TOPIC 3 - RESONANCE

DET20033-ELECTRICAL
CIRCUITS

TOPIC 3: RESONANCE

Understand resonance in series and parallel circuits [CLO1]

Resonance

Reference : CHAPTER 15

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

RESONANCE PHENOMENON

Condition in a series RLC circuit in which the capacitive and
inductive reactance are equal in magnitude

SERIES RESONANT

For an R–L–C series circuit, when XL = XC , the applied voltage V and the
current I are in phase. This effect is called series resonance. At resonance:

(i) VL =VC
(ii) Z =R (i.e. the minimum circuit impedance possible in an L–C–R circuit)
(iii) I =V/R (i.e. the maximum current possible in an L–C–R circuit)

SERIES RESONANT

(iv) Since XL =XC, then 2πfrL =1/2πfrC from which,

*Series resonant circuit is often described as an acceptor
circuit since it has its minimum impedance, and thus
maximum current, at the resonant frequency.

SERIES RESONANT FREQUENCY

GRAPH IMPEDANCE vs FREQUENCY
(SERIES RESONANCE)

Exercise

(XC=500 Ω, Zr=100<0°)

Exercise

(fr = 328kHz)
If C = 0.01 uF in Figure 17-12, what is the resonant frequency? (fr = 22.5KHz)
Explain the difference base on graph impedance vs frequency

Exercise

Problem 1.

A coil having a resistance of 10 and an inductance of
125mH is connected in series with a 60 μF capacitor
across a 120V supply. At what frequency does resonance
occur? Find the current flowing at the resonant frequency.
(fr=58.12Hz, I=12A)

Problem 2.

The current at resonance in a series L–C–R circuit is 100 μA.
If the applied voltage is 2mV at a frequency of 200 kHz, and
the Circuit inductance is 50 μH, find
(a) the circuit resistance, (20ohm)
(b) the circuit capacitance. (C=12.7nF)

DET20033-ELECTRICAL CIRCUITS
TOPIC 3: RESONANCE

Q FACTOR

Understand resonance in series and parallel circuits [CLO1]

Reference : CHAPTER 15

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

by
TS ZULKIFLI & TS SHALIZAN/JKE/PKK/2018

Q-FACTOR

• Ratio of measuring the quality of a circuit (V magnification)

OR , Q is ratio of power stored to power dissipated in the circuit reactance and
resistance

• If R compared to XL and Xc so VL and Vc is than Vs

Problem 1. Exercise

A coil of inductance 80mH and negligible resistance

is connected in series with a capacitance of 0.25 μF

and a resistor of resistance 12.5Ω across a 100V,

variable frequency supply. Determine

(a)the resonant frequency (fr=1125.4Hz)

(b)The current at resonance. (I=8A)

(c) How many times greater than the supply voltage is

the voltage across the reactance’s at resonance?
(Q=45.25)

Exercise

Problem 2.

A series circuit comprises a coil of resistance
2Ω and inductance 60 mH, and a 30 μF
capacitor. Determine the Q-factor of the
circuit at resonance. (Q=22.37)

Exercise

Problem 3.

What is the Q factor a series circuit that
resonates at 6kHz, has equal reactance 4kΩ
each and resistance is 50Ω (Q=80)

DET20033-ELECTRICAL CIRCUITS
TOPIC 3: RESONANCE

PARALLEL RESONANCE

Understand resonance in series and parallel circuits [CLO1]

Reference : CHAPTER 16

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

by
TS ZULKIFLI & TS SHALIZAN/JKE/PKK/2018

Parallel Resonance

• Resonance occurs in the two branch network containing
capacitance C in parallel with inductance L and resistance R
in series (see Fig.) when the quadrature (i.e. vertical)
component of current ILR is equal to IC. *IC = ILR Sin ϴ.

• At this condition the supply current I is in-phase with the
supply voltage V.

Parallel Frequency
Resonance

GRAPH IMPEDANCE vs FREQUENCY
(PARALLEL RESONANCE)

Current at Resonance

** I min at resonance

Dynamic resistance

• Since the current at resonance is in-phase with the
voltage the impedance of the circuit acts as a
resistance.

• This resistance is known as the dynamic resistance,
RD (or sometimes, the dynamic impedance).

Q Factor

The Q-factor
of a parallel resonant circuit is

the ratio of the current
circulating in the parallel
branches of the circuit to the
supply current, i.e. the current

magnification.

