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. 10W
• B. 5W
• C. 20W
• D. None of these

Answer 1

Answer: (C)

20W

Answer 2

$\frac{H}{t} = P = \frac{V^{2}}{R} \Rightarrow P \propto \frac{1}{R}$ also $R \propto \frac{l}{A} \propto \frac{l^{2}\rho}{A.l\rho}$

⇒ $R \propto \frac{l^{2}}{m}$ ⇒ $R \propto l^{2}$ (for same mass)

So $\frac{P_{A}}{P_{B}} = \frac{l_{B}^{2}}{l_{A}^{2}} = \frac{4}{1} \Rightarrow P_{A} = 20W$