Resistance, Reactance and Impedance

When considering voltages, currents and powers in  AC circuits we need to take into account other issues including inductance, capacitance as well as resistance. Different loads have different characteristics.


The effect that capacitive and inductive loads have on an AC circuit is that they cause a shift in phase between the voltage and currents of a circuit. These loads posses a quality called reactance, this is the opposition to current flow that a component like a capacitor or inductor have. Loads with capacitive or inductive loads are called reactive loads.

A motor is an inductive load

A power factor correction capacitor

A filament lamp is a resistive load

Resistive Loads

In a circuit with a resistive load the voltage and the current are in phase and the current can be calculated by using the Ohm’s law formula:

Inductive Loads

In a circuit with an inductive load (such as an induction motor) the voltage and currents are out of phase. The current is said to be lagging the supply voltage.


The opposition to current flow in this case is called inductive reactance (XL) and is measured in Ohms. It depends upon the supply frequency and the inductance of the inductive load (measured in Henrys).


The ‘R’ in Ohm’s law can be replaced with XL in the Ohm’s law triangle:

Capacitive loads

In a capacitive load the voltage and currents are also out of phase. In this case the current leads the voltage.


The opposition to current flow in this case is called capacitive reactance (XC) and is also measured in Ohms. It depends upon the supply frequency and the capacitance (measured in Farads).


The ‘R’ in Ohm’s law can be replaced with XC in the Ohm’s law triangle:

Impedance

Some loads posses a combination of resistive and reactive elements. The total opposition to current flow caused by these elements is called the impedance (Z) which is measured in Ohms. Because we are dealing with out of phase currents we can use an impedance triangle to calculate the impedance.

Resistance (R)

Reactance (XL)

Impedance (Z)

Impedance triangles

Calculate:

1. Inductive reactance

2. Impedance

  1. 3.Voltage across the two component

4. The total current


Knowing that:

Resistance = 10 Ohms

Inductance = 0.1 Henry

Supply voltage = 230V

Supply frequency = 50 Hertz

XL = 31.41 Ohms

R = 10 Ohms

Z = 32.96 Ohms

Example: