Series and parallel circuits: Difference between revisions

Revision as of 16:52, 22 February 2023

Revision as of 16:55, 22 February 2023

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[[File:Series circuit.svg|thumb|A series circuit with a [[voltage source]] (such as a battery, or in this case a cell) and three resistance units]]

[[Terminal (electronics)|Two-terminal]] components and [[electrical networks]] can be connected in '''series''' or '''parallel'''. The resulting electrical network will have two terminals, and itself can participate in a series or parallel [[Topology (electrical circuits)|topology]]. Whether a two-terminal "object" is an electrical component (e.g. a [[resistor]]) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks.

Components connected in series are connected along a single "electrical path", and each component has the same [[electric current|current]] through it, equal to the current through the network. The voltage across the network is equal to the sum of the voltages across each component.<ref name="Resnick_1966"/><ref name="Smith_1966"/>

Components connected in parallel are connected along multiple paths, and each component has the same [[voltage]] across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each component.

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A circuit composed solely of components connected in series is known as a '''series circuit'''; likewise, one connected completely in parallel is known as a '''parallel circuit'''. Many circuits can be analyzed as a combination of series and parallel circuits, along with [[Topology (electrical circuits)|other configurations]].

In a series circuit, the current that flows through each of the components is the same, and the [[voltage]] across the circuit is the sum of the individual [[voltage drop]]s across each component.<ref name="Resnick_1966"/> In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents flowing through each component.<ref name="Resnick_1966"/>

Consider a very simple circuit consisting of four light bulbs and a 12-volt [[automotive battery]]. If a wire joins the battery to one bulb, to the next bulb, to the next bulb, to the next bulb, then back to the battery in one continuous loop, the bulbs are said to be in series. If each bulb is wired to the battery in a separate loop, the bulbs are said to be in parallel. If the four light bulbs are connected in series, the same current flows through all of them and the voltage drop is 3 volts across each bulb, which may not be sufficient to make them glow. If the light bulbs are connected in parallel, the currents through the light bulbs combine to form the current in the battery, while the voltage drop is 12 volts across each bulb and they all glow.

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<!-- "Series circuit" redirects here. "Battery (electricity)" links here. -->

{{Electromagnetism|Network}}

'''Series circuits''' are sometimes referred to as current-coupled or [[Daisy chain (electrical engineering)|daisy chain]]-coupled. The [[electric current]] in a series circuit goes through every component in the circuit. Therefore, all of the components in a series connection carry the same current.

A series circuit has only one path through which its current can flow. Opening or breaking a series circuit at any [[Single point of failure|point]] causes the entire circuit to "open" or stop operating. For example, if even one of the light bulbs in an older-style string of [[Christmas tree lights]] burns out or is removed, the entire string becomes inoperable until the faulty bulb is replaced.

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===Cells and batteries===

A [[Battery (electricity)|battery]] is a collection of [[electrochemical cell]]s. If the cells are connected in series, the [[voltage]] of the battery will be the sum of the cell voltages. For example, a 12 volt [[car battery]] contains six 2-volt cells connected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed the 24-volt system.

==Parallel circuits<span class="anchor" id="Zparallel"></span><span class="anchor" id="Xparallel"></span><span class="anchor" id="Yparallel"></span><span class="anchor" id="Bparallel"></span><span class="anchor" id="Parallel_circuit_anchor"></span>==

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<math display="block">G_\text{eq} = G_1 + G_2.</math>

For two conductances <math>G_1</math> and <math>G_2</math> in '''series''' the current through them will be the same and Kirchhoff's Voltage Law says that the voltage across them is the sum of the voltages across each conductance, that is,

<math display="block">V_\text{eq} = V_1 + V_2.</math>