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Parallel Circuits

Resistance, voltage and current in parallel networks

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electrical parallel circuit

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

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

where

In = 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 / Rn             (2)

where

Rn = parallel resistance (ohms, Ω)

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

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

Resulting Resistance (Ω)
R2
(Ω)
R1 (Ω)
1 1.5 2.2 3.3 4.7 6.8 10 15 22 33 47 68
1 0.5 0.6 0.69 0.77 0.83 0.87 0.91 0.93 0.95 0.97 0.98 0.99
1.5 0.6 0.75 0.89 1.03 1.14 1.22 1.30 1.36 1.40 1.43 1.45 1.46
2.2 0.69 0.89 1.1 1.32 1.50 1.66 1.82 1.92 2.0 2.06 2.10 2.13
3.3 0.77 1.03 1.32 1.65 1.94 2.22 2.48 2.70 2.87 3.00 3.08 3.14
4.7 0.83 1.14 1.50 1.94 2.35 2.78 3.20 3.58 3.87 4.12 4.27 4.39
6.8 0.87 1.22 1.66 2.22 2.78 3.40 4.05 4.68 5.19 5.64 5.94 6.18
10 0.91 1.30 1.82 2.48 3.20 4.05 5.0 6.0 6.9 7.7 8.3 8.7
15 0.93 1.36 1.92 2.70 3.58 4.68 6.0 7.50 8.9 10.3 11.4 12.2
22 0.95 1.40 2.00 2.87 3.87 5.19 6.9 8.9 11.0 13.2 15.0 16.6
33 0.97 1.43 2.06 3.0 4.12 5.64 7.7 10.3 13.2 16.5 19.4 22.2
47 0.98 1.45 2.1 3.08 4.27 5.94 8.3 11.4 15.0 19.4 23.5 27.8
68 0.99 1.46 2.13 3.14 4.39 6.18 8.7 12.2 16.6 22.2 27.8 34.0
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