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 = 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
| 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 |
Related Topics
• Electrical
Electrical engineering with units, amps and electrical wiring. Wire gauges, electrical formulas, motors and more.
Related Documents
Board Feet Chart and Calculator
Board feet is used as a volume measurement of lumber.
Current Divider - Online Calculator
An electric current divider outputs a current that is a fraction of the input current.
Electric Circuit Diagram - Drawing Template
Online shareable electric circuit diagram.
Electrical Conductivity - Elements and other Materials
Electric conductance is the ability of a element to conduct an electric current.
Electrical Resistance in Serial and Parallel Networks
Resistors in parallel and serial connections.
Electrical Series Circuits
Voltage and current in electrical series circuits.
Kirchhoff's Voltage and Current Laws
Kirchhoff's current and voltage laws.
Ohm's Law
The relation between voltage, current and electrical resistance.
Resistance vs. Resistivity
Electrical resistance and resistivity.
Resistors - Color Codes Calculator
Color codes for fixed resistors - values and tolerances - online calculator.
Resistors - Letters and Digit Codes
Letter and digit codes to indicating resistor values.
Resistors - Standard Values
Preferred number series for resistors.
Voltage Dividers - Online Calculator
Output voltage potential divider.
Voltage Sources vs. Current Sources
Voltage and Current Sources