Current Electricity - Result Question 10
11. The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then
(a) the resistance and the specific resistance, will both remain unchanged
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(b) the resistance will be doubled and the specific resistance will be halved
(c) the resistance will be halved and the specific resistance will remain unchanged
(d) the resistance will be halved and the specific resistance will be doubled
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Answer:
Correct Answer: 11. (c)
Solution:
- (c) $R=\frac{\rho \ell_1}{A_1}$, now $\ell_2=2 \ell_1$
$ \begin{aligned} & A_2=\pi(r_2)^{2}=\pi(2 r_1)^{2}=4 \pi r_1^{2}=4 A_1 \\ & \therefore \quad R_2=\frac{\rho(2 \ell_1)}{4 A_1}=\frac{\rho \ell_1}{2 A_1}=\frac{R}{2} \end{aligned} $
$\therefore$ Resistance is halved, but specific resistance remains the same.
