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:

Increased 8 times

Doubled

Halved

Unchanged

Rate of heat developed in the wire=P=V²/R
R1 = ρL/A = ρL/πr²
R2 = ρ(L/2)/π(2r)² = ρL/8πr² = R1/8
P1 = V²/R1
P2 = V²/R2 = V²/(R1/8) = 8V²/R1 = 8P1