Two wires `'A'` and `'B'` of the same material have their lengths in the ratio `1 : 2` and radii in the ratio `2 : 1` The two wires are connected in parallel across a battery. The ratio of the heat produced in `'A'` to the heat produced in `'B'` for the same time is

Options

A. `1:2`
B. `2:1`
C. `1:8`
D. `8:1`

Answer

D

Explanation

`I_(1) = 1,I_(2) = 2l, r_(1) = 2r, r_(2)=r`
`R_(1)/R_(2) = (l/(pi(2r)^(2)))/((2l)/(pir^(2))) = 1/8`
as `P prop 1/R`
`P_(1)/P_(2) = 8:1`