# Formula Equivalent resistance of a parallel circuit of resistors Equivalent resistance Single resistance

## Equivalent resistance

`$$ R $$`Unit

`$$ \mathrm{\Omega} $$`

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

`$$ R_1 $$`Unit

`$$ \mathrm{\Omega} $$`

One of the resistances of the parallel circuit.