Equivalent resistance of a parallel association

What is a parallel association?

Two (or more) resistors are in parallel when they are connected between the same two nodes of the circuit: they therefore share the same voltage U across their terminals, but the total current is distributed between the different branches.

The law of inverses

For n resistors R1, R2, ..., Rn in parallel, the equivalent resistance Req satisfies:

1/Req = 1/R1 + 1/R2 + ... + 1/Rn

For just two resistors, there is a very handy direct formula:

Req = (R1 * R2) / (R1 + R2)

Concrete example

R1 = 60 ohm and R2 = 30 ohm in parallel:

Req = (60 * 30) / (60 + 30) = 1800 / 90 = 20 ohm

Another example: two identical resistors R = 100 ohm in parallel give Req = 50 ohm, i.e. half.

Summary table

Quantity	In parallel
Voltage	Identical across each branch: U
Total current	I = I1 + I2 + ...
Equivalent resistance	1/Req = 1/R1 + 1/R2 + ...

Common pitfall

The equivalent resistance of a parallel group is ALWAYS lower than the smallest resistance in the group. If you find a result greater than R1 or R2, you've made a mistake: you probably forgot to invert the final result after calculating 1/Req.