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Question:

The resistance of a wire is proportional to its length and inversely proportional to the square of its radius. Two wires of the same material have the same resistance and their radii are in the ratio 4 : 3. If the length of the first wire is 64 cms., find the length of the other.

Explanation:

If T is the resistance, l is the length and r is radius.

R ∝ l/r²

∴ R = $\frac{k l}{r^{2}}$ (where k is a constant)

∴ $\frac{R_{1}}{R_{2}} = \frac{\frac{l_{1}}{{r_{1}}^{2}}}{\frac{l_{2}}{{r_{2}}^{2}}} = \frac{l_{1} \times {r_{2}}^{2}}{l_{2} \times {r_{1}}^{2}}$

∴ $\frac{1}{1} = \frac{64 \times 9}{l_{2} \times 16}$ (∵ R₁ = R₂)

⇒ l₂= (64 × 9)/16 = 36 cms.

Hence, option (c).

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