# Electronics/Capacitors

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Usually, a capacitor is a device used to store an electric charge, consisting of one or more pairs of conductors separated by an insulator.

## Theoretical capacitors

Def. an

1. "electronic component capable of storing electrical energy in an electric field; especially one consisting of two conductors separated by a dielectric"[1] or
2. "electronic component capable of storing an electric charge; especially one consisting of two conductors separated by a dielectric"[2]

is called a capacitor.

## Capacitances

This is a simple capacitor circuit with a resistor and ammeter in series. Credit: Sjlegg.

Def. a "property of an electric circuit or its element that permits it to store charge, defined as the ratio of stored charge to potential over that element or circuit (Q/V); SI unit: farad (F)"[3] or a "property of an element of an electrical circuit that permits it to store charge"[4] is called a capacitance.

In the simple, ideal circuit on the right there is a capacitor (two equal parallel plates) with a resistor (rectangular box) and ammeter (A) in series, a voltmeter (V) in parallel, and a switch (at the top) and cell (two different length parallel plates) for charging.

"If you place two conducting plates near each other, with an insulator (known as a dielectric) in between, and you charge one plate positively and the other negatively, there will be a uniform electric field between them."[5]

"The capacitance C of a capacitor is:

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

where Q is the charge stored by the capacitor, and V is the potential difference between the plates. C is therefore the amount of charge stored on the capcitor per unit potential difference. Capacitance is measured in farads (F). Just as 1 coulomb is a massive amount of charge, a 1F capacitor stores a lot of charge per volt."[5]

"Any capacitor, unless it is physically altered, has a constant capacitance. If it is left uncharged, Q = 0, and so the potential difference across it is 0. If a DC power source is connected to the capacitor, we create a voltage across the capacitor, causing electrons to move around the circuit. This creates a charge on the capacitor equal to CV. If we then disconnect the power source, the charge remains there since it has nowhere to go. The potential difference across the capacitor causes the charge to 'want' to cross the dielectric, creating a spark. However, until the voltage between the plates reaches a certain level (the breakdown voltage of the capacitor), it cannot do this. So, the charge is stored."[5]

"If charge is stored, it can also be released by reconnecting the circuit. If we were to connect a wire of negligible resistance to both ends of the capacitor, all the charge would flow back to where it came from, and so the charge on the capacitor would again, almost instantaneously, be 0. If, however, we put a resistor (or another component with a resistance) in series with the capacitor, the flow of charge (current) is slowed, and so the charge on the capacitor does not become 0 instantly. Instead, we can use the charge to power a component, such as a camera flash."[5]

"Current is the rate of flow of charge. However, current is given by the formula:

${\displaystyle I={\frac {V}{R}}.}$"[5]

"But, in a capacitor, the voltage depends on the amount of charge left in the capacitor, and so the current is a function of the charge left on the capacitor. The rate of change of charge depends on the value of the charge itself. And so, we should expect to find an exponential relationship:

${\displaystyle Q=Q_{0}e^{-{\frac {t}{RC}}}}$,

where R is the resistance of the resistor in series with the capacitor, Q is the charge on the capacitor at a time t and Q0 was the charge on the capacitor at t = 0. Since Q = IΔt:

${\displaystyle I\Delta t=I_{0}\Delta te^{-{\frac {t}{RC}}}}$
${\displaystyle I=I_{0}e^{-{\frac {t}{RC}}}}$,

where I is the current flowing at a time t and I0 was the initial current flowing at t = 0. Since V = IR:

${\displaystyle V=V_{0}e^{-{\frac {t}{RC}}}.}$"[5]

## Electronic devices

This is a cut-away drawing of a ceramic disc capacitor. Credit: Inductiveload.
This shows a 100 pF up to 1000 volts ceramic capacitor. Credit: Jens Both Elcap.

In the cut-away drawing on the right the components are as follows:

English
2 Dipped blue dyed phenolic coating
3 Soldered connection
4 Silver electrode
5 Ceramic dielectric

## Capacitor

Capacitor is a electric component that can store electric field energy

## Construction

Resistor is made from 2 parallel plates separated by an insulator.

${\displaystyle C=\epsilon {\frac {A}{l}}}$

## Capacitor in DC Circuit

### Capacitance

Capacitance has a symbol C measured in Farat unit F

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

### Charge

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

### Current

${\displaystyle I={\frac {Q}{t}}}$

### Voltage

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

### Power

${\displaystyle P_{C}=IV={\frac {Q}{t}}{\frac {W}{Q}}={\frac {W}{t}}}$

## Resistor in AC Circuit

### Voltage

${\displaystyle v_{C}={\frac {1}{C}}\int idt}$

### Current

${\displaystyle i_{C}=C{\frac {dv}{dt}}}$

### Reactance

Resistance to the AC current flow

In time domain

${\displaystyle X_{C}={\frac {v_{C}}{i_{C}}}={\frac {{\frac {1}{C}}\int idt}{C{\frac {dv}{dt}}}}}$

In frequency domain

${\displaystyle X_{C}(j\omega )={\frac {1}{j\omega C}}}$

In phasor domain

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

### Impedance

Resistance to the AC current flow

${\displaystyle Z_{C}=R_{C}+X_{C}}$

In frequency domain

${\displaystyle Z_{C}=R_{C}+{\frac {1}{j\omega C}}}$
${\displaystyle Z_{C}={\frac {j\omega T+1}{j\omega C}}}$

In phasor domain

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

### Time Constant

${\displaystyle T=CR_{C}}$

### Power

Power of the capacitor

${\displaystyle p={\frac {1}{2}}Cv_{C}^{2}}$

## Capacitor Configuration

### Capacitor in Series

For n capacitors connected adjacent to each other as shown

The total resistance

${\displaystyle {\frac {1}{CR_{1}}}+{\frac {1}{C_{2}}}+...+{\frac {1}{C_{n}}}}$

For 2 series capacitor of same value

${\displaystyle {\frac {1}{C_{t}}}={\frac {C}{R_{1}}}+{\frac {1}{C_{2}}}={\frac {C_{1}+C_{2}}{C_{1}C_{2}}}}$
${\displaystyle C_{t}={\frac {C_{1}C_{2}}{C_{1}+C_{2}}}={\frac {c^{2}}{2C}}={\frac {1}{2}}C}$

### Capacitors in parallel

For n capacitors connected facing each other as shown

The total resistance

${\displaystyle C_{1}+C_{2}+...+C_{n}}$

For 2 parallel capacitor of same value

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