Question

A potentiometer wire is 4m long and potential difference of 3V is maintained between the ends. The e.m.f. of the cell which balances against a length of 100 cm of the potentiometer wire is

• A. \(0.75\) V
• B. \(0.5\) V
• C. \(0.25\) V
• D. \(1.5\) V

Hint:

Potential gradient is 3 V per 4 m; multiply by 1 m.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In a potentiometer the potential difference along the wire is proportional to length. The cell balances when its emf equals the potential drop over the balancing length.

Step 2: Potential gradient:
\[ k = \frac{3\ \text{V}}{4\ \text{m}} = 0.75\ \text{V/m} \]

Step 3: EMF:
Balancing length \(= 100\) cm \(= 1\) m, so
\[ E = k\,l = 0.75\times1 = 0.75\ \text{V} \]

Step 4: Check:
Option (A). Option (B) 0.5 V would be for 2/3 m, and (D) 1.5 V would need 2 m.

Final Answer:
Potential gradient 0.75 V/m times 1 m. \[ \boxed{\text{(A) }0.75\ \text{V}} \]