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Series and Parallel

In a series connection the current is the same through every component, and the voltages add up. In a parallel connection the voltage is the same across every branch, and the currents split. These two basic rules are used to simplify almost any resistive circuit step by step.

R_{tot}=R_1+R_2+\dots

series: resistances add

\dfrac{1}{R_{tot}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dots

parallel: inverse resistances add

U_2=U\dfrac{R_2}{R_1+R_2}

voltage divider for two resistors in series

Symbols

$R_{tot}$	total resistance	$\Omega$
$R_1,\ R_2$	individual resistors	$\Omega$
$U$	voltage across the whole combination	V

Example

$R_1=12$ Ω and $R_2=6$ Ω in parallel:

$1/R_{tot}=1/12+1/6=1/4$ , so $R_{tot}=4$ Ω.

In series the current is shared, in parallel the voltage is shared – identify which quantity is common before combining.

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Part of Electric Circuits: Direct current.