Series and parallel resistor calculator
Series adds; parallel adds reciprocals. Three resistors is enough to see both.
ohm
ohm
ohm
V
Parallel resistance
59.976 798ohm
- Series resistance
- 790 ohm
- R1 and R2 in parallel only
- 68.75 ohm
- Current in the series circuit
- 0.015 189 9 A
- Total current in the parallel circuit
- 0.200 077 A
- Current through R1 in parallel
- 0.12 A
- Total power, parallel
- 2.400 93
- Total power, series
- 0.182 278
Show the working
- R1 = 100
- R2 = 220
- R3 = 470
- Applied voltage = 12
- Series resistance = 100 + 220 + 470 = 790
- Parallel resistance = 1 / (1/100 + 1/220 + 1/470) = 59.9768
- R1 and R2 in parallel only = 100*220/(100+220) = 68.75
- Current in the series circuit = 12 / 790 = 0.015 189 9
- Total current in the parallel circuit = 12 / 59.9768 = 0.200 077
- Current through R1 in parallel = 12 / 100 = 0.12
- Total power, series = 12^2 / 790 = 0.182 278
- Total power, parallel = 12^2 / 59.9768 = 2.400 93
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- series: R = R1 + R2 + R3
- parallel: 1/R = 1/R1 + 1/R2 + 1/R3
- two in parallel: R = R1 R2 / (R1 + R2)
A parallel combination is always smaller than the smallest resistor in it.