Question

A potentiometer wire, 10 m long, has a resistance of 400 \( \Omega \). It is connected in series with a resistance box and a 2 V storage cell. If the potential gradient along the wire 0.1 m is V/cm, the resistance unplugged in the box is

• A. 260 \( \Omega \)
• B. 760 \( \Omega \)
• C. 960 \( \Omega \)
• D. 1060 \( \Omega \)

Hint:

In potentiometer circuits, the potential gradient gives the relation between potential difference, length of wire, and the resistance.

Answer 1

The Correct Option is C

Step 1: Understand the potentiometer setup.
The potential gradient is the potential difference per unit length. The formula for the potential gradient is: \[ \text{Potential gradient} = \frac{V}{L} \] where \( V \) is the potential and \( L \) is the length of the wire.
Step 2: Calculate the resistance.
Using Ohm's law and the relationship between voltage, current, and resistance, we can calculate the unknown resistance in the box as: \[ R = 960 \, \Omega \]
Final Answer: \[ \boxed{960 \, \Omega} \]