Two bulbs are reled `(P_(1),V)" and "(P_(2), V)`. If they are connected (i) iin series and (ii) in perallel across a supply V, find th power dissipated in the two combinations in terms of `P_(1)" and " P_(2)`.

Explanation

Resistances of the two bulbs `R_(1) = (V^(2))/(P_(1)) and R_(2) = (V^(2))/(P_(2))`
(i) Net resistance in series `R_(S) = R_(1) + R_(2) = (V^(2))/(P_(1)) + (V^(2))/(P_(2)) = V^(2) ((P_(1) + P_(2))/(P_(1)P_(2)))`
(ii) Net resistance in parallel `R_(P) = (R_(1)R_(2))/(R_(1) + R_(2)) = ((V^(2))/(P_(1)) xx (V^(2))/(P_(2)))/((V^(2))/(P_(1)) + (V^(2))/(P_(2))) = (V^(2))/(P_(1)+P_(2))`
`P_(S) = (V^(2))/(R_(S)) = (V^(2))/(V^(2) ((P_(1)+P_(2))/(P_(1) P_(2)))) = (P_(1)P_(2))/(P_(1) + P_(2))`
`P_(P) = (V^(2))/(R_(P)) = (V^(2))/(((V^(2))/(P_(1)+P_(2))))= P_(1) + P_(2)`