Question

Derive an expression for the equivalent resistance in case of three resistance connected in parallel

Answer 1

equivalent resistant (R)=1/r1+1/r2+1/r3

Answer 2

Consider two resistors connected in parallel, It is clear, that the potential drop across the two resistors is the same. In general, however, the currents  and which flow through resistors  and , respectively, are different. According to Ohm's law, the equivalent resistance between  and  is the ratio of the potential drop  across these points and the current  which flows between them. This current must equal the sum of the currents  and  flowing through the two resistors, otherwise charge would build up at one or both of the junctions in the circuit. Thus, 

It follows that 1/R eq. = I/V =( I1 +I2) / V

giving 1/R eq. = 1/R1 + 1/R2

Here, we have made use of the fact that the potential drop  is common to all three resistors. Clearly, the rule is

The reciprocal of the equivalent resistance of two resistances connected in parallel is the sum of the reciprocals of the individual