Trigonometry

# Power and Impedance Triangles

# What is going on here?

This is the point where I am going to ask you to take my hand and to trust me. Okay, you don’t have to take my hand, but you do have to trust me. We are going to start using some terms before totally going into the theory behind them. I promise that we will get more in-depth into these concepts in future lessons.

# Impedance triangles

When dealing with DC circuits the only thing that opposes current is the **resistance** in the circuit.

As we will learn in later units, AC adds a component that opposes current as well. This is called **reactance** and it runs 90 degrees to the circuit resistance. This means it is not possible to add them together arithmetically; it has to be done using the Pythagoras’ theorem. When you add these two together, you get a total opposition to current flow called **impedance**.

The triangle that is created when adding the resistance to the reactance is known as an **impedance triangle**.

In an impedance triangle, the resistance (r) is always on the bottom of the triangle, the reactance (x) always goes on the side and the hypotenuse is always the impedance (z).

# Power triangles

When dealing with a purely resistive circuit, the power being dissipated is in the form of heat or light and is measured in watts and is known as **true or active power**. It is a product of I^{2}R.

In an AC circuit with inductance, watts are still present. There is also a reactive power present as current passes across the reactance. This power is called **reactive power** and is also called **wattless or quadrature power**. Its unit is the Vars.

Much like the impedance triangle, we can not just add the two powers together to get overall power. They must be added using the Pythagoras’ theorem. Their sum is equal to the **apparent power** (VA).

When calculating for reactive power, we are still able to use the power formulas. We just have to use them with reactance instead of resistance.

- I
^{2}X = Vars - E
^{2}(inductor voltage)^{ }/X = Vars - I x E (inductor voltage) = Vars

### Remember

When building an impedance or power triangle, the resistive component always goes on the bottom of the triangle and the reactive component always goes on the side.