Question

A wire of resistance \(R\) is stretched to triple its original length. Find the new resistance.

• A. \(3R\)
• B. \(6R\)
• C. \(9R\)
• D. \(R\)

Hint:

When a wire is stretched, its length increases and area decreases while volume remains constant. Resistance changes proportionally to \( \frac{L}{A} \).

Answer 1

The Correct Option is C

Concept: Resistance of a wire is given by \[ R = \rho \frac{L}{A} \] When the wire is stretched, its volume remains constant. \[ AL = \text{constant} \]

Step 1: Determine the new length. \[ L' = 3L \] Since volume is constant, \[ A'L' = AL \] \[ A' = \frac{A}{3} \]

Step 2: Find the new resistance. \[ R' = \rho \frac{L'}{A'} \] \[ R' = \rho \frac{3L}{A/3} \] \[ R' = 9 \rho \frac{L}{A} \] \[ R' = 9R \]