Electrical Parallel Circuits
Resistance, voltage and current in electrical parallel circuits.
In a parallel circuit there is more than one path the electrons can flow.
The Parallel Circuit Rules:
 The total current in parallel circuit is equal to the sum of the currents in all the branches of the circuit.
 The total voltage across a parallel circuit is equal to the voltage across any of the branches in the circuit.
 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 = I_{1} + I_{2}+ ... + 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 / R_{1} + 1 / R_{2}+ ... + 1 / R _{ n } (2)
where
R _{ n } = 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 R_{1} = 10 Ω, R_{2}= 20 Ω and R_{3} = 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
I_{1} = U / R_{1}
= (12 V) / (10 Ω)
= 1.2 (Amps)
I_{2}= U / R_{2}
= (12 V) / (20 Ω)
= 0.6 (Amps)
I_{3} = U / R_{3}
= (12 V) / (30 Ω)
= 0.4 (Amps)
Resistors in Parallel and resulting Resistance
Two resistors in parallel  resistance ranging 1  100 ohm
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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