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 $B$ dissipation in $A$, is

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

Answer 1

Answer: (C)

$20W$

Heat dissipation rate P= $i^{2}R=\frac{V^2}{R}=\frac{V^{2}a}{\rho l}=\frac{V^2\left(al\right)}{\rho l^2}$
$P=\frac{V^2}{\rho l^2}\frac{m}{d}$
m is the mass and d is the density.
V is the common voltage source and $\rho$ is resistivity. which are all constant for the two materials.
$P\propto \frac{1}{l^2}$
Heat dissipation is A be $P_A$ with length $l_A$
Heat dissipation is A be $P_B$ with length $l_B$
Thus $\frac{P_A}{P_B}=\frac{l_B^2}{l_A^2}=2^2$P_A=5\times 4=20 W$