Q119 / 200 · NEET 2004 · Physics

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then:

  • A
    the resistance will be doubled and the specific resistance will be halved
  • Correct answer
    B
    the resistance will be halved and the specific resistance will remain unchanged
  • C
    the resistance will be halved and the specific resistance will be doubled
  • D
    the resistance and the specific resistance, both will remain unchanged

Solution

Resistance of wire $R=\rho \frac{l}{A}$ Means $R \propto \frac{l}{A}=\frac{l}{\pi r^2}$ According to the question when $l$ and $R$ are doubled $$ \begin{aligned} & \therefore R_1 \propto \frac{2 l}{\pi(2 r)^2} \\ & \Rightarrow R_1 \propto \frac{1}{2} R \end{aligned} $$ Here specific resistance of wire is independent of geometry wire so it depends on the material of wire.

Hence, the correct answer is option: 'B'.

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