Why is reactive component of impedance termed Imaginary?

This question is often in the minds of learners – as to why the reactance or ‘imaginary resistance” of capacitor and inductor is called imaginary? This needs a little clarification. In reality, there is nothing imaginary about it.  The term ‘imaginary’ is a misnomer, which has stuck for a purpose.

In AC circuits, there is a phase difference between current and voltage, depending on values of R, L, and C. In an ideal capacitor or inductor, there is a phase difference of 90° between current and voltage, while this difference is zero in case of resistance. If current passes through a combination of all these components, voltages across them do not add up automatically in simple manner, but it is a combination of vector items across components.

Waveform for voltages and currents for resistance, capacitor and inductor load are as under, along with vector representations of voltages and currents. One may note the vector reference directions of current and voltages in the vector diagrams.

In vector representation, impedance components are shown as follows. These components are added up to get vector sums as resultant overall impedance during calculations. On the vector diagram, horizontal axis represents real terms, while vertical axis shows imaginary (or out of phase) components.

In order to differentiate between these components of currents and voltages, they are divided into in-phase and out-of-phase (differing by 90°) components. Entities across resistance are treated as real (they result in actual (or real) energy consumption. Those across capacitor and inductor do not generate physical (or real) power, and are termed imaginary. This enables these vector quantities to be mathematically treated in same manner as imaginary numbers in calculations.

The component of voltage, current or power associated with capacitors or inductors are very much ‘real’ and are an indivisible part of the electrical circuit parameters. Their mathematical treatment allows us to keep in-phase and out-of-phase components separate and deal with them accordingly for mathematical calculations and analysis. This makes things easy and practical to treat and calculate all quantities – current, voltage or impedance in proper way to get net quantities with phase angle associated with them. It also enables to easily identify resistive, inductive and capacitive components in the circuit.