In this article we talk about resistors in parallel, the equivalent resistance and the current divider rule for parallel connection of resistors. Let’s consider this circuit:
In circuit 1 we have two resistors R1 and R2 connected in parallel and in circuit 2 the equivalent resistance Rp. I is the total current, I1 is the current that flows through R1 and I2 is the current that flows through R2.
Using the Kirchhoff’s current law (KCL) in circuit 1
Ip = I1 + I2 or Ip = V/R1 + V/R2
for n resistors
Ip = I1 + I2 + … + In or Ip = V/R1 + V/R2 + … + V/Rn
Using the Ohm’s Law in circuit 1 and 2
Ip = V/Rp => Ip = V/R1 + V/R2
The equivalent resistance Rp for resistors in parallel
1/Rp = 1/R1 + 1/R2 + … + 1/Rn
So the current through R1 is
I1 = (Ip * Rp)/R1
Ix = (Ip * Rp)/Rx
where Ix is the current through the Rx.
For 2 resistors in parallel you can use this formula
Rp = (R1 * R2)/R1 + R2 (only for 2 resistors in parallel)