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 Vab 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 = IR1 R1
V = IR2 R2
V = IR3 R3
The can be found out to be
I = V/R
IR1 = V/R1
IR2 = V/R2
IR3 = 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 = IR1 + IR2 + IR3
V/R = V/R1 + V/R2 + V/R3
Or 1/R = 1/R1 + 1/R2+ 1/R3
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