# 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.

**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:

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**is the capacitive reactance_{C }**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.

Related Posts:

- Capacitance and Inductance from Reactance Calculator
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**Energy Stored in a Capacitor:**

The Energy E stored in a capacitor is given by:

**E = ½ CV ^{2}**

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}** = CV ^{2} / 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

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**Capacitance Formulas**

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

- 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

**Self Capacitance of a Coil (Medhurst Formula)**

**C _{2} ≈ (0.256479 h_{2} + 1.57292 r_{2}) pF**

Where:

- h
_{2}and r_{2}in inches

**Self Capacitance of a Sphere Formula**

**C _{2b} ≈ 4πε_{o}r**

Where:

- r is the radius of sphere

**Self Capacitance of a Toroid Inductor Formula**

- r is the small radius
- R is the large radius

**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.

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