PARALLEL RESONANCE

• Rejector circuit

• The parallel resonant circuit is often described as a rejector
circuit since it presents its maximum impedance at the resonant
frequency and the resultant current is a minimum.

• Note that in a parallel circuit the Q-factor is a measure of current
magnification, whereas in a series circuit it is a measure of
voltage magnification.

Problem 1. Exercise

A pure inductance of 150mH is connected in
parallel

with a 40 μF capacitor across a 50V, variable

frequency supply. Determine

(a) The resonant frequency of the circuit.
(fr=64.97Hz)

(b) the current circulating in the capacitor and
inductance at

resonance.(I=0.816A)

Problem 2. Exercise

A coil of inductance 0.20H and resistance 60 is

connected in parallel with a 20 μF capacitor
across

a 20V, variable frequency supply. Calculate

(a) the resonant frequency.(fr=63.66Hz)

(b) the dynamic resistance.(Rd=166.7Ω)

(c) the current at resonance
resonance.(I=0.12A)

(d) the circuit Q-factor at resonance.(Q=1.33)

DET20033-ELECTRICAL CIRCUITS
TOPIC 3: RESONANCE

BANDWIDTH AND SELECTIVITY

Understand resonance in series and parallel circuits [CLO1]

Reference : CHAPTER 15

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

by
TS ZULKIFLI & TS SHALIZAN/JKE/PKK/2018

BANDWIDTH AND SELECTIVITY

A, B : Half power points

Bandwidth, BW = f2-f1

Q , BW = more selective
Q , BW = less selective

• Advantages in communication
• Disadvantages in power circuit

BANDWIDTH AND SELECTIVITY

• Selectivity is the ability of a circuit to respond more readily to signals of

a particular frequency to which it is tuned than to signals of other
frequencies. The response becomes progressively weaker as the
frequency departs from the resonant frequency.

• The higher the Q-factor, the narrower the bandwidth and the more

selective is the circuit. Circuits having high Q-factors (say, in the order
of 100 to 300) are therefore useful in communications engineering.

• A high Q-factor in a series power circuit has disadvantages in that it

can lead to dangerously high voltages across the insulation and may
result in electrical breakdown.

Q , BW = more selective
Q , BW = less selective

Problem 1. Exercise

A filter in the form of a series L–R–C circuit is designed to

operate at a resonant frequency of 5 kHz. Included within the

filter is a 20mH inductance and 10 resistance. Determine the

bandwidth of the filter. (BW=79.6Hz)

Problem 2.
A resonant circuit has a lower critical frequency of 8 kHz and
an upper critical frequency of 12 kHz Determine the

bandwidth and center (resonant) frequency.
(BW=4kHz, fr=10kHz)

Exercise

Problem 3.

What is the BW of the below circuit ? (BW=7.95kHz)

TUTORIAL 3• A coil of resistance 25 and inductance 100mH is connected in
series with a capacitance of 0.12 μF across a 200V, variable
frequency supply. Calculate (a) the resonant frequency, (b)
the current at resonance and (c) the factor by which the
voltage across the reactance is greater than the supply
voltage.

[(a) 1.453 kHz (b) 8A (c) 36.51]

• Calculate the inductance which must be connected in series
with a 1000 pF capacitor to give a resonant frequency of 400
kHz.

[0.158 mH]

• A series circuit comprises a coil of resistance 20and
inductance 2mHand a 500 pF capacitor. Determine the Q-
factor of the circuit at resonance. If the supply voltage is 1.5V,
what is the voltage across the capacitor?

[100, 150V]

TUTORIAL 3

• A coil of resistance 25 and inductance 150mH is

connected in parallel with a 10 Μf capacitor across a
60V, variable frequency supply. Calculate (a) the
resonant frequency, (b) the dynamic resistance, (c)
the current at resonance and (d) the Q-factor at
resonance.
[(a) 127.2 Hz (b) 600 (c) 0.10A (d) 4.80]

• A coil of resistance 1.5 k and 0.25H inductance is

connected in parallel with a variable capacitance
across a 10V, 8 kHz supply. Calculate (a) the
capacitance of the capacitor when the supply
current is a minimum, (b) the dynamic resistance, and
(c) the supply current.
[(a) 1561 pF (b) 106.8 k (c) 93.66 μA]