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Question: A constant voltage is applied between the two ends of a metallic wire. If both the length and the ra...

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

A

Will be doubled

B

Will be halved

C

Will remain the same

D

Will be quadrupled

Answer

Will be doubled

Explanation

Solution

H∝1RH \propto \frac{1}{R} (If V = constant) ⇒ H1H2=R2R1=l2A1l1A2=l2r12l1r22\frac{H_{1}}{H_{2}} = \frac{R_{2}}{R_{1}} = \frac{l_{2}A_{1}}{l_{1}A_{2}} = \frac{l_{2}r_{1}^{2}}{l_{1}r_{2}^{2}}

⇒ H2=2H1H_{2} = 2H_{1}