Alexander Fufaev

Formula: Equivalent resistance of a parallel circuit of resistors

Parallel connection of three resistors

Equivalent resistance

The total resistance (equivalent resistance) of a parallel circuit is not the sum of individual resistances, but the sum of their reciprocals. For example, if you have a parallel circuit with two impedances \(R_1\) and \(R_2\), then the total resistance \(R\) is given by: \[ \frac{1}{R} ~=~ \frac{1}{R_1} ~+~ \frac{1}{R_2} \]

Then, rearrange for \(R\): \[ R ~=~ \frac{R_1 ~\cdot~ R_2}{R_1 ~+~ R_2} \]

For example, if the first resistance is \(R_1 = 200 \, \Omega \) and the second resistance is \(R_2 = 50 \, \Omega \) and the two are connected in parallel, then the total resistance of the parallel connection is: \begin{align} R &~=~ \frac{200 \, \Omega ~\cdot~ 50 \, \Omega}{200 \, \Omega ~+~ 50 \, \Omega} &~=~ 40 \, \Omega \end{align}

Single resistance

One of the resistances of the parallel circuit.