Question

deduce the expression for the equivalent resistance of the parallel combination of two resistace R1 and R2

Answer 1

Answer:1/Rp=1/R1+1/R2

Explanation:

Consider two resistors R1 and R2 connected in parallel. The current through each resistors will be different whereas the potential difference through each resistor would be the same.

I=I1+I2...........(eq1)

But I=V/Rp

where Rp is the effective resistance in parallel combination.

Similarly , I1=V/R1

I2=V/R2

Putting in eq 1

V/Rp=V/R1+V/R2

V/Rp=V(1/R1+1/R2)

1/Rp=1/R1+1/R2

Thus, we may conclude 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 individuals resistances. It can also be written as

1/Rp=R2+R1/R1.R2