1. Resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC). 2. At resonance, the circuit phase angle is 0° and the effective impedance is just the resistance. 3. Very high currents can exist at resonance in AC power systems, so it should be avoided. However, resonance is used in tuned circuits like radio.

1. AC Circuits – Series Resonance
There is also a condition when XL = XC this is known as the ‘resonant condition’
and should be avoided in AC power systems because very large currents can
exist when resonance occurs.
Resonance is common in tuned circuits, eg radio and transmission circuits.
(XL = XC )
Ø = tan-1
(XL – XC )
R
= 0ºI
VR
VL
VC
VL = VC
The frequency at which a circuit becomes resonant is called the resonant
frequency (fo ).
fo =
2π LC
1
Z = R2
+ (XL - XC )2Impedance,
= R

2. AC Circuits – Series Resonance
When resonance occurs in a series network the current is limited by the circuit
resistance only since under this condition XL = XC therefore the circuit
impedance, Z = R.
A series resonant circuit is called an acceptor circuit because the current is at
a maximum at the resonant frequency
(XL = XC )
Resonant Frequency
0
20
40
60
80
100
120
140
35 45 55 65 75 85 95 105 115 125 135
frequency (Hz)
Current(mA)
XL
XC
I

3. AC Circuits – Series Resonance
Activity
1. A capacitor of 47μF is connected in series with an inductance of 50mH
having a resistance of 2 ohms. This combination is then operated from a
240V supply. Determine,
a) the resonant frequency
b) the current flowing at resonance.
c) the current flowing at 90% and 110% resonance.
d) determine the phase angle at the frequencies in part (c) and at resonance
e) state if the circuit is capacitive, inductive or resistive giving reasons.
f) sketch the phasor diagram for all three conditions.

4. Resonance – Summary
• Resonance occurs when XL = XC.
• The frequency at which resonance occurs is called the resonant frequency, fo.
• The circuit phase angle at resonance is 0º.
• The effective impedance at resonance is the dc resistance of the circuit.
• Resonance I power circuits cause very high currents to exist.
• Resonance is used in electronic tuning circuits.

5. AC Circuits – Series Resonance
At resonance the quality factor is given as
Quality Factor
The Q-factor is also known as the circuit magnification factor and is dependant
on the ratio of reactance to the circuit resistance.
Reactance (either XL or XC)
Resistance
Q-factor =
Qo =
C
L1
R
The smaller the circuit resistance the greater the Q-factor.
In radio (tuned) circuits a high Q-factor produces high selectivity enabling fine
tuning.
In power circuits a high Q-factor leads to high currents at the resonant frequency
which in turn produce high voltages across reactive components such as
capacitors and inductors since VC = IXC and VL = IXL

6. AC Circuits – Series Resonance
Quality Factor
Activity
A coil of resistance 5 ohms and inductance 100mH is connected in series with
a capacitor of 2µF to a 50V variable frequency supply.
When the frequency is adjusted to bring the circuit into resonance determine,
a) the Q-factor at resonance,
b) the current at resonance
and
c) the voltages that appear across all three components

7. AC Circuits – Series Resonance
Quality Factor
Activity
A coil of resistance 5 ohms and inductance 100mH is connected in series with
a capacitor of 2µF to a 50V variable frequency supply.
When the frequency is adjusted to bring the circuit into resonance determine,
a) the Q-factor at resonance,
b) the current at resonance
and
c) the voltages that appear across all three components