Capacitance in Terms of Current and Time Varying Voltage

A capacitance matrix can also represent the relationship between currents and time varying voltages in a system of conductors. Given the three transmission lines shown below, the currents caused by the time varying voltage source on each line are given by the following equation:

If dV₂ / dt and dV₃ / dt are set to zero, this relationship becomes the following:

This gives the currents that are induced on Line 2 and Line 3 when a time varying voltage source is applied to Line 1 – that is, the capacitive coupling between the three lines, or the short circuit capacitance.

The capacitance matrix can be exported to a circuit/system simulator, such as Twin Builder, where it can be used in a transient simulation.