A constant voltage is applied between the two ends of a uniform metallic wire, heat ‘H’ is developed in it. If another wire of the same material, double the radius and twice the length as compared to original wire is used then the heat developed in it will be-

Options

A. `(H)/(2)`
B. H
C. 2H
D. 4H

Answer

C

Explanation

Given: Voltage = V. Heat = H,
Let us assume : length = l, radius = r,
Initially, `H=(V^(2)t)/(R)=(V^(2)tpir^(2))/(rhol) [ R=rho(l)/(pir^(2))]`
If length is made 21 and radius is 2r. Whiler is constant then:
`H.=(V^(2)tpi (2r)^(2))/(rho 2l)=(V^(2)t pi)/(rho) (4r^(2))/(2l)`
`=(V^(2)t pir^(2))/(rho l)2=2H`
Hence, new heat is twice of the old one.