Resistors in parallel

Current divider and special cases

Principle of the current divider

When two resistors R1 and R2 are in parallel and carry a total current I, this current is distributed between the two branches inversely proportional to the resistances:

I1 = I * R2 / (R1 + R2)

I2 = I * R1 / (R1 + R2)

Warning: in the numerator, it is the resistance of the OTHER branch that appears. The branch with the least resistance receives the strongest current.

Concrete example

I = 3 A, R1 = 10 ohm, R2 = 20 ohm.

I1 = 3 * 20 / (10+20) = 60/30 = 2 A

I2 = 3 * 10/30 = 1 A

We check that I1 + I2 = 3 A, and that the weaker resistance (R1) indeed receives the strongest current.

Special case: n identical resistors

If n identical resistors of value R are in parallel, then Req = R / n. Example: 4 resistors of 40 ohm in parallel give Req = 40/4 = 10 ohm.

Limiting case: the short circuit

If a 0 ohm resistor (a simple wire) is placed in parallel with another resistor, then Req = 0: this is a short circuit, all the current flows through the wire and the resistor in parallel becomes useless.

Common pitfall