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

• 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}=20 \,W$