Question:
The resistance of a wire of length \(l\) and cross sectional area \(A\) is \(R\). The resistance of another wire of the same material of length \(3l\) and cross sectional area \(\frac{A}{3}\) is
The resistance of a wire of length \(l\) and cross sectional area \(A\) is \(R\). The resistance of another wire of the same material of length \(3l\) and cross sectional area \(\frac{A}{3}\) is
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Resistance is directly proportional to length and inversely proportional to cross-sectional area.
Updated On: Apr 24, 2026
- 3R
- R
- 9R
- R/3
- R/9
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Resistance is given by \(R = \rho \frac{l}{A}\), where \(\rho\) is resistivity (constant for the same material).
Step 2: Detailed Explanation:
For the first wire: \(R = \rho \frac{l}{A}\). For the second wire: length \(l' = 3l\), area \(A' = A/3\). Resistance, \(R' = \rho \frac{l'}{A'} = \rho \frac{3l}{A/3} = \rho \frac{3l \times 3}{A} = 9 \left( \rho \frac{l}{A} \right) = 9R\).
Step 3: Final Answer:
The resistance of the second wire is \(9R\).
Resistance is given by \(R = \rho \frac{l}{A}\), where \(\rho\) is resistivity (constant for the same material).
Step 2: Detailed Explanation:
For the first wire: \(R = \rho \frac{l}{A}\). For the second wire: length \(l' = 3l\), area \(A' = A/3\). Resistance, \(R' = \rho \frac{l'}{A'} = \rho \frac{3l}{A/3} = \rho \frac{3l \times 3}{A} = 9 \left( \rho \frac{l}{A} \right) = 9R\).
Step 3: Final Answer:
The resistance of the second wire is \(9R\).
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