Summarizing Resistors in Series and Parallel

Summary

• The total resistance of an electrical circuit with resistors wired in a series is the sum of the individual resistances: \({R}_{\text{s}}={R}_{1}+{R}_{2}+{R}_{3}+\text{.}\text{.}\text{.}\text{.}\)
• Each resistor in a series circuit has the same amount of current flowing through it.
• The voltage drop, or power dissipation, across each individual resistor in a series is different, and their combined total adds up to the power source input.
• The total resistance of an electrical circuit with resistors wired in parallel is less than the lowest resistance of any of the components and can be determined using the formula:

  \(\cfrac{1}{{R}_{\text{p}}}=\cfrac{1}{{R}_{1}}+\cfrac{1}{{R}_{2}}+\cfrac{1}{{R}_{3}}+\text{.}\text{.}\text{.}\text{.}\)

• Each resistor in a parallel circuit has the same full voltage of the source applied to it.
• The current flowing through each resistor in a parallel circuit is different, depending on the resistance.
• If a more complex connection of resistors is a combination of series and parallel, it can be reduced to a single equivalent resistance by identifying its various parts as series or parallel, reducing each to its equivalent, and continuing until a single resistance is eventually reached.

Glossary

series

a sequence of resistors or other components wired into a circuit one after the other

resistor

a component that provides resistance to the current flowing through an electrical circuit

resistance

causing a loss of electrical power in a circuit

Ohm’s law

the relationship between current, voltage, and resistance within an electrical circuit: \(V=\text{IR}\)

voltage

the electrical potential energy per unit charge; electric pressure created by a power source, such as a battery

voltage drop

the loss of electrical power as a current travels through a resistor, wire or other component

current

the flow of charge through an electric circuit past a given point of measurement

Joule’s law

the relationship between potential electrical power, voltage, and resistance in an electrical circuit, given by: \({P}_{e}=\text{IV}\)

parallel

the wiring of resistors or other components in an electrical circuit such that each component receives an equal voltage from the power source; often pictured in a ladder-shaped diagram, with each component on a rung of the ladder