Current, Resistance, and Ohm’s Law

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A CURRENT, \(I\), of electricity exist in a region when a net electric charge is transported from one point to another in that region. Suppose the charge is moving through a wire. If a charge \(q\) is transported through a given cross section of the wire in a time \(t\), then the current through the wire is :
Here, \(q\) is in \(coulomb\), \(C\) , \(t\) is in seconds, \(s\) and \(I\) is in \(ampere\), \(A\).
It is mean that the current have value 1 \(ampere\) if in 1 \(second\) flow charge 1 \(coulomb\).
Then \(1\,elektron=1,6x10^{-19}\,coulomb\), so 1 \(coulomb\) = \(\frac{1}{1,6x10^{-19}}=6,25x10^{18}\,electrons\).
By custom the direction of the current is taken to be in the direction of flow of positive charge, thus, a flow of electrons to the right corresponds to a current to the left.

A BATERY is a source of electrical energy. If no internal energy losses occur in the battery, then the potential difference between its terminals is called the \(electromotive\,force\) (emf) of the battery. Unless, otherwise stated, it will be assumed that the terminal potential difference of a battery is equal to its emf. The unit for emf is the same as the unit for potential difference, the \(volt\), V.

THE RESISTANCE (R) of a wire or other object is a measure of the potential difference \(V\) that must be impressed across the object to cause a current of one ampere to flow throuugh it:
The unit of resistance is the \(ohm\), for which the symbol \(\Omega\) (Greek omega). 1 \(\Omega\) = 1 \(V/A\).

OHM’S LAW originally contained two parts. Its first part was simply the defining equation for resistance, \(V\) = \(I\) \(R\). We often refer to this equation as being Ohm’s Law. However, Ohm also stated that \(R\) is a constant independent of \(V\) and \(I\). This latter part of the Law is only approximately correct.

The relation \(V\) = \(I\) \(R\) can be applied to any resistor, where \(V\) is the potential difference (p.d.) the two ends of the resistor, \(I\) is the current through the resistor, and \(R\) is the resistance of the resistor under those conditions.

THE TERMINAL POTENTIAL DIFFERENCE (\(or\,Voltage\)) of a battery or generator when it delivers a current \(I\) is related to its electromotive force( \(emf\) or \(\epsilon\)) and its internal resistance, \(r\).
1.      When delivering current (on discharge):
Terminal voltage = (emf) – (voltage drop in internal resistance r ) ,\(V\)= \(\epsilon\,-\,I\,r\)
2.      When recieving current (on charge):
Terminal voltage = (emf) + (voltage drop in internal resistance r ) ,\(V\)= \(\epsilon\,+\,I\,r\)
3.      When no current exists:
Terminal voltage = (emf of battery or generator),\(V\)= \(\epsilon\)
Potensial Jepit = ggl,\(V\) = \(\epsilon\)

RESISTIVITY: The resistance  \(R\) of awire of length \(L\) and cross-sectional area \(A\) is: \[R=\rho\frac{L}{A}\]
where \(\rho\) is a constant called the \(resistivity\). The resistivity is a characteristic of the material from which the wire is made. For  \(L\) in meter, \(A\) in \(m^{2}\) and \(R\) in \(\Omega\), so the units of \(\rho\) is \(\Omega\,m\).

RESISTANCE VARIES TEMPERATURE: If a wire has a resistance  \(R_{0}\) at temperature \(T_{0}\), then its resistance \(R\) at a temperature \(T\) is \[R=R_{0}+\alpha R_{0}(T-T_{0})\]
where \(\alpha\) is the \(temperature\,\,coefficient\,\,of\,\,resistance\) of the material of the wire. Usually \(\alpha\) varies with temperature and so this relation is applicable only over a small temperature range. The units of \(\alpha\) are \(K^{-1}\) or \(^{\circ}C^{-1}\).

A similar relation applies to the variation of resistivity with temperature. If \(\rho_{0}\) and \(\rho\) are the resistivities at \(T_{0}\) and \(T\), respectively, then \[\rho=\rho_{0}+\alpha \rho_{0}(T-T_{0})\]

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Current, Resistance, and Ohm’s Law