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 \(R\):
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\[ R ~=~ \frac{R_1 ~\cdot~ R_2}{R_1 ~+~ R_2} \]
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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}
`