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Resistance

Two metallic ...

Question

Two metallic wires of same material and same length have different diameters. When the wires are connected in parallel across an ideal battery, the rate of heat produced in the thinner wire is $Q_{1}$ and that in thicker wire is $Q_{2}$ . The correct statement is

Q_{1} = Q_{2}

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Q_{1} < Q_{2}

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Q_{1} > Q_{2}

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Solution

The correct option is D $Q_{1} < Q_{2}$
second wire is given thicker than first wire hence $d_{1} < d_{2}$
we know that resistance of wire depends upon the area of cross-section or diameter of wire.

$\Rightarrow R \propto \frac{1}{d^{2}}$
As wires are connected in parallel and $V$ is same for both wires.
$\Rightarrow Q_{1} \propto V^{2} d_{1}^{2}$

$Q_{2} \propto V^{2} d_{2}^{2}$

As $d_{1} < d_{2}$

$\Rightarrow Q_{1} < Q_{2}$

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Two metallic wires of same material and same length have different diameters. When the wires are connected in parallel across an ideal battery, the rate of heat produced in the thinner wire is Q1 and that in thicker wire is Q2. The correct statement is

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