Question

How does the balancing length change if the length of the potentiometer wire is doubled?

Answer 1

Potentiometer:

1. A Potentiometer is a circuit that is used to measure the potential difference between two points.
2. In a potentiometer, we use this potential difference to measure the EMF of a cell and the internal resistance of the cell.
3. The gradient for the potentiometer is calculated by the formula $\frac{V}{L}$, where $V$ is potential difference between two points and $L$ is distance between two points.

Circuit diagram of a potentiometer

1. There is a resistance wire $AB$ and a moving point on this wire which is called jockey $\left(J\right)$. Now if the circuit is closed the current flows through the circuit and point $J$ is moved on the resistance wire $AB$ . There will be a condition where the current through the galvanometer $G$ is zero, then the length on the resistance wire is called as balancing length.
2. Here in the balancing condition, the voltage drop across the balancing length $AJ$ will be equal to the EMF $E$ of the secondary cell.
3. Potential drop on resistance wire $AB$ depends on a potential gradient which is simply the resistance of total wire divided by the length of wire. It can be calculated by the formula $\frac{V}{L}$, where $V$ is potential difference between two points and $L$ is distance between two points.
4. Now if we double the length of wire $AB$ then the potential gradient will drop because the potential gradient is inversely proportional to the length of the wire.
5. But the EMF of the cell $E$ remains the same.
6. So to get the same amount of potential drop in an increased length of wire balancing length will also get increased.

Hence, balancing length will be increased if the potentiometer wire is doubled.