First slide

Ohm's law

Question

If a wire is stretched such that its area of cross-section becomes (1 / n) times, then its resistance will became

Moderate

A

n times
B

n² times
C

(1/ n) times
D

(1 / n²) times

Solution

we know that $R = ρ (\frac{l}{A})$
$\begin{array}{l} ∴ R = ρ (\frac{V}{A^{2}}) or R \propto \frac{1}{A^{2}} \\ ∴ \frac{R_{1}}{R_{2}} = {(\frac{A_{2}}{A_{1}})}^{2} = {(\frac{A}{nA})}^{2} = \frac{1}{n^{2}} \end{array}$
or $R_{2} = n^{2} R_{1}$

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