Question

Deduce the expression for the equivalent resistance of the parallel combination of three resistors r1,r2,r3

Answer 1

take 3 resistors r1, r2, r3 connected in parallel and connect a battery of V volts. in this case the p.d across the ends will be the same.the current flowing, however, is not the same.

 total I = I1 + I2 + I3 _______[1]

 from ohm's law--

 I = V / r _______[2]

 I1 = V / r1 _________[3]

 I2 = V / r2 __________[4]

 I3 = V / r3  _________[5] 

putting the values of I1, I2 and I3 in [1] 

V / r = V / r1 + V / r2 + V / r3 

= V / r = V [1 / r1 + 1 / r2 + 1 / r3] 

= 1 / r = 1 / r1 + 1 / r2 +1 / r3 

I hope it will help you

regards

Answer 2

Answer:they are in parallel so maybe it would be

I=V/R

I=I1+I2+I3

V/R=V/R1+V/R2+V/R3

V/R=V[1/R1+1/R2+1/R3]

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