MathML formula | Formula Image | Straight text formula |
---|---|---|

${X}_{c}=\frac{1}{2\pi fC}$ | X_{c} = 1 / (2πfC) |

Where:

X_{c} = capacitive reactance, Ohms

f = frequency, Hertz

C = capacitance, Farads

Reactance, X_{C} =

## Capacitors - Complex Impedance

When working with circuits that contain combinations of ideal capacitances, inductances and resistance, it is more correct to deal with capacitance in terms of a "complex impedance". In this form, components have a combination of a "real" resistance part, and an "imaginary" reactance part. The pure capacitor, of course, has a zero real part (it doesn't have resistance) but a negative imaginary part.

MathML formula | Formula Image | Straight text formula |
---|---|---|

${X}_{c}=\frac{\mathrm{-j}}{\omega C}=\frac{\mathrm{-j}}{2\pi fC}$ | X_{c} = -j / (ωC) = -j / (2πfC) |

Where:

j = √-1

X_{c} = capacitive reactance, Ohms

ω = angular frequency, radians per second

f = frequency, Hertz

C = capacitance, Farads

Note that the above expression can also be modified by multiplying above and below by j to give:

MathML formula | Formula Image | Straight text formula |
---|---|---|

${X}_{c}=\frac{1}{j\omega C}=\frac{1}{j2\pi fC}$ | X_{c} = 1 / (jωC) = 1 / (j2πfC) |