give the derivation of resultant power in series and parallel

P = I^2 * R or V^2/R

 

For a series connection with resistors R1, R2, R3...etc connected in series

R = R1+R2+R3+ ....

And the current in this circuit remains constant, 

so, P = I^2 ( R1+R2+R3+ ....)

 

For a parallel connection with resistors R1, R2, R3...etc connected in parallel

1/R = 1/R1+1/R2+1/R3+ ....

And the voltage drop in this circuit remains constant, 

so, P = V^2 /( 1/R1+1/R2+1/R3+ ....)