1. AC Circuits - Reactance
AC circuits usually comprise inductance (motors, transformers or any
component containing a coil) or capacitance or both. In such circuits the
current flowing is dependant on the reactance of the component.
I
V
(AC)
C
I
V
(AC)
L
Reactance is the resistance to current flow in an AC circuit due to the
capacitance and/or inductance present in the circuit and is measured in
ohms.
There are two types of reactance;
Capacitive Reactance XC and Inductive Reactance XL.
Reactance is dependent on the frequency of the current flowing through the
circuit as well as its capacitance/inductance.
I =
V
XL
I =
V
XC

2. AC Circuits - Reactance
Inductive Reactance
XL = 2πfL
where f is the supply frequency in Hertz.
and L is the inductance of the circuit in Henry’s
Capacitive Reactance
where f is the supply frequency in Hertz.
and C is the capacitance of the circuit in Farad’s
In each case the unit of reactance is the Ohm.
AC circuits with purely resistive elements do not have reactance
and can be treated using Ohm’s law.
XC =
1
2πfC

3. AC Circuits - Reactance
Activity
Inductive (XL )
1. Calculate the inductive reactance of a coil having an inductance of 150mH
when connected to a 50Hz. supply. If the supply voltage is 230 V determine
the current flowing.
2. Calculate the inductive reactance and current flowing if the supply frequency
is doubled to 100Hz.
Capacitive (XC )
3. Calculate the capacitive reactance of a 470µF capacitor when connected to a
50Hz. supply. If the supply voltage is 230 V determine the current flowing.
4. Calculate the capacitive reactance and current flowing if the supply
frequency is doubled to 100Hz.

4. AC Circuits – Phase Angle
When an alternating current flows in a circuit containing reactance the current
is no longer in step (phase) with the applied voltage.
In an inductive circuit this is due to the magnetic effects causing opposition to
the current flow.
In capacitive circuits this is due to the electrostatic effects within the dielectric
material.
This effect is known as the circuit ‘phase angle’ and is used to represent the
angle between applied voltage and the current flowing in the circuit.
VC
IC
Current leading voltage
by 90°
(capacitive)
Current lagging voltage
by 90°
(inductive)
VL
IL
IR
VR
Current in step with
voltage
(resistive)

5. AC Circuits – The Phasor Diagram
It is common practice to identify quantities in an electric circuit by use of
vectors (phasor diagrams).
As with force vectors, phasor’s are drawn to scale. The length of the phasor
represents the magnitude of the quantity and the angle represents the
circuit phase angle between the quantities.
i
Pure
Capacitance
v
i
Pure
Resistance
v
In purely resistive circuits the
phase angle is zero.
The current is ‘in-step’ with the
applied emf.
i
Pure
Inductance
v
In purely inductive circuits the
phase angle is 90° ‘lagging’.
The current is behind the
applied emf by 90°
In purely capacitive circuits the
phase angle is 90° ‘leading’.
The current is ahead of the
applied emf by 90°
“CIVIL”

6. AC Circuits - The Phasor Diagram - Resistive Load
It is common practice to identify quantities in an electric circuit by use of
vectors (phasor diagrams).
As with force vectors, phasor’s are drawn to scale. The length of the phasor
represents the magnitude of the quantity and the angle represents the
circuit phase angle between the quantities.
Pure
Resistance
In purely resistive circuits the
phase angle is 0°.
The current is ‘in step’ with the
applied emf.
v
i
-1.5
-1
-0.5
0
0.5
1
1.5
0
40
80
120
160
200
240
280
320
360

7. AC Circuits – The Phasor Diagram – Capacitive Load
It is common practice to identify quantities in an electric circuit by use of
vectors (phasor diagrams).
As with force vectors, phasor’s are drawn to scale. The length of the phasor
represents the magnitude of the quantity and the angle represents the
circuit phase angle between the quantities.
In purely capacitive circuits the
phase angle is 90° ‘leading’.
The current is ahead of the
applied emf by 90°
i
Pure
Capacitance
v
-1.5
-1
-0.5
0
0.5
1
1.5
0
40
80
120
160
200
240
280
320
360
90°

8. AC Circuits – The Phasor Diagram – Inductive Load
It is common practice to identify quantities in an electric circuit by use of
vectors (phasor diagrams).
As with force vectors, phasor’s are drawn to scale. The length of the phasor
represents the magnitude of the quantity and the angle represents the
circuit phase angle between the quantities.
-1.5
-1
-0.5
0
0.5
1
1.5
0
40
80
120
160
200
240
280
320
360
In purely inductive circuits the
phase angle is 90° ‘lagging’.
The current is behind the
applied emf by 90°
Pure
Inductance
i
v
90°

9. AC Circuits – Phasor Diagrams
Activity
1. Draw the phasor diagram for a purely inductive electrical system having a
supply voltage of 50 volts and a current of 20 amps.
2. Draw the phasor diagram for a purely capacitive electrical system having a
supply voltage for 25 volts and a current of 10 amps flowing.
3. Draw the phasor diagram for a purely resistive circuit operating from a
supply voltage of 100 volts with a load resistance of 20 ohms.
In each case sketch the waveforms you would expect from the phasor diagrams
and label the circuit phase angle and amplitude.

10. AC Circuits – What did we learn
• Most AC circuits contain ‘reactance’.
• There are two forms of reactance ‘Inductive (XL )’ and ‘capacitive (XC )’.
• Reactance has units of Ohms.
• Circuits containing pure inductance or pure capacitance cause the current
to be out of phase (phase angle) with the applied emf by 90º.
• Capacitive circuits cause the current to ‘lead’ the voltage.
• Inductive circuits cause the current ‘lag’ the voltage.
• Alternating quantities can be represented by ‘phasor diagrams’.