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:

Step-by-step solution

Rate of heat i.e., Power developed in the wire =P= V^2 R Resistance of the wire of length, L R₁= L A = L r^2 Power, P₁= V^2 R₁ Resistance of the wire when length is halved i.e., L / 2 R₂= L 2 (2 r)^2 = L 8 r^2 = R₁ 8 Power, P₂= V R₁ 8 = 8 V R₁ or, P ₂=8 P ₁ i.e., power increased 8 times of previous or original wire.