CBSE Class 10 Answered

For the equivalent resistance of resistors in parallel, an equivalent resistor R can replace the parallel combination of R1, R2 and R3 such that the voltage V_ab is unchanged and the current through R is the total that would be drawn by R1, R2 and R3 in combination.

Thus for R,

V = I R

For R1, R2 and R3

V = I_R1 R1
V = I_R2 R2

V = I_R3 R3

The can be found out to be

I = V/R
I_R1 = V/R1
I_R2 = V/R2

I_R3 = V/R3

 But we know that for the equivalent resistor R the current draw is the sum of the currents drawn by R1, R2, and R3,

I = I_R1 + I_R2 + I_R3
V/R = V/R1 + V/R2 + V/R3

Or 1/R = 1/R1 + 1/R2+ 1/R3