Resistors in Parallel
Total resistance of resistors in parallel.
Formula
Variables
Example
Two 4 Ω resistors in parallel give 2 Ω.
How it works
When resistors are connected in parallel, they all share the same voltage, and the current splits among the different branches. Because each branch provides an additional path for charge to flow, the total ease of current flow increases, so the equivalent resistance becomes smaller than any individual resistor. The reciprocal form appears because branch currents add, while each branch current is proportional to 1/R by Ohm’s law.
When to use it
Use this formula whenever a circuit has two or more resistors connected across the same two points, such as parallel branches in electronic circuits or wiring systems. It is especially useful for finding the overall load seen by a power source.
Worked example, step by step
Suppose three resistors are connected in parallel: R1 = 6 Ω, R2 = 3 Ω, and R3 = 2 Ω. 1/R_eq = 1/6 + 1/3 + 1/2 1/R_eq = 1/6 + 2/6 + 3/6 1/R_eq = 6/6 = 1 R_eq = 1/1 = 1 Ω So the equivalent resistance of the parallel combination is 1 Ω.
Common mistakes to avoid
- Adding parallel resistances directly instead of adding their reciprocals
- Forgetting that the equivalent resistance in parallel must be less than the smallest resistor
- Mixing up parallel and series rules when solving multi-branch circuits
Did You Know?
Adding a parallel resistor lowers total resistance — more lanes for the current to flow.
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