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Summary of Series and Parallel Combination Rules

Module by: Don Johnson

Summary: Series and parallel combination rules.

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Figure 1 summarizes the series and parallel combination results. These results are easy to remember and very useful. Keep in mind that for series combinations, voltage and resistance are the key quantities, while for parallel combinations current and conductance are more important. In series combinations, the currents through each element are the same; in parallel ones, the voltages are the same.

Figure 1: Series and parallel combination rules.
series and parallel combination rules
series combination ruleparallel combination rule
(a) R T =∑n=1N R n R T n 1 N R n    v n = R n R T v v n R n R T v (b) G T =∑n=1N G n G T n 1 N G n    i n = G n G T i i n G n G T i
series combination rule (seriesex.png)parallel combination rule (parallelex.png)

Exercise 1

Contrast a series combination of resistors with a parallel one. Which variable (voltage or current) is the same for each and which differs? What are the equivalent resistances? When resistors are placed in series, is the equivalent resistance bigger, in between, or smaller than the component resistances? What is this relationship for a parallel combination?

Solution

In a series combination of resistors, the current is the same in each; in a parallel combination, the voltage is the same. For a series combination, the equivalent resistance is the sum of the resistances, which will be larger than any component resistor's value; for a parallel combination, the equivalent conductance is the sum of the component conductances, which is larger than any component conductance. The equivalent resistance is therefore smaller than any component resistance.

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