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Parallel connection

When components are connected in parallel, the voltage is the same across each of them, while the current splits between the branches. The total resistance is always smaller than the smallest individual resistance, because the current gets more paths to take.

\dfrac{1}{R_{par}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}

inverse total resistance in parallel

R_{par} = \dfrac{R_1R_2}{R_1+R_2}

for exactly two resistors

Symbols

$R_{par}$	total resistance	$\Omega$
$U$	same voltage across all branches	V

Example

Two resistors $R_1 = 6.0$ Ω and $R_2 = 12.0$ Ω are in parallel. $R_{par} = \dfrac{6.0\cdot 12.0}{6.0+12.0} = 4.0$ Ω.

Do not forget to take the inverse at the end of

1/R = 1/R_1 + 1/R_2

– the answer is not

1/R

, but

R

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Part of Foundations of Physics: Electricity.