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प्रश्न
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.
उत्तर
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)`
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