Series and parallel circuits: Difference between revisions

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===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 seriesResistors_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]]
 
[[File:Resistors in series.svg|This is a diagram of several resistors, connected end to end, with the same amount of current through each.]]
<math display="block">R = \sum_{i=1}^n R_i = R_1 + R_2 + R_3 \cdots + R_n.</math>
{{anchor|Lseries}}
Here, the subscript ''s'' in {{math|''R''<sub>s</sub>}} denotes "series", and {{math|''R''<sub>s</sub>}} denotes resistance in a series.
 
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<math display="block">G = \frac{G_1 G_2}{G_1 + G_2}.</math>
 
===Inductors <span class="anchor" id="Lseries"/>===
[[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>
 
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[[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 seriesCapacitors_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]]
 
[[File:Capacitors in series.svg|A diagram of several capacitors, connected end to end, with the same amount of current going through each.]]
<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>
 
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===Resistance units===
To find the total [[Electrical resistance|resistance]] of all components, add the [[Multiplicative inverse|reciprocals]] of the resistances <math>R_i</math> of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:
[[File:Resistors in parallelResistors_in_parallel.svg|alt=A diagram of several resistors, side by side, both leads of each connected to the same wires.|border|center|x120px]]
 
[[File:Resistors in parallel.svg|A diagram of several resistors, side by side, both leads of each connected to the same wires.]]
<math display="block">R = \left(\sum_{i=1}^n{1\over R_i}\right)^{-1} = \left({1\over R_1} + {1\over R_2} + {1\over R_3} + \dots + {1\over R_n}\right)^{-1}</math>
 
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===Inductors<span class="anchor" id="Lparallel"></span>===
[[Inductor]]s follow the same law, in that the total [[inductance]] of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
[[File:Inductors in parallelInductors_in_parallel.svg|alt=A diagram of several inductors, side by side, both leads of each connected to the same wires.|border|center|x120px]]
 
[[File:Inductors in parallel.svg|A diagram of several inductors, side by side, both leads of each connected to the same wires.]]
<math display="block">L = \left(\sum_{i=1}^n{1\over L_i}\right)^{-1} = \left({1\over L_1} + {1\over L_2} + {1\over L_3} + \dots + {1\over L_n}\right)^{-1}.</math>
 
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===Capacitors<span class="anchor" id="Cparallel"></span>===
The total [[capacitance]] of [[capacitors]] in parallel is equal to the sum of their individual capacitances:
[[File:Capacitors in parallelCapacitors_in_parallel.svg|alt=A diagram of several capacitors, side by side, both leads of each connected to the same wires.|border|center|x120px]]
 
[[File:Capacitors in parallel.svg|A diagram of several capacitors, side by side, both leads of each connected to the same wires.]]
<math display="block">C = \sum_{i=1}^n C_i = C_1 + C_2 + C_3 \cdots + C_n.</math>