rope.  Friction with the hands of the resistor person means they can feel the energy transferred as heat.

There are some nice points to this analogy.  For example it's clear that energy is transferred very quickly, even though the rope can be moving quite slowly.  This the idea that the charges are already there and they all start moving everywhere at the same time.

You can also intuitively get big resistance means small current and you can see that energy is transferred where there is a big resistance.

It's not very good at explaining voltage or power. 

Unless the battery person is very disciplined at keeping the tension they feel constant, rather than trying to make the speed of the rope constant, you might get the impression that the bigger the resistance the quicker energy is transferred.

In other words, there's quite a temptation for the battery person to pull harder and harder as the resistance increases.  So they'd think that big resistances make the battery work harder.  This is an example of the constant current misconception.

In fact the opposite is the case.  If you make the resistance really big, the current is really small and the energy transfer is very slow.

The band saw

A band saw is a very long, flexible saw curved back onto itself into a loop.  The loop is stretched taught between two big wheels mounted above and below a saw bench.  A motor connected to one of the wheels drives the loop round so there's a continuous flow of saw through the bench so you can cut things.

This is a very similar analogy to the rope-loop.  The battery is the drive motor and energy is transferred where the wood is being cut.

If you think of each centimetre of saw representing one coulomb of charge then you can model voltage (which is energy per coulomb) as enery transferred per centimetre of saw.

You can think of the motor having to provide a certain amount of energy for each centimeter of saw that passes and you can also think of the same amount of energy per centimeter being transferred to the wood.

This gives you the idea that the battery voltage is the same as the p.d. across the load, e.g. a lightbulb.

Thanks to Jon Scaife at Sheffield University for telling me about this analogy.

Water flowing in a pipe 'The water circuit'

In this well-known analogy a battery is seen as a pump and resistances as constrictions in a pipe.  The pipes form a circuit and are already full of water.

A more powerful pump means a higher voltage battery.  This nicely shows that a big voltage causes a big current.

A narrow constriction means a big resistance so you also have the relationship big resistance means small current.

I have to declare an interest and say that I am not a fan of the water-in-pipes analogy (to put it mildly), though I do use a bath to try and explain parallel circuits.

There are so many problems with it but the most basic one is that students and teachers have very little understanding of fluid flow in pipes.  This alone should be enough to condemn it.

In particular, the idea of potential difference is often explained as a difference in pressure across either side of the constriction.  Can  you explain why there is a difference in pressure?  What is it physically about the water that make the pressure different?  I would suggest that even if you can answer these questions with confidence it's unlikely your students can.  So why use it as an analogy for something else?

The other problem is that there's no obvious distinction between what goes round and round (water) and what gets transferred (pressure?).  Yeuuch!

Uneven ground

Imagine a ring of people holding hands and moving in a circle.  If there's a patch of bumpy ground they have to walk over then this slows down the ring everywhere.

The bumpier the ground the higher the resistance and the slower the current.

A ring of people each holding a ball

In this analogy everyone stands in a circle and holds a ball.  To show the current flowing each person passes their ball to the person next to them.

You can show resistance by someone throwing the ball up in the air and catching it before they pass it on.  This tends to slow the progress of the balls everywhere in the circuit.

This is a very basic analogy and isn't great for anything other than showing that the charges are already there and they move everywhere at the same time.

The number of buses on a bus route

This analogy is good for explaining how an insulator works at a sub-atomic level.  Essentially there are fewer charges that are free to move.

Think of travelling from a-b, then b-c and finally c-d by three different buses.  For the first and third legs there are lots of buses but in the middle leg the buses are very infrequent.

This is closer to the model of resistance for a circuit where the wire narrows, or perhaps there's a component made of a different material.  It's not that the middle leg necessarily 'resists' the flow of buses it's just that in some parts of the circuit there are fewer mobile charge carriers (e.g. free electrons) than in others.

The speed of the journey from a-d is governed by the frequency of the buses in the middle leg.

For any given number of passengers going from a to d the average speed of any given bus has to be higher in the middle leg so the amount of bumping around per bus will be bigger.  The middle leg is where the most energy is converted.

Hot water system

This analogy tries to improve on the water circuit.  Instead of a pump with constrictions you have a boiler with radiators.  The boiler puts heat energy into the system, like a battery and the radiator transfers heat energy out of the system.

Question:  if you want your radiators to heat your room as quickly as possible do you want the water to flow through them very quickly or very slowly?  Even if you know the answer to this question do you think students have a good grasp of domestic heating installation?

It's one of those analogies that works quite well to describe roughly what's going on.  Something goes round and round and there's an energy transfer, but it very quickly becomes a rather cumbersome tool if you try and make it explain too many things.

Horse and sugar lump

This is another very basic analogy.  Imagine a big circle of horses walking nose-to-tail.  You feed them sugar lumps as they go past.  The more sugar you give them the faster they can all walk.  Resistance is modelled as a jump or some other activity that means they have to expend more energy.

One problem with this analogy is that the energy transfer happens slowly.  In other words, the energy from a sugar lump only travels as quickly as the horse that's eaten it.

Train and coal trucks

This is similar to the horse and sugar lump analogy.  Imagine a train the same length as a circular track.  As each truck passes a point it picks up coal from a big heap (the battery) and delivers it where it's needed (the load).

Since the trucks don't use the coal they're carrying you slightly lose the link that big voltage (i.e. lots of coal per truck) gives you big current.


This analogy equates height with voltage.  In other words gravitational potential with electrical potential.

You often see it with balls or sometimes even with water.

There's some kind of lift that raises the balls (say) to a given height, representing the voltage of the battery.  The higher it's raised the bigger the battery voltage.  The balls roll under gravity, often down stairs of varying heights (representing resistances).

You can see that the total gravitaional potential energy (GPE) lost by a ball rolling down the stairs is the same as the GPE it gained being raised by the lift.

Rough sea

This is more of an analogy for electrical resistance rather than for a whole circuit.

A boat travels quickly over a bumpy sea in a big circle (so it never goes anywhere).  The captain staggers slowly from one end of the boat to the other.  The rougher the sea and the faster the boat, the more the captain staggers and the slower he goes up the boat.

The total movement of the captain represents the motion of an electron in a circuit.

The speed of the boat represents the random thermal movement of the electrons in a wire, which is very fast.  The speed of the captain represents the very slow drift speed of the electrons because of the battery.

If the wire is hotter then the high random velocity of the electron is even higher, i.e. the boat moves faster.  This means the staggering speed of the captain is lower.  This accounts for why the resistance of a metal increases with temperature.

Crowded room

Imagine walking across a crowded room.  It takes longer if the crowd are moving about rather than standing still.

Here you represent an electron and the other people represent the lattice of positive ions in a metal.

Just like the rough sea analogy, this accounts for why resistance increases with temperature for a wire but does it in terms of movement of the ionic lattice rather than the electrons.

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