# Capacitor

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A capacitor is an electronic component designed to obey the equation:

${\displaystyle I=C{\frac {dV}{dt}}\,}$

See Introduction to Electricity II for theoretical details about capacitors.

The current that an ideal capacitor "passes" through it depends on the rate of change of the voltage applied across it. The direction of the current will be in such a way as to counteract the change of voltage. A capacitor is not the same as a battery. A capacitor stores energy through charge and battery stores energy through a chemical change. The fundamental prototype of a capacitor consists of two conducting parallel plates separated by an insulating material called the dielectric.

## Factors affecting capacitance

• The charge held depends on the applied voltage
• The capacitance increases as the total area of the opposing surfaces of the plates increases, because a larger plate area can hold a greater charge.
• The capacitance increases as the distance between the plates decreases because the electric field then becomes more concentrated
• The capacitance depends upon the dielectric material

## Uses of the capacitor

• Since there is an insulator, the device can be used to block the passage of DC current. However, alternating or AC current of certain frequencies will pass through.
• A capacitor can be used in a rectifier as a filter, so that pure DC is obtained as output.

Real capacitors have non-zero DC leakage current, non-zero lead resistance and inductance, memory behavior etc. Capacitor Symbol

## Charge Stored

${\displaystyle Q=\int Idt}$

## Capacitance

The capability of a capacitor to store charge of a voltage

${\displaystyle C={\frac {Q}{V}}}$

## Voltage

${\displaystyle V={\frac {1}{C}}Q={\frac {1}{C}}\int Idt}$

## Reactance

${\displaystyle X_{C}={\frac {V}{I}}}$
${\displaystyle X_{C}={\frac {1}{\omega C}}\angle -90^{o}}$
${\displaystyle X_{C}={\frac {1}{j\omega C}}}$
${\displaystyle X_{C}={\frac {1}{sC}}}$

## Impedance

${\displaystyle Z_{C}=R_{C}+X_{C}}$
${\displaystyle Z_{C}=R+{\frac {1}{\omega C}}\angle -90^{o}}$
${\displaystyle Z_{C}=R+{\frac {1}{j\omega C}}={\frac {1+j\omega CR_{C}}{j\omega C}}}$
${\displaystyle Z_{C}=R+{\frac {1}{sC}}={\frac {1+sCR}{j\omega C}}}$

## Frequency Response

${\displaystyle \omega =0,X_{C}=00(infinite)}$ . DC Applied, capacitor is an open circuit , I = 0
${\displaystyle \omega =00(infinite),X_{C}=0}$ . HF AC applied, capacitor is a short circuit , I - limited by rest of circuit
${\displaystyle \omega =\omega _{o},,X_{C}=R_{C}}$ . ${\displaystyle I={\frac {V}{2R_{C}}}}$

With Current's values at three point ${\displaystyle \omega =0,00,{\frac {1}{CR_{C}}}}$ a I - ш can be drawn.

## Phase Angle

For capacitor without resistance, Voltage and current have a phase difference of 90o

For capacitor with resistance, Voltage and current have a phase difference of θ

${\displaystyle Tan\theta ={\frac {1}{\omega T}}}$
${\displaystyle T=RC}$
${\displaystyle \omega =2\pi f}$
${\displaystyle f={\frac {1}{t}}}$