Parallel Resistors Formula | To solve resistance in parallel

Parallel resistors formula is used to solve two or more resistors which are connected in the parallel configuration.

Formulas

Calculator

Replace 1 in the boxes with your desired resistance value. Choose the prefix. Use only those boxes which are needed. Don’t change others.

Example # 1: 3 Parallel resistive components having their values as 20 Ω, 30 Ω and 50 Ω are connected in the parallel configuration.  Find the equivalent resistance.

Solution: 1/Req = 1/20 Ω + 1/30 Ω + 1/50 Ω

1/Req = 0.05 + 0.033 + 0.02

1/Req = 0.103

Req = 9.7 Ω

Theory

A parallel circuit is formed when one end of all components share one node and other ends of components share the other node. The circuit below displays the parallel circuit configuration with three resistors.

resistors-in-parallel-formulaDerivation

Let’s consider the circuit configuration where a current source is powering the entire circuit.

circuit-upload-1349834

The current enters the node junction and splits between the two resistors. The voltage v remains same across both resistors since it is a parallel circuit configuration. From the Kirchhoff’s current law the current It at node divides by:

It = I1 + I2

From Ohm’s law

It = (v/R1) + (v/R2)

It = (1/R1 + 1/R2) * v

The It itself can be expressed in terms of current and voltage by using Ohm’s law.

It = v/Req

v/Req = (1/R1 + 1/R2) * v

1/Req = 1/R1 + 1/R2

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