Resistors in Parallel

6 September 2013 - Basic Electronics, Passive Components, Resistor - Hypsine Electronics - No Comments

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

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, 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

The Current Divider Rule

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

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