Two wires A and B of same material and mass have their lengths in the ratio `1 : 2`. On connecting them to the same source, the rate of heat dissipation in B is found to be 5 W . The rate of heat dissipation in A is

Options

A. 10 W
B. 5 W
C. 20 W
D. None of these

Answer

C

Explanation

`l_(1) =1, l_(2) = 2l`
If mass is same then `m_(1) = m_(2)`
`rArr A_(1)l_(1) = A_(2)l_(2) rArr A_(1)/A_(2) = l_(2)/l_(1) = 2 rArr A_(1) = 2A` [Let `A_(2) =A`]
Now, `R_(1)/R_(2) = l/(2A) xx A/(2l) = 1/4 rArr R_(2) = 4R_(1)`
`P prop 1/R rArr P_(1)/P_(2) = 4 rArr P_(1) = 4P_(2) = 4 xx 5 = 20 W`