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Formula and Equations For Capacitor and Capacitance

Capacitor and Capacitance Formulas and Equations

The following formulas and equations can be used to calculate the capacitance and related quantities of different shapes of capacitors as follow.

Capacitor and Capacitance Formulas and Equations

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. Capacitive reactance is calculated using:

capacitive reactance

Where

  • Xis 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 = XC/ESR

Where

  • Xis 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/XC

Where

  • DF is the dissipation factor
  • δ is the angle between capacitive reactance victor & negative axis.
  • Xis the capacitive reactance
  • ESR is the equivalent series resistance of the circuit.

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Energy Stored in a Capacitor:

The Energy E stored in a capacitor is given by:

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:

Pav = 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:

Capacitor charging

During Discharging:

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

Capacitor discharging

Where

  • VC 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

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Capacitance Formulas

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

Wheredielectric constant

  • k is the dielectric constant
  • εis the permittivity of the dielectric
  • ε0 ­­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

Capacitance of a Plate Capacitor

Where:

  • C is capacitance in farads
  • A is the plat area
  • n is the number of plates
  • d is the plate separation distance
  • εr is the relative permeability of the substance between the plates
  • εo absolute permittivity

Self Capacitance of a Coil (Medhurst Formula)

C2 ≈ (0.256479 h2 + 1.57292 r2) pF

Where:

  • h2 and r2 in inches

Self Capacitance of a Sphere Formula

C2b ≈ 4πεor

Where:

  • r is the radius of sphere

Self Capacitance of a Toroid Inductor Formula

Self Capacitance of a Toroid InductorWhere:

  • r is the small radius
  • R is the large radius

Ohm’s Law for Capacitor:

Q = CV

By differentiating the equation, we get:Ohm’s Law for capacitor

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.

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