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

Step 1: Understanding the Question:
The question explores how stretching a wire (changing geometry) affects its electrical resistance.
The topic is Current Electricity.
Step 2: Key Formula or Approach:
The resistance of a wire is \( R = \rho \frac{L}{A} \).
When a wire is stretched, its volume \( V = A \times L \) remains constant.
Step 3: Detailed Explanation:
Given the new length \( L' = 3L \).
Since \( V = A'L' = AL \), we have:
\[ A' = \frac{AL}{L'} = \frac{AL}{3L} = \frac{A}{3} \]
Now, calculate the new resistance \( R' \):
\[ R' = \rho \frac{L'}{A'} \]
\[ R' = \rho \frac{3L}{A/3} \]
\[ R' = \rho \frac{9L}{A} = 9 \left( \rho \frac{L}{A} \right) \]
Step 4: Final Answer:
\[ R' = 9R \]