Question

In a potentiometer experiment for measuring the emf of a cell, the null point is at 240 cm when we have a 500 Ω resistor in series with the cell and galvanometer. If the series resistance is reduced to half, then the null point will be at:

• A. 480 cm
• B. 240 cm
• C. 120 cm
• D. 60 cm

Hint:

Potentiometer measures emf directly; null point does not depend on series resistance.

Answer 1

The Correct Option is B

To solve the problem, we must understand the working of a potentiometer and the concept of null point measurement.

In a potentiometer experiment, the potential difference across a certain length of the wire is balanced against the emf of the cell. The balance (or null point) occurs when there is no current flowing through the galvanometer, meaning the potential drop across the selected length of the potentiometer wire equals the emf of the cell.

The key fact is that the null point is determined by the balance of potential difference, and it doesn't depend on the external series resistance when the cell’s emf and the potentiometer wire's resistance remain unchanged.

Let's dive into the steps for solving this problem:

1. Initially, with a 500 Ω resistor in the circuit, the null point is observed at a length of 240 cm.
2. The formula for the potential drop across the potentiometer wire is given by: \(V = K \cdot l\), where \(V\) is the voltage, \(K\) is the potential gradient, and \(l\) is the length.
3. The null point length \(l\) directly corresponds to the emf of the cell if balanced: \(\text{emf} = K \cdot 240 \, \text{cm}\).
4. Changing the series resistance affects the total resistance of the circuit but does not affect the balance point when measured based on emf, because the potentiometer still compares emf alone, and the wire length needed to balance the emf will be unchanged.
5. Reducing the series resistance to half means the external current's effect on balance is adjusted, but the null point nature based on potential remains constant.

Thus, the null point remains the same at 240 cm when the series resistance is reduced. Therefore, the correct answer is:

240 cm

This solution shows that the key to understanding this problem is recognizing that the potentiometer balances potential differences and isn't affected by series resistance changes.