Editing Series and parallel circuits (section)

==Series circuits<span class="anchor" id="Zseries"></span><span class="anchor" id="Xseries"></span><span class="anchor" id="Yseries"></span><span class="anchor" id="Bseries"></span>==
<!-- "Series circuit" redirects here. "Battery (electricity)" links here. -->
{{Electromagnetism|Network}}
'''Series circuits''' are sometimes referred to as current-coupled. The 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.

===Current<span class="anchor" id="Iseries"></span>===
<math display="block">I = I_1 = I_2 = \cdots = I_n</math>

In a series circuit, the current is the same for all of the elements.

===Voltage===
In a series circuit, the voltage is the sum of the voltage drops of the individual components (resistance units).
<math display="block">V = \sum_{i=1}^n V_i = I\sum_{i=1}^n R_i</math>

===Resistance units<span class="anchor" id="Rseries"></span>===
The total resistance of two or more resistors connected in series is equal to the sum of their individual resistances:
[[File:Resistors_in_series.svg|alt=This is a diagram of several resistors, connected end to end, with the same amount of current through each.|border|center|x100px]]
<math display="block">R = \sum_{i=1}^n R_i = R_1 + R_2 + R_3 \cdots + R_n.</math>
Here, the subscript ''s'' in {{math|''R''<sub>s</sub>}} denotes "series", and {{math|''R''<sub>s</sub>}} denotes resistance in a series.

==== Conductance ====
[[Electrical conductance]] presents a reciprocal quantity to resistance. Total conductance of a series circuits of pure resistances, therefore, can be calculated from the following expression:
<math display="block">G = \left(\sum_{i=1}^n{1\over G_i}\right)^{-1} = \left({1\over G_1} + {1\over G_2} + {1\over G_3} + \dots + {1\over G_n}\right)^{-1}.</math>

For a special case of two conductances in series, the total conductance is equal to:
<math display="block">G = \frac{G_1 G_2}{G_1 + G_2}.</math>

===Inductors <span class="anchor" id="Lseries"></span>===
[[Inductor]]s follow the same law, in that the total [[inductance]] of non-coupled inductors in series is equal to the sum of their individual inductances:

[[File:Inductors in series.svg|A diagram of several inductors, connected end to end, with the same amount of current going through each.|border|center|x100px]]
<math display="block">L = \sum_{i=1}^n L_i = L_1 + L_2 + L_3 \cdots + L_n.</math>

However, in some situations, it is difficult to prevent adjacent inductors from influencing each other as the magnetic field of one device couples with the windings of its neighbors. This influence is defined by the mutual inductance M. For example, if two inductors are in series, there are two possible equivalent inductances depending on how the magnetic fields of both inductors influence each other.

When there are more than two inductors, the mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the mutual inductance of each given coil with itself, which is termed self-inductance or simply inductance. For three coils, there are six mutual inductances <math>M_{12}</math>, <math>M_{13}</math>, <math>M_{23}</math> and <math>M_{21}</math>, <math>M_{31}</math> and <math>M_{32}</math>. There are also the three self-inductances of the three coils: <math>M_{11}</math>, <math>M_{22}</math> and <math>M_{33}</math>.

Therefore
<math display="block">L = \left(M_{11} + M_{22} + M_{33}\right) + \left(M_{12} + M_{13} + M_{23}\right) + \left(M_{21} + M_{31} + M_{32}\right)</math>

By reciprocity, <math>M_{ij}</math> = <math>M_{ji}</math> so that the last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such a coil all turns are in series.

===Capacitors<span class="anchor" id="Cseries"></span>===
{{See also|Capacitor#Networks}}

[[Capacitor]]s follow the same law using the reciprocals. The total [[capacitance]] of capacitors in series is equal to the reciprocal of the sum of the [[Multiplicative inverse|reciprocals]] of their individual capacitances:
[[File:Capacitors_in_series.svg|alt=A diagram of several capacitors, connected end to end, with the same amount of current going through each.|border|center|x100px]]
<math display="block">C = \left(\sum_{i=1}^n{1\over C_i}\right)^{-1} = \left({1\over C_1} + {1\over C_2} + {1\over C_3} + \dots + {1\over C_n}\right)^{-1}.</math>

Equivalently using [[elastance]] (the reciprocal of capacitance), the total series elastance equals the sum of each capacitor's elastance.

===Switches===
Two or more [[switch]]es in series form a [[Logical conjunction|logical AND]]; the circuit only carries current if all switches are closed. See [[AND gate]].

===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.