Electrical Parallel Circuits

In a parallel circuit there is more than one path the electrons can flow. 

The Parallel Circuit Rules:

1. The total current in parallel circuit is equal to the sum of the currents in all the branches of the circuit.
2. The total voltage across a parallel circuit is equal to the voltage across any of the branches in the circuit.
3. The total resistance of a parallel circuit is calculated by using Ohm's law on the voltage and current of the whole circuit. 

The sum of currents in a parallel network can be calculated as

I = I₁ + I₂ + ... + I_n             (1)

where

I_n = parallel current (amps)

I = sum of currents (amps)

The total resistance in a parallel circuit can be calculated as

1 / R = 1 / R₁ + 1 / R₂ + ... + 1 / R_n             (2)

where

R_n = parallel resistance (ohms, Ω)

R = total resistance in the parallel network (ohms, Ω)

• Parallel connected resistors - Calculator

Example - Parallel Network

The total resistance in a network with three resistors R₁ = 10 Ω, R₂ = 20 Ω  and R₃ = 30 Ω can be calculated as

1 / R = 1 / (10 Ω) + 1 / (20 Ω) + 1 / (30 Ω)

    = 0.183 (1/Ω)

R = 1 / 0.183

    = 5.46 (Ω)

Connected to a 12 V battery the sum of currents can be calculated

I = U / R

    =  (12 V) / (5.46 Ω)

    = 2.2 Amps)   

The current through each resistor can be calculated as

I₁= U / R₁

    =  (12 V) / (10 Ω)

    = 1.2 (Amps)   

I₂= U / R₂

    =  (12 V) / (20 Ω)

    = 0.6 (Amps)   

I₃= U / R₃

    =  (12 V) / (30 Ω)

    = 0.4 (Amps)   

Resistors in Parallel and resulting Resistance

Two resistors in parallel - resistance ranging 1 - 100 ohm

Download and print Resistors in parallel chart

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Length m
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Area m²
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