# 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:

**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:

#### Answer

**b)** Determine the reactive power of the inductor.