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

• A. 10 W
• B. 5 W
• C. 20 W
• D. none of these

Answer 1

Answer: (C)

$\frac{H}{t}=P=\frac{V^2}{R}$
$\Rightarrow P\propto \frac{1}{R};$ Also $R\propto \frac{l}{A}\propto \frac{l^2\rho }{A\cdot l\rho }$.
$\Rightarrow R\propto \frac{l^2}{m}\Rightarrow R\propto l^2$ (for same mass)
So $\frac{P_A}{P_B}=\frac{l_B^2}{l_A^2}=\frac{4}{1}$
$\Rightarrow P_A=20W$