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Resistors in Parallel Circuit, Formula, Explanation, and Calculator

When resistors are connected in parallel, they share the same voltage. Each resistor provides an independent path for the current to flow.

The total current flowing from the source is split between the paths in inverse proportion to their resistances.

Published: August 1, 2023.

Resistors in Parallel Circuit and Formula

Resistors connected in a parallel circuit is a rather basic one:

resistors in parallel r n

The formula for calculating the total resistance (Rt) of a parallel circuit is given by the reciprocal of the sum of the reciprocals of the individual resistances. This can be written as:

1/Rt = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

For a parallel circuit with just two resistors, the formula can be simplified to:

Rt = R1||R2 = (R1 * R2) / (R1 + R2)

Note: when two resistors, for example, R1 and R2, are connected in parallel, that is often written as R1||R2.

The total resistance of a parallel circuit will always be less than the smallest resistance in the circuit.

This is because the current has more than one path it can take, and the more resistors (paths for current) that are added, the less resistance there will be in total.

Resistors in Parallel Calculator

Two resistors connected in parallel is the simplest "resistors in parallel" circuit:

resistors in parallel

To find out the total resistance of the circuit, feel free to use the following calculator - write your values and click Calculate:

Resistance (Ω)

Rt(Ω) = R1||R2 = (R1*R2)/(R1+R2)

Resistance R1 (Ω):

Resistance R2 (Ω):

Resistance Rt (Ω):

For example, if you have two resistors of 1kΩ each in parallel, the total resistance is:

Rt = (1000Ω * 1000Ω) / (1000Ω + 1000Ω) = 1000000Ω2 / 2000Ω = 500Ω

As you can see, the total resistance (500 ohms) is less than the smallest individual resistance (1000 ohms).

In addition to providing a reduced total resistance, connecting resistors in parallel also increases the circuit's reliability. This is because if one path fails (e.g., one resistor burns out), the current can still flow through the other paths.

This characteristic is used in practical applications, such as the wiring of electrical devices in homes, where appliances are typically connected in parallel to allow them to operate independently of each other.