Question

Derive the formula for equivalent resistance of the resistor arranged in parallel combination

Answer 1

let I1,I2,I3 be the current flowing through R1,R2,R3 respectively

therefore, I=I1+I2+I3_____________(i)

let the effective resistance of this parallel combination be Rp, then using, Ohm's law

I=V/Rp_______________________(ii)

As V is same for all resistor, therefore

I1=V/R1 ,I2=V/R2 ,I3=V/R3_________(iii)

hence, from eqn (i), (ii),(ii), we get

V/Rp=V/P1+V/R2+V/R3+V[ 1/R1+1/R2+1/R3]

|____________________ |

|     1/R1 + 1/R2+ 1/R3            |                          

|____________________|