Question:
A wire of resistance R is stretched uniformly to double its original length. The new resistance will be:
A wire of resistance R is stretched uniformly to double its original length. The new resistance will be:
Show Hint
If length becomes \(nL\), then:
\[
R \propto n^2
\]
Updated On: Jun 10, 2026
- \( 2R \)
- \( 4R \)
- \( \frac{R}{2} \)
- \( \frac{R}{4} \)
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The Correct Option is B
Solution and Explanation
Concept:
Resistance:
\[
R = \rho \frac{L}{A}
\]
When wire is stretched, volume remains constant:
\[
A L = \text{constant}
\]
Step 1: New length \[ L_2 = 2L \]
Step 2: New area \[ A_2 = \frac{A}{2} \]
Step 3: New resistance \[ R_2 = \rho \frac{2L}{A/2} \] \[ R_2 = 4 \rho \frac{L}{A} \] \[ R_2 = 4R \]
Step 1: New length \[ L_2 = 2L \]
Step 2: New area \[ A_2 = \frac{A}{2} \]
Step 3: New resistance \[ R_2 = \rho \frac{2L}{A/2} \] \[ R_2 = 4 \rho \frac{L}{A} \] \[ R_2 = 4R \]
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