Editing Series and parallel circuits (section)

===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_parallel.svg|alt=A diagram of several resistors, side by side, both leads of each connected to the same wires.|border|center|x120px]]
<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>

For only two resistances, the unreciprocated expression is reasonably simple:
<math display="block">R = \frac{R_1 R_2}{R_1 + R_2} .</math>

This sometimes goes by the mnemonic ''product over sum''.

For ''N'' equal resistances in parallel, the reciprocal sum expression simplifies to:
<math display="block">\frac{1}{R} = N \frac{1}{R}.</math>
and therefore to:
<math display="block">R = \frac{R}{N}.</math>

To find the [[current (electricity)|current]] in a component with resistance <math>R_i</math>, use Ohm's law again:
<math display="block">I_i = \frac{V}{R_i}\,.</math>

The components divide the current according to their reciprocal resistances, so, in the case of two resistors,
<math display="block">\frac{I_1}{I_2} = \frac{R_2}{R_1}.</math>

An old term for devices connected in parallel is ''multiple'', such as multiple connections for [[arc lamp]]s.

==== Conductance ====
Since electrical conductance <math>G</math> is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors is simply:
<math display="block">G = \sum_{i=1}^n G_i = G_1 + G_2 + G_3 \cdots + G_n.</math>

The relations for total conductance and resistance stand in a complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of conductances, and vice versa.