Question

With the help of a suitable circuit diagram prove that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.

Answer 1

Since charge must be conserved, therefore the current I that enters at point ‘a’ must be equal to the current that leaves that point. Therefore we have

I = I1 + I2 ...(i)

Since the resistors are connected in parallel therefore the potential across each resistor must be same, hence by Ohm’* law we have

substituting in equation (i) we have,

Let RP be the equivalent resistance of the parallel combination, then by Ohm’* law we have,

Hence from equations (ii) and (iii) we have,

An extension of this analysis to three or more resistors in parallel gives the following general expression