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Current Electricity question

2004 · Q124
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Current Electricity question

2004 · Q124

NEETPhysicsCurrent ElectricityMCQ+4 / −1
The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then
  1. A
    The resistance will be doubled and the specific resistance will be halved.
  2. B
    The resistance will be halved and the specific resistance will remain unchanged.
  3. C
    The resistance will be halved and the specific resistance will be doubled.
  4. D
    The resistance and the specific resistance, will both remain unchanged.
View written solutionFree

Correct answer: B

Resistance of wire = ρlA\rho {l \over A}ρAl​

R∝lA=lπr2R \propto {l \over A} = {l \over {\pi {r^2}}}R∝Al​=πr2l​

When length and radius are both doubled

R1∝2lπ(2r)2⇒R1∝12R{R_1} \propto {{2l} \over {\pi {{\left( {2r} \right)}^2}}} \Rightarrow {R_1} \propto {1 \over 2}RR1​∝π(2r)22l​⇒R1​∝21​R

The specific resistance of wire is independent of geometry of the wire, it only depends on the material of the wire.

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