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

Electrical Parallel Circuits

R2 (Ω)	Resulting Resistance (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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