What is the relationship between I, I1, I2 and I3?
✅ Answer: It is observed that the total current I, is equal to the sum of the separate currents through each branch.
I = I1 + I2 + I3
Let Rp be the equivalent resistance of the parallel combination of resistors.
Hence, I = V/Rp
On applying Ohm’s law to each resistor, we have
I1 = V /R1 I2 = V /R2 I3 = V /R3
V/Rp = V/R1 + V/R2 + V/R3
1/Rp = 1/R1 + 1/R2 + 1/R3
Thus, 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.