Editing Series and parallel circuits (section)

==Combining conductances<span class="anchor" id="Gparallel"></span><span class="anchor" id="Gseries"></span>==
From [[Kirchhoff's circuit laws]] the rules for combining conductance can be deducted. For two conductances <math>G_1</math> and <math>G_2</math> in ''parallel'', the voltage across them is the same and from Kirchhoff's current law (KCL) the total current is
<math display="block">I = I_1 + I_2.</math>

Substituting Ohm's law for conductances gives
<math display="block">G V = G_1 V + G_2 V</math>
and the equivalent conductance will be,
<math display="block">G = 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 = V_1 + V_2.</math>

Substituting Ohm's law for conductance then gives,
<math display="block">\frac{I}{G} = \frac{I}{G_1} + \frac{I}{G_2}</math>
which in turn gives the formula for the equivalent conductance,
<math display="block">\frac{1}{G} = \frac{1}{G_1} + \frac{1}{G_2}.</math>

This equation can be rearranged slightly, though this is a special case that will only rearrange like this for two components.

<math display="block">G = \frac{G_1 G_2}{G_1 + G_2}.</math>
For three conductances in series,
<math display="block">G = \frac{G_1 G_2 G_3}{G_1 G_2 + G_1 G_3 + G_2 G_3}.</math>