# What is Reactive Power?

Reactive Power is how we describe the power contained within energy storage elements which are capacitors and inductors.

This differs to the power dissipated by resistors which is converted into heat whereas a capacitor stores energy in an electric field and inductor stores energy in a magnetic field. This power dissipated by resistors is commonly referred to as true power.

Similar to the concept of impedance we can elegantly express both types of powers in a single expression via complex number notation where the real part denotes True Power and the imaginary part is the Reactive Power, i.e.

Where P is the Real Power, Q (W-Watts) is the Reactive Power (VAR-Volt Amperes Reactive) and S (VA-Volt Amperes) is known as the Apparent Power. This means we can also express this in phasor notation as we have also seen previously for both impedance and AC voltages. So there are many symmetries between these concepts which is always nice for learning (makes things easier).

This is all nicely illustrated with the following triangle:

So as we can see the Real Component is Real Power and the Imaginary Component is Reactive Power with the Resultant Power being known as the Apparent Power.

Note: The formulas we have already learnt relating power to voltage, current and resistance carry over with the only difference being each quantity is now a complex number and resistance becomes impedance. We can then determine the real and imaginary parts of the apparent power to find the real and reactive power.

## Examples

1. a) Determine the reactive power of the capacitor in the circuit below:

We have a simple series circuit involving a resistor and capacitor so it follows that the voltage source will deliver complex power to the circuit and from this the real and reactive power components delivered can be determined which is then dissipated in the resistor and stored in the capacitor respectively. We can then express this back into rectangular coordinates to calculate the imaginary component which represents the reactive power.

b) Determine the power dissipated through the resistor

## Questions

1. a) Determine the power dissipated in the resistor in the circuit below:

2mW

b) Determine the reactive power of the inductor.

38uVAR