# Physics with Calculus/Electromagnetism/Capacitance, Inductance, LRC Circuits

2/27/06 Capacitance (c)

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The capacitance is usually defined as the total electric charge placed on the object divided by the potential of the object:

       $C={\frac {Q}{V}}$ or, according to Gauss's law, the capacitance can be expressed as the electric flux per volt

      $C={\frac {\Phi }{V}}$ where

   C is the capacitance in farads
Q is the charge in coulombs
V is the potential in volts
Φ is the electric flux associated with the charge Q in coulombs


Conductors have equal and opposite charge The charge (aka current) is split up Each capacitor will have part of the total charge that is available for the group (there is a certain amount of charge in each branch there will be charge and when you add the charge of the branches that will be the total charge.) Voltage is split up Each capacitor in series gets a part of the total available charge They all acquire the same voltage Each parallelel branch gets the same voltage as all other Total equivalent Capacitance

   $I_{\mathrm {total} }=V\cdot \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}\right)$ 