Question

A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be:

• A. Increased 8 times
• B. Doubled
• C. Halved
• D. Unchanged

Answer 1

The correct option is A Increased 8 times

Rate of heat developed in the wire=$P=\frac{V^2}{R}$

$R_1=\frac{\rho L}{A}$=$\frac{\rho L}{\pi r^2}$

$P_1=\frac{V^2}{R_1}$

$R_2=\frac{\rho \frac{L}{2}}{\pi (2r{)}^2}=\frac{\rho L}{\pi 8r^2}=\frac{R_1}{8}$

$P_2=\frac{V}{\frac{R_1}{8}}$=$\frac{8V}{R_1}$

$P_2=8P_1$