Two wires of the same material and same length have radii 1 mm and 2 mm respectively. Compare (i) their resistances, (ii) their specific resistance.

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Solution

(i) Resistance is inversely proportional to cross-sectional area.

$\frac{R_{1}}{R_{2}} = \frac{A_{2}}{A_{1}} = \frac{π r_{2}^{2}}{π r_{1}^{2}} = \frac{2^{2}}{1^{2}} = 4 : 1$

(ii) As they are made up of the same material, their specific resistances are the same.

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