CAPACITANCE

Cuthbert Nyack

If 2 objects have equal and opposite charges(magnitude q) and the potential difference between them is V, then the 2 can be said to constitute a capacitor of capacitance C given by the following relation. Q has units of Coulomb, V of Volt and C of Farad.

The capacitance of a capacitor depends on geometric factors and can be evaluated analytically for some simple cases. For parallel plates of area A and separation d, the capacitance is given by:-

For a length l of coaxial cable with inner radius a and outer radius b, the capacitance is given by:-

When a sinusoidal current is flowing through a capacitor, it appears to have an impedance of 1/(jwC. The 1/j means that the voltage lags the current by 90º. Circuits in which the voltage lags the current are often referred to as Capacitive. Because of the phase relation between current and voltage, no power is dissipated in an ideal capacitor. Capacitors with dielectrics may have a phase slightly different from 90º and dissipate some power.

In the more general case the impedance is 1/sC where s is the Laplace Variable.

When a capacitor is charged, the energy stored in the electric field is given by:-

Capacitors are used extensively in almost all kinds of electronic circuits. Applications include coupling, bypass, smoothing, impedance matching, energy storage etc.

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