Question

Two heating elements of resistances R₁ and R₂ when operated at a constant supply of voltage, V, consume powers P₁ and P₂ respectively. Deduce the expressions for the power of their combination whey they are, in turn, connected in (i) series and (ii) parallel across the same voltage supply.

Answer 1

Given

`P_1 = V^2/R_1      &      P_2=V_2/ R_2`

(i) Power when they are connected in series

`P_(eq) =V^2/R_(eq) = V^2/(R_1 +R_2)`    `(\text { From given information}  R_1 =V^2/P_2;R_2 =V^2/P_2)`

`=> P_(eq) = V^2/(V^2/P_1 + V^2/P_2)`

`P =(P_1P_2)/(P_1+P_2)`

(ii) Power when they are connected in parallel

`P_(eq) = V^2/R_(eq)`

`1/R_(eq) = 1/R_1 +1/R_2`

`=>P_(eq) =V^2 (1/R_1 +1/R_2)`

`=V^2/R_1 +V^2/R_2`

`P_(eq =P_1 +P_2)`