Question

A potentiometer wire is 4 m 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 poteniometer wire is

• A. \(0.25\) V
• B. \(0.50\) V
• C. \(0.75\) V
• D. \(1.0\) V

Hint:

The potential gradient is the total voltage over the wire length, and the emf equals gradient times balancing length.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In a potentiometer, the potential drop is uniform along the wire. The emf of a cell is 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 \(l = 100\) cm \(= 1\) m.
\[ E = k\,l = 0.75\times 1 = 0.75\text{ V} \]

Step 4: Check the options.
0.25 V would result from using 1/12 of the wire, and 1.0 V from using 4/3 m. Only 0.75 V fits.

Final Answer:
The emf of the cell is 0.75 V, option (C). \[ \boxed{0.75\text{ V}} \]