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Plz send derivation of this relation of equivalent power in series

Plz send derivation of this relation of equivalent power in series

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Grade:12

1 Answers

Arun
25763 Points
3 years ago
Let I be the current through the series circuit. 
Let R1,R2 and R3 be the three resistors. 
P1,P2 and P3 be the power consumed across R1,R2 and R3 respectively. 
So,P1=I^2R1 
P2=I^2R2 
P3=I^2R3 
Since power is a scalar quantity,the net power consumed in the series circuit 
P=P1+P2+P3=I^2R1+I^2R2+I^2R3 
P=I^2(R1+R2+R3)=I^2 X total resistance R 
The reciprocal of power 1/P=1/VI,V is the total p.d. across the series circuit. 
1/P=R/I^2=(R1+R2+R3)/I^2=R1/I^2 + R2/I^2+ R3/I^2=1/P1 +1/P2+1/P3(proved)

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