## Resistors in Parallel

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:

resistors in parallel and equivalent resistor (click to enlarge)

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, I_{1} is the current that flows through R1 and I_{2} is the current that flows through R2.

Using the Kirchhoff’s current law (KCL) in circuit 1

Ior_{p}= I_{1}+ I_{2}I_{p}= V/R1 + V/R2

for n resistors

Ior_{p}= I_{1}+ I_{2}+ … + I_{n}I_{p}= V/R1 + V/R2 + … + V/Rn

Using the Ohm’s Law in circuit 1 and 2

I=>_{p}= V/RpI_{p}= 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

I_{1}= (I_{p}* Rp)/R1

## The Current Divider Rule

I_{x}= (I_{p}* 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