Question

A (2.5 V) battery is connected to a potentiometer wire. A cell of e.m.f. (1.08 V) is balanced by the voltage drop across (2.16 m) of wire. The length of the potentiometer wire is

• A. (2.5 m)
• B. (3 m)
• C. (5 m)
• D. (6 m)

Hint:

Potential gradient is constant for a uniform wire with a steady current.

Answer 1

The Correct Option is C

Step 1: Formula
The principle of a potentiometer states that $E = k \cdot l$, where $k$ is the potential gradient ($V/L$).

Step 2: Calculate Potential Gradient
$k = \frac{E_{cell}}{l_{balance}} = \frac{1.08 \text{ V}}{2.16 \text{ m}} = 0.5 \text{ V/m}$.

Step 3: Find Total Length
The total voltage of the battery is applied across the total length $L$.
$V = k \cdot L \implies 2.5 \text{ V} = 0.5 \text{ V/m} \cdot L$.
$L = \frac{2.5}{0.5} = 5 \text{ m}$.
Final Answer: (C)