Capacitor is an energy
storage element, which stores energy in the form of electrical energy.
Capacitance is measured in 'Farad'.

where ω=2πf, f=frequency

In the above circuit pulsed voltage source is used across capacitor. Pulse duration is 1ms, and rise time and fall time are 1ns. So this makes voltage across capacitor to change suddenly. Using Ic ammeter, we are measuring current through capacitor. Below figure shows the simulation results.

Simplest capacitor is a parallel plate capacitor. Two
conductive plates each having area of 'A' and are separated by a distance’d’,
arranged parallel acts as a parallel plate capacitor. The capacitance C offered
by this structure is given by

Where ℰ is given by
permittivity of dielectric between plates. If air is the
dielectric then ℰ=ℰ0. If any other dielectric
material is used then ℰ=ℰ0ℰr.

If V is the potential
difference applied across parallel plate capacitor C, then charge Q stored in
the capacitor is given by

Q=CV

The energy E stored in
a parallel plate capacitor is

Capacitor won't allow
sudden changes in voltage.

**Symbols:**

So if the voltage
across the capacitor is changed suddenly in 0 time, then ideally current through
capacitor is infinite. (since dt =0)

Impedance offered by
the capacitor 'C' is

where ω=2πf, f=frequency

As the frequency 'f'
increases the impedance offered by the capacitor reduces. So high frequency AC
signals simply pass through capacitor. Since DC signal has '0' frequency, impedance
offered by capacitor to DC signal is infinity. So DC will be blocked by
capacitor.

In ideal capacitor
current leads thee voltage by 90 degrees.

__Transient response of a capacitor:__In the above circuit pulsed voltage source is used across capacitor. Pulse duration is 1ms, and rise time and fall time are 1ns. So this makes voltage across capacitor to change suddenly. Using Ic ammeter, we are measuring current through capacitor. Below figure shows the simulation results.

You
can observe, the current through capacitor is abnormally high. So capacitor
won’t allow sudden change in voltage and acts as short circuit. That’s the
reason why current through it increased abnormally high.

__Capacitor equivalent circuit:__
'C'
is the ideal capacitance

Rd,
Cd represents dielectric absorption properties

RL
is the leakage resistance

ESR
is the equivalent series resistance of the device. This is due to electrode
resistance, lead resistance etc.

ESL is the equivalent series inductance
of the capacitor. This is also due to inductance of electrode and lead
inductance.

**Capacitor parameters:**

__Working DC voltage__: This is the maximum peak DC voltage that can be applied across a capacitor continuously.

__Reverse Voltage and polarity__: Reverse voltage means applying negative voltage to positive pin. All capacitors having polarity, will get damaged if a reverse voltage is applied across it.

__DC Leakage current__: This is the current, which flows through a capacitor, when voltage is applied across it. (After one to five minute charging period is over)

__Equivalent series resistor__: ESR is the high frequency parameter. It represents capacitor ohmic resistance. As temperature increases ESR reduces.

__AC Power dissipation__: Maximum power dissipation depends on case size (package size) of the capacitor.

__Dissipation factor/Loss tangent__: Any ideal capacitor will have 90 degree phase difference between applied voltage and current. I.e. Current leads the voltage by 90 degrees. But because of ESR of capacitor, this phase difference will change. You can see this from the below figure, V

_{practical}is having less phase difference than V

_{ideal}.

So the 'V' will have
two components VR and VC. VR is in phase with the current I, which will
dissipate power . tanδ is called loss tangent (or) dissipation
factor.

Reciprocal of loss
tangent is called quality factor.

Dissipation factor is
measured at 120Hz, up to 1Vrms max and up to 2V DC max. at 25

^{o}C. Dissipation factor increases with temperature. This is a useful measurement of resistive component of capacitor at low frequencies
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