Editing Electrical reactance (section)

=== Phase relationship ===

The phase of the voltage across a purely reactive device (i.e. with zero [[Parasitic element (electrical networks)|parasitic resistance]]) ''lags'' the current by <math>\tfrac{\pi}{2}</math> radians for a capacitive reactance and ''leads'' the current by <math>\tfrac{\pi}{2}</math> radians for an inductive reactance. Without knowledge of both the resistance and reactance the relationship between voltage and current cannot be determined.

The origin of the different signs for capacitive and inductive reactance is the phase factor <math>e^{\pm \mathbf{j}{\frac{\pi}{2}}}</math> in the impedance.

:<math>\begin{align}
  \mathbf{Z}_C &= {1 \over \omega C}e^{-\mathbf{j}{\pi \over 2}} = \mathbf{j}\left({ -\frac{1}{\omega C}}\right) = \mathbf{j}X_C \\
  \mathbf{Z}_L &= \omega Le^{\mathbf{j}{\pi \over 2}} = \mathbf{j}\omega L = \mathbf{j}X_L\quad
\end{align}</math>

For a reactive component the sinusoidal voltage across the component is in quadrature (a <math>\tfrac{\pi}{2}</math> phase difference) with the sinusoidal current through the component. The component alternately absorbs energy from the circuit and then returns energy to the circuit, thus a pure reactance does not dissipate power.