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 $5W.$ The rate of heat dissipation in $A$ is

Question

Dr. Abubacker · Accepted Answer

(c) $\frac{H}{t} = P = \frac{V^{2}}{R} \Rightarrow P \propto \frac{1}{R}\ also\ R \propto \frac{1}{A} \propto \frac{l^{2}\rho}{A.l\rho}$
$\Rightarrow R \propto \frac{l^{2}}{m} \Rightarrow R \propto l^{2}$ [for same mass]
So $\frac{P_{A}}{P_{B}} = \frac{l_{B}^{2}}{l_{A}^{2}} = \frac{4}{1} \Rightarrow P_{A} = 20W$

Q. 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 $5W.$ The rate of heat dissipation in $A$ is

Explanation

Reviewed by Dr. Abubacker

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