Represent the Inductor, L, by its reactance as a vector directed along the positive jy axis as shown by the Blue arrow in the figure below. Represent the capacitor, C, by its reactance as a vector along the negative jy axis, shown in Green.

Rotate the two reactance vectors so that their lengths appear o;ong the x axis.

For the smaller of the two reactances, form a square with each side equal to the value of the reactance.

Capacitor in parallel with an inductor.

Join the end of the larger reactance on the x axis to the corner of the square formed by the smaller reactance with a straight line (yellow in the diagram) and extend this line until it intersects the jy axis. The resultance reactance (red arrow in the diagram) will be the vector from the origin to this point of intersection.

Most elementary electrical engineering texts show the resultant combination of parallel connected reactances as the inverse of the sum of the admittances, which are inverses of the reactances. The parallel combinations are shown as vector sums in the admittance-plane, or Y-Plane, which is the complex inverse of the Z-plane.

An alternative method of visualizing parallel reactances is shown in the figure below. This alternative method uses the geometric "inversion circle" to form the inverse vectors of the reactances and adds them together, then inverts the result using the same inversion circle. It is less accurate because it is more difficult to indentify the points of tangency to a circle than it is to identify the intersections of straight lines as needed in the previous construction.

Alternative Visualization of Parallel Reactances using the "inversion" circle.

The advantage of the visualizations shown here is that both series and parallel combinations can be treated in the same diagram. The value of this is in the synthesis of a.c. circuits which will be shown in subsequent web pages.