First slide

Electrical power

Question

Two wires A and B of same material and mass have their lengths in the ratio 1 : 2. On connecting them to the same source, the rate of heat dissipation in B is found to be 5 W. The rate of heat dissipation in A is

Moderate

A

10 W
B

5 W
C

20 W
D

none of these

Solution

$\begin{array}{l} \frac{H}{t} = P = \frac{V^{2}}{R} \Rightarrow P \propto \frac{1}{R}; Also R \propto \frac{l}{A} \propto \frac{l^{2} ρ}{A . lρ} \\ \Rightarrow R \propto \frac{l^{2}}{m} \Rightarrow R \propto l^{2} (for same mass) \\ So \frac{P_{A}}{P_{B}} = \frac{l_{B}^{2}}{l_{A}^{2}} = \frac{4}{1} \Rightarrow P_{A} = 20 W \end{array}$

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