Two wires of same mass , having ratio of lengths `1 : 2, density 1 : 3`, and respectively` 2 : 1`, are connected one by one to the same volltage supply. The rate of heat dissipation in the wire is found to be `10 W`. Find the rate of heat dissipation in the second wire.

Explanation

Given
`(l_(1))/(l_(2)) = (1)/(2) , (d_(1))/(d_(2)) = (1)/(3) , (rho_(1))/( rho_(2)) = (2)/(1)`
`m = A_(1)l_(1) d_(1) = A_(2) l_(2) d_(2)`
`:. (P_(2))/(P_(1)) = (V^(2)//R_(2))/(V^(2)// R_(1))`
`= ( R _(1))/( R_(2)) = (rho_(1)l_(1)A_(2))/( rho_(2) l_(2) A_(1)) = (rho_(1)l_(1) ^(2)d_(1))/( rho_(2) l_(2)^(2) d_(2))`
` = (2)/(1) xx ((1)/(2))^(2) xx(1)/(3) = (1)/(6)`
`P_(2) = (P_(1))/(6) = (10)/(6) = (5)/(3) W`