Question

In a potentiometer experiment for measuring the emf of a cell, the null potential is at 240cm when we have a $500\Omega $ resistor in series with the cell and the galvanometer. If the series resistance reduced to half, then the null point will be at:
A. 480 cm
B. 240 cm
C. 120 cm
D. 60 cm

Answer 1

Hint: In a potentiometer for measuring the emf of a cell, the null point depends upon the current that flows through the circuit. When the new resistance of half the value of the original resistance is used in series, the flow of current remains the same. So the null point does not shift and remains as it is.

Complete step by step answer:
A potentiometer is an electric device used to measure an unknown emf or potential difference accurately. It consists of a usually 1-meter long wire fixed on a wooden board parallel to each other. These wires are also mostly in series by thick copper strips. A meter scale is a fixed parallel to the wire ends.
The basic principle of a potentiometer is that when a constant current flows through the wire of uniform cross-sectional area and composition, the potential drop across any length of the wire is directly proportional to that length.
We know that by Ohm’s law,
$V = IR = I.\dfrac{{\rho l}}{A}{\text{ }}\left[ {\because R = \rho \dfrac{l}{A}} \right]$
For a wire of uniform cross-section and uniform composition, the resistivity $\rho $ and area of cross-section A are constant. Therefore, when a steady current flows through the wire,
$\dfrac{{I\rho }}{A} = a$ constant, k
Now, in the question it is given that:
Null point is at, $l = 240cm$
Resistance of resistor, $R = 500\Omega $
When this resistor is replaced by another resistor of half its resistance then, the current flowing through the circuit remains unchanged as the resistor is in series connection. And in series connection, the voltage drop across the resistor changes but the current flowing through remains the same. So the null point remains unaltered.
Therefore, the correct answer is B i.e., 240cm

Note: The potential drop per unit length of the potentiometer wire is known as the potential gradient of the potentiometer for that circuit. Its Si unit is $V{m^{ - 1}}$. The potentiometer can also be used to compare the emf of two primary cells and the internal resistance of the primary cell.