A constant voltage is applied between the two ends of a uniform metallic . . .

Question : 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 

a) H/2
b) H
c) 2H
d) 4H

Doubt by Tushar

Solution :

We know 

R=ρl/A

R=ρl/πr²
R'=ρ2l/π(2r)²
R'=2ρl/4πr²
R'=ρl/2πr²
R'=R/2

Both the wires have constant voltage
So 
H = V²t/R 
H∝1/R 
∵ R'=R/2

∴ H'=2H

Hence, c) would be the correct option.