Question:
The electric resistance of a wire is \( R \). If the length of the wire is increased to double by stretching it, then the new resistance of the wire is
The electric resistance of a wire is \( R \). If the length of the wire is increased to double by stretching it, then the new resistance of the wire is
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Stretching wire $\longrightarrow$ length ↑, area ↓ $\longrightarrow$ resistance increases rapidly (here \( \propto L^2 \)).
Updated On: Apr 22, 2026
- \( 2R \)
- \( 4R \)
- \( R \)
- \( 16R \)
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The Correct Option is B
Solution and Explanation
Concept:
\[
R = \rho \frac{L}{A}
\]
When stretched, volume remains constant:
\[
A L = \text{constant}
\]
Step 1: New length.
\[ L' = 2L \]
Step 2: New area using volume conservation.
\[ A' = \frac{A}{2} \]
Step 3: New resistance.
\[ R' = \rho \frac{L'}{A'} = \rho \frac{2L}{A/2} = 4 \rho \frac{L}{A} = 4R \]
Step 1: New length.
\[ L' = 2L \]
Step 2: New area using volume conservation.
\[ A' = \frac{A}{2} \]
Step 3: New resistance.
\[ R' = \rho \frac{L'}{A'} = \rho \frac{2L}{A/2} = 4 \rho \frac{L}{A} = 4R \]
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