Current Electricity - Result Question 5
6. The resistance of a wire is ’ $R$ ’ ohm. If it is melted and stretched to ’ $n$ ’ times its original length, its new resistance will be :-
[2017]
(a) $\frac{R}{n}$
(b) $n^{2} R$
(c) $\frac{R}{n^{2}}$
(d) $nR$
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Answer:
Correct Answer: 6. (b)
Solution:
- (b) We know that, $R=\frac{\rho \ell}{A}$
or $R=\frac{\rho \ell^{2}}{\text{ Volume }} \Rightarrow R \propto \ell^{2}$
According to question $\ell_2=n \ell_1$
$ \frac{R_2}{R_1}=\frac{n^{2} l_1^{2}}{l_1^{2}} $
or, $\frac{R_2}{R_1}=n^{2}$
$\Rightarrow R_2=n^{2} R_1$
