Question

Prove 1/P = 1/P1 + 1/P2 in Series
P is Power
P1 is Power for first resistor
P2 is Power for second resistor​

Answer 1

To prove:

1/P = 1/P1 + 1/P2 ,

where P is Power ;

P1 is Power for first resistor,

P2 is Power for second resistor.

Proof:

|----------(R1)-------------(R2)---------|

Let the resistances be R1 , R2 connected in series. And the potential difference be V ;

We know that :

P1 = V²/R1 ..........(1) and

P2 = V²/R2 ...........(2)

In series combination , the net resistance is the algebraic addition of individual resistance :

$\therefore$ R = R1 + R2

=> V²/P = V²/P1 + V²/P2

=> 1/P = 1/P1 + 1/P2

[Hence proved]