Basic Electronics and Electrical Engineering:
ECE 249
UNIT 2: Fundamentals of A.C.
Circuits
Lecture No.: 14
Topic: Resonance, Three Phase
Circuits, Star-Delta Connections,
Line and Phase
Delivered By: Dr. Irfan Ahmad Pindoo
Assistant Professor
VLSI Design, ECE
Division of Research and Development
Intellectual Property Rights Cell
Resonance in Series RLC Circuits
The point of intersection where the inductive and capacitive reactance
becomes equal i.e, 𝑋𝐿 = 𝑋𝐶
and the frequency at which these two reactances become equal, is called
resonant frequency 𝑓𝑟 .
Delivered by: Dr. Irfan Ahmad Pindoo
2
Quick Quiz
Determine the resonant frequency (kHz) for the circuit shown below
A. 2.25
B. 22.5
C. 225
D. 2250
Delