Capacitor's construction

A device is made from two conductive "plates" separated by a thin layer of insulation called dielectric.

Capacitor's symbol

Capacitance

Capacitance is defined as the capability of storing charge of a given voltage on each plate which is directly proportional to dielectric constant, the area of the plate and inversely proportional to the separation distance between two plates.

${\displaystyle C={\frac {Q}{V}}}$ = ε ${\displaystyle {\frac {A}{l}}}$

Capacitance has a symbol C measured in unit farad which has symbol F.

Charge

Q = q₁ + q₂ + ...

${\displaystyle Q=\int Idt}$

Capacitance

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

Voltage

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

Current

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

Reactance

Reactance is defined as the ratio of voltage over current.

${\displaystyle X_{C}={\frac {{\frac {1}{C}}\int Idt}{I}}}$

${\displaystyle X_{C}={\frac {1}{\omega C}}}$/_-90

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

${\displaystyle X_{C}={\frac {1}{sC}}}$

Impedance

Since all conductor has resistance the real capacitor's impedance is defined as the sum of reactance and resistance of capacitor.

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

${\displaystyle Z_{C}={\sqrt {R_{C}^{2}+({\frac {1}{sC}})^{2}}}}$/_ Tan^-1${\displaystyle {\frac {1}{\omega RC}}}$

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

${\displaystyle Z_{C}=R_{C}+{\frac {1}{sC}}}$

Frequency respond

Capacitor is a tool depends on frequency ${\displaystyle \omega }$.

• ${\displaystyle \omega =0,X_{C}=00}$, Capacitor Opened circuit, I = 0
• ${\displaystyle \omega =00,X_{C}=0}$, Capacitor Closed circuit, I ≠ 0
• ${\displaystyle \omega ={\frac {1}{CR_{C}}}}$

${\displaystyle X_{C}=R_{C}}$ ,

${\displaystyle Z_{C}={\sqrt {2}}R_{C}}$ ,

${\displaystyle V_{C}={\frac {V}{2}}}$

${\displaystyle I_{C}={\frac {V}{2R_{C}}}}$

With the value of I at three frequency points ω = 0, 00 , 1 / CR_C I - f curve can be drawn to give a picture of current in the capacitor over time.

Phase angle

When a voltage is applied across capacitor, it will take some time before capacitor conducts current. Therefore, current on the capacitor will lags behind voltage at an angle θ.

For ideal losses capacitor which has no internal resistance, current will lage behind voltage at an angle 90°. For non-ideal lossless capacitor which has an internal resistance, current will lage behind Voltage at an angle θ.

${\displaystyle Tan\theta ={\frac {1}{2\pi f}}{\frac {1}{CR}}}$

Phase angle relates to time frequecy or time and the value of C and R_C. When there is a change in phase angle time and frequency also change. For this reason RC network is used in phase shifting.

${\displaystyle f={\frac {1}{2\pi }}{\frac {1}{Tan\theta }}{\frac {1}{CR}}}$

t = 2π Tanθ CR_C

Series connection

Several capacitors in series.

When n capacitor connected in series, the total capacitance:

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

When there are two capacitor of the same capacitance connected in series, the total capacitance of the two capacitors is exactly halved.

Parallel Connection

Several capacitors in parallel.

When n capacitor connected in parallel, the total capacitance

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

When there are two capacitor of the same capacitance connected in parallel, the total capacitance of the two capacitors is exactly doubled.

Ceramic Disc

Ceramic capacitors generally take the form of a disc of ceramic with two legs protruding downwards. These capacitors are not polarised - it doesn't matter which way round they are put into a circuit. The capacitances vary from a lower limit of less than 1pF, up to about 100nF. They sometimes exhibit drifting which is where capacitance changes, due to ambient conditions. This is not usually a problem, but it is something you should be aware of.

Electrolytic

Axial (top) and radial (bottom) electrolytic capacitors.

Electrolytic capacitors have very large capacitance per volume unit, which makes them good for capacitances over 1μF. They take the form of cylinders which range form a few millimetres in height to several hundred. There are two main types of packaging: axial and radial. Axial capacitors are generally rarer than radial capacitors and have a lead on each end of the cylinder. Radial capacitors have both leads on the same end.

These capacitors are polarised and must be connected the right way around. The negative terminal, or cathode, is usually marked in any of the following ways:

• A stripe down the cathode side of the capacitor, usually with minus signs printed on it
• A shorter lead at the anode than at the cathode (not found on axial capacitors)
• A minus sign printed on the end of the capacitor, next to the negative lead.

Electrolytic capacitors can explode violently if they are connected incorrectly, overheat, or have too much voltage across them. Larger capacitors have vents scored into the metal ends, but they will still make a very loud noise (which can damage hearing) and spray hot electrolyte from the rupture.

They generally have poor tolerances, and are used mostly where precise capacitance is unimportant, such as for power supply smoothing, stiffening, etc.