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

(ii) parallel across the same voltage supply.

Given
P1=V2R1 and P2=V2R2  --1
(i) When resistance are connected in series
Equivalent resistance in the circuit will be , Re=R1+R2
And hence total power consumed is given by
Pt=V2Re=V2R1+R2 
Putting the values of R1 and R2 from Eq.(1) we get
Pt=V2V2P1+V2P2=11P1+1P2=P1P2P1+P2
(ii) When resistance are connected in parallel
Equivalent resistance in the circuit will be given by
1Re=1R1+1R2
And hence total power consumed is given by
Pt=V2Re=V21R1+1R2=V2R1+V2R2=P1+P2  (using eq.(1))

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