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Parallel Circuits

Resistors connected in parallel

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parallel circuit

The sum of current in a parallel network can be expressed as

I = I1 + I2 + ... + In         (1)

where

I = sum of currents (Amps)

The total resistance in a parallel circuit can be expressed as

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

where

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)   

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