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

`Q=(V^(2))/(R)`
`(Q_(1))/(Q_(2))=(R_(2))/(R_(1))=(l_(2))/(l_(1))xx(r_(1)^(2))/(r_(2)^(2))`
`(Q_(1))/(Q_(2))=(2)/(1)xx((2)^(2))/(1^(2))=(8)/(1)`