Question

Derive an expression for current flowing through a circuit when external resistance is connected to a real emf device.

Answer 1

We are given a circuit consisting of the two major components which are an electrical energy source with an electromotive force (emf) and an external resistance connected to it. We need to find the current flowing through the circuit.

Complete step by step answer:
We know that the emf is the potential difference of a source when there is no current in it or no current is flowing through it. And we are given a real emf device which means that the terminal voltage for the device is not the same as the device’s emf because all materials irrespective of being a conductor poses some internal resistance to the current flowing through it.

Therefore let us assume that the internal resistance of the device is $r$ and the external resistance connected to it is $R$. We know from Ohm’s law that current $I = \dfrac{V}{R}$ , where $V$ is the terminal voltage of the circuit which is given by where $E$ is the emf of the device and $R$ is the total resistance of the circuit.Now for the given circuit total resistance is equal to $R + r$.Therefore the current through the circuit is
$I = \dfrac{E}{{R + r}}$
And the potential difference or the terminal voltage is
$\therefore V = \dfrac{E}{{R + r}}R$

Note: We should not get confused with terminal voltage and the electromotive force (emf) of a battery or device. The terminal voltage is the potential difference between two points in a circuit consisting of the resistance whereas the emf is the potential difference of a device when no current is flowing through it like in the case of an open circuit.