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Series and parallel

In a series connection the same current goes through every component, and the voltages add. The total resistance is the sum. In a parallel connection the same voltage lies across every branch, and the currents add. Then it is the reciprocal resistances that are added. Two equal resistors in parallel give half the resistance of one of them. An open switch in series stops the whole circuit.

R=R1+R2R = R_1 + R_2series
1R=1R1+1R2\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}parallel

Symbols

RRtotal resistanceΩ\Omega
R1, R2R_1,\ R_2individual resistancesΩ\Omega

Example

6 Ω and 3 Ω in series: R=6+3=9R = 6 + 3 = 9 Ω.

The same two in parallel: 1R=16+13\dfrac{1}{R} = \dfrac{1}{6} + \dfrac{1}{3}, so R=2R = 2 Ω.

Parallel always gives a smaller total resistance than the smallest of the branches.
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