Free tool
Enter 2 to 8 resistors, pick series or parallel, and get the equivalent resistance. Add a source voltage to see the total current and the current, voltage drop and power for every resistor, with the working shown.
Built for college physics and AP Physics 2 circuits2 to 8 resistors.
Leave blank for resistance only. Assumes an ideal source with no internal resistance.
Enter at least two resistances greater than zero.
Series and parallel rules come up in every circuits unit. Encodr keeps formulas like these on a spaced-repetition schedule so they are still there on the final.
Get started freeSeries: Rs = R1 + R2 + R3 + ...
Every resistor carries the same current, and the source voltage is shared between them in proportion to
resistance (V = IR for each). The total is always larger than the largest resistor.
Parallel: 1/Rp = 1/R1 + 1/R2 + 1/R3 + ...
Every resistor has the full source voltage across it, and the current splits, with the most current through the
smallest resistor. The total is always smaller than the smallest resistor. For two resistors,
Rp = R1R2 / (R1 + R2).
Power: P = IV = I2R = V2/R. The powers of the individual
resistors add up to the power the source delivers.
A 12.0 V source drives 1.00, 6.00 and 13.0 ohm resistors in series (the same numbers as OpenStax College Physics Example 21.1). Rs = 1.00 + 6.00 + 13.0 = 20.0 ohm, so I = 12.0 / 20.0 = 0.600 A. The drops are 0.600, 3.60 and 7.80 V, which add back to 12.0 V, and the source delivers 12.0 x 0.600 = 7.20 W.
Put the same three in parallel and 1/Rp = 1/1.00 + 1/6.00 + 1/13.0, so Rp = 0.804 ohm. Each resistor now has 12.0 V across it, so the currents are 12.0, 2.00 and 0.923 A, for a total of 14.9 A. This tool handles a circuit that is entirely series or entirely parallel; for a mixed network, reduce each parallel group first and then add it in series. The series vs parallel guide walks through one.
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