Question

In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire '$x$' cm long. If length of potentiometer wire is increased by few centimeter without changing the cell, the balancing length will [Driving source is not changed]

• A. will not change
• B. increase
• C. decrease
• D. become zero

Hint:

Increasing the total length of a potentiometer wire decreases its potential gradient, which fundamentally increases its sensitivity. A more sensitive potentiometer always requires a longer balancing length for the same cell.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to determine what happens to the balancing length of a specific cell in a potentiometer if the total length of the main potentiometer wire is increased (while keeping the primary driving voltage source constant).

Step 2: Key Formula or Approach:
The potential gradient ($K$) of a potentiometer wire is the potential difference per unit length: $K = \frac{V}{L}$, where $V$ is the voltage across the total wire and $L$ is the total length of the wire.
The balancing length ($l$) for a cell of EMF $E$ is given by $E = K \times l \implies l = \frac{E}{K}$.

Step 3: Detailed Explanation:
The driving source is not changed, so the total potential difference $V$ across the entire wire remains constant.
When the total length of the potentiometer wire $L$ is increased, the potential gradient $K = \frac{V}{L}$ will strictly decrease because $L$ is in the denominator.
Since the EMF of the test cell $E$ is constant, and $l = \frac{E}{K}$:
If $K$ decreases, the balancing length $l$ must increase to compensate and measure the exact same potential difference $E$.

Step 4: Final Answer:
The balancing length will increase, matching option (B).