How to Determine Resistance in a Series or Parallel Circuit

Multiple resistors in a circuit have an equivalent resistance.

When multiple resistors are wired in a circuit, they can either be in series, where the current travels through one resistor before the other, or in parallel, where the current splits before traveling through resistors. Resistors in series can simply be added together and treated as a single resistor, while parallel resistors must have the reciprocal of each resistor added together to find the equivalent single resistance. In the event that a circuit has a combination of parallel and series resistors, begin by combining the two farthest resistors from the voltage source, and then repeat until all resistors are accounted for.

Things You'll Need

• Calculator

Instructions

1. Determine what the orientation of the resistors is. If the circuit is wired such that current must pass through one resistor before it reaches the second, then the two resistors are wired in series. Otherwise they are in parallel.

2. Add up the resistances of each individual resistor if they are wired in series. This sum, in ohms, is the equivalent resistance of all resistors in the circuit, as if they were replaced by a single resistor. For example, resistors of 3, 8, and 2 ohms wired in series have an equivalent resistance of 13 ohms.

3. Take the reciprocal of each resistor if they are wired in parallel. Sum up each reciprocal, and take the reciprocal of that sum. For example, resistors of 3, 5 and 6 ohms wired in parallel have a resistance of 1 / (1/3 + 1/5 + 1/6) = 10/7 ohms.

References

• So You Wanna: How to Determine Resistance in a Parallel Circuit
• Bucknell University: Resistor Combinations - Series and Parallel
• All About Circuits: Series and Parallel Circuits