Question

The terminal voltage of a cell is equal to
A. Potential across an external resistance
B. Potential across the internal resistance
C. Potential across the sum of external resistance and internal resistance
D. emf of the cell

Answer 1

Hint: As we all know that the work required to bring a unit positive charge from one point to another point is called a potential difference. We should know that if a potential difference exists between two bodies, the charge or current flows from a body at the higher potential to a body at lower potential.

Complete step by step answer:
We must know that when the circuit is switched on, then the potential difference across the terminals of the load is called Terminal voltage. It is a voltage of any device like the alternator, generator, and cell measured across its terminals. Here the load can be a resistor, capacitor, etc.
So we can say that option (A) is correct.
In the case of no-load, there is no potential difference across the load and hence the potential across internal resistance is the emf of the cell. We know that emf is defined by,
$E = V + i\,r$…… (I)
Here $E$ is the emf, $V$ is the voltage across the load, $i$ is the current and $r$ is the resistance.
So we can say that in the case of no-load $V = 0$ and hence the equation (I) becomes,
$ \Rightarrow E = i\,r$
Suppose if the load is not zero, then also the terminal voltage is not the voltage across the internal resistance.
Hence this option (B) is wrong as there is no description of the terminal voltage.
In option (C), it is talking about the complete potential difference including external resistance and internal resistance. It can happen only when some current is flowing through the circuit. Let us suppose a circuit with load resistor $R$ is connected to a battery of emf $E$ and internal resistance $r$ with the current flowing is $i$.We know that the potential difference $V$ across the load $R$ is given by
$V = iR$
Therefore, equation ($I$) becomes,
$ \Rightarrow E = iR + ir$
Hence we can see that now the potential difference across both the resistance is $E$ which is the emf and not the terminal voltage.
Therefore, option (C) is wrong.
We know that in general, when no current is flowing in the circuit, the potential difference across the poles of the cells equal to emf. Hence when no current is flowing then there can be no potential difference across a load.
We can say now that option (D) is also wrong.

$\therefore$ Only option (A) is correct.

Note:
We should keep in mind that the terminal voltage is measured by voltmeter and the emf is measured by the potentiometer. Terminal voltage is always smaller than emf due to the drop in potential difference due to the current passing through the internal resistance of the cell.