# Fundamental Physics/Electronics/Capacitors

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## Capacitor Capacitor is a electric component that can store electric field energy . Capacitor is made from 2 parallel plates separated by an insulator

### Symbol ### Capacitance

Capacitance is a characteristic of capacitor which indicates capacitor's capability to store energy under Electric field

$C=\epsilon {\frac {A}{l}}$ ## Capacitor in DC Circuit

### Capacitance

Capacitance has a symbol C measured in Farat unit F

$C={\frac {V}{Q}}$ ### Charge

$Q={\frac {V}{C}}$ ### Current

$I={\frac {Q}{t}}$ ### Voltage

$V={\frac {W}{Q}}$ ### Power

$P_{C}=IV={\frac {Q}{t}}{\frac {W}{Q}}={\frac {W}{t}}$ ## Capacitor in AC Circuit

### Voltage

$v_{C}={\frac {1}{C}}\int idt$ ### Current

$i_{C}=C{\frac {dv}{dt}}$ ### Reactance

Resistance to the AC current flow

In time domain

$X_{C}={\frac {v_{C}}{i_{C}}}={\frac {{\frac {1}{C}}\int idt}{C{\frac {dv}{dt}}}}$ In frequency domain

$X_{C}(j\omega )={\frac {1}{j\omega C}}$ In phasor domain

$X_{C}(\omega \theta )={\frac {1}{\omega C}}\angle -90$ ### Impedance

Resistance to the AC current flow

$Z_{C}=R_{C}+X_{C}$ In frequency domain

$Z_{C}=R_{C}+{\frac {1}{j\omega C}}$ $Z_{C}={\frac {j\omega T+1}{j\omega C}}$ In phasor domain

$Z_{C}=R_{C}\angle 0+{\frac {1}{\omega C}}\angle -90$ $Z_{C}={\sqrt {R_{C}^{2}+({\frac {1}{\omega T}})^{2}}}\angle {\frac {1}{\omega T}}$ ### Time Constant

$T=CR_{C}$ ### Power

Power of the capacitor

$p={\frac {1}{2}}Cv_{C}^{2}$ ## Capacitor Configuration

### Capacitor in Series

For n capacitors connected adjacent to each other as shown

The total resistance

${\frac {1}{CR_{1}}}+{\frac {1}{C_{2}}}+...+{\frac {1}{C_{n}}}$ For 2 series capacitor of same value

${\frac {1}{C_{t}}}={\frac {C}{R_{1}}}+{\frac {1}{C_{2}}}={\frac {C_{1}+C_{2}}{C_{1}C_{2}}}$ $C_{t}={\frac {C_{1}C_{2}}{C_{1}+C_{2}}}={\frac {c^{2}}{2C}}={\frac {1}{2}}C$ ### Capacitors in parallel

For n capacitors connected facing each other as shown

The total resistance

$C_{1}+C_{2}+...+C_{n}$ For 2 parallel capacitor of same value

${\frac {1}{C_{t}}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}={\frac {C_{1}+C_{2}}{C_{1}C_{2}}}={\frac {C+C}{CC}}={\frac {2}{C}}$ $C_{t}={\frac {1}{2}}C$ 