# Capacitor Equations

### - key equations and calculations for capacitors and capacitance in electronics circuits including reactance, charge, value, etc.

### In this section

There are many calculations and equations associated with capacitors. The capacitor reactance equations and calculations are common, but there are many more capacitor calculations that may need to be performed.

Capacitor equations and capacitor calculations include many aspects of capacitor operation including the capacitor charge, capacitor voltage capacitor reactance calculations and many more.

## Basic capacitance formulae

The very basic capacitor equations link the capacitance with the charge held on the capacitor, and the voltage across the plates.

where

C is the capacitance in Farads

Q is the charge held on the plates in coulombs

V is the potential difference across the plates in volts

This equation can then be developed to calculate the work required for charging a capacitor, and hence the energy stored in it.

## Capacitor reactance

In a direct current circuit where there may be a battery and a resistor, it is the resistor that resists the flow of current in the circuit. This is basic Ohms Law. The same is true for an alternating current circuit with a capacitor. A capacitor with a small plate area will only be able to store a small amount of charge, and this will impede the flow of current. A larger capacitor will allow a greater flow of current. A capacitor is said to have a certain reactance. This name is chosen to be different to that of a resistor, but it is measured in Ohms just the same. The reactance of a capacitor is dependent upon the value of the capacitor and also the frequency of operation. The higher the frequency the smaller the reactance.

The actual reactance can be calculated from the formula:

where

Xc is the capacitive reactance in ohms

f is the frequency in Hertz

C is the capacitance in Farads

## Current calculations

The reactance of the capacitor that is calculated from the formula above is measured in Ohms. The current flowing in the circuit can then be calculated in the normal way using Ohms Law:

## Adding resistance and reactance

Although resistance and reactance are very similar, and the values of both are measured in Ohms, they are not exactly the same. As a result it is not possible to add them together directly. Instead they have to be summed "vectorially". In other words it is necessary to square each value, and then add these together and take the square root of this figure. Put in a more mathematical format:

where

Xtot is the total impedance in ohms

Xc is the capacitive reactance in ohms

R is the DC resistance in ohms

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