What is Cacacitor and Capacitor formula in details:

What is a capacitor: 

A capacitor is electronic  device that store energy in an electric field 

 Capacitance of Capacitor

The capacitance is the amount of charge stored in a capacitor per volt of potential between its plates. Capacitance can be calculated when charge Q  & voltage V of the capacitor are known:

C = Q/V

Charge Stored in a Capacitor:

If capacitance C and voltage V is known then the charge Q can be calculated by:

Q = C V

Voltage of the Capacitor:

And you can calculate the voltage of the capacitor if the other two quantities (Q & C) are known:

V = Q/C

Where

Q is the charge stored between the plates in Coulombs

C is the capacitance in farads

V is the potential difference between the plates in Volts

Reactance of the Capacitor:

Reactance is the opposition of capacitor to Alternating current AC which depends on its frequency and is measured in Ohm like resistance. Capacitor  reactance is calculated using:

Where

X_C is the capacitive reactance

F is the applied frequency

C is the capacitance

Quality Factor of Capacitor-

Q factor or Quality factor is the efficiency of the capacitor in terms of energy losses & it is given by:

QF = X_C/ESR

Where

X_C is the capacitive reactance

ESR is the equivalent series resistance of the capacitor.

 

Dissipation Factor of Capacitor-

D factor or dissipation factor is the inverse of the Quality factor, it shows the power dissipation inside the capacitor & is given by:

DF = tan δ = ESR/X_C

Where

DF is the dissipation factor

δ is the angle between capacitive reactance victor & negative axis.

X_C is the capacitive reactance

ESR is the equivalent series resistance of the circuit.

 Energy Stored in a Capacitor-

 The Energy E stored in a capacitor is given by following way-

                                                                E = ½ CV2

Where

E is the energy in joules

C is the capacitance in farads

V is the voltage in volts

 

Average Power of Capacitor

The Average power of the capacitor is given by:

P_av = CV² / 2t

where

t is the time in seconds.

 

Capacitor Voltage During Charge / Discharge-

When a capacitor is being charged through a resistor R, it takes upto 5 time constant or 5T to reach upto its full charge. The voltage at any specific time can by found using these charging and discharging formulas below-

 

During Charging:

The voltage of capacitor at any time during charging is given by:

During Discharging:

The voltage of capacitor at any time during discharging is given by:

     Where

        V_C is the voltage across the capacitor

Vs is the voltage supplied

t  is the time passed after supplying voltage.

RC = τ is the time constant of the RC charging circuit

   

 

 

Capacitance Formulas:

The capacitance between two conducting plates with a dielectric between then can be calculated by

 

,

Where

k is the dielectric constant

ε_d is the permittivity of the dielectric

ε_{0 ­­}is the permittivity of space which is equal to 8.854 x 10^-12 F/m

A is the area of the plates

d is the separation between the plates

 

 

Capacitance of a Plate Capacitor Formula-

Where:

C is capacitance in farads

A is the plat area

n is the number of plates

d is the plate separation distance

ε_r is the relative permeability of the substance between the plates

ε_o absolute permittivity

 

 

Ohm’s Law for Capacitor:

                                                                     Q = CV

By differentiating the equation, we get-

where

i is the instantaneous current through the capacitor

C is the capacitance of the capacitor

Dv/dt is the instantaneous rate of change of voltage applied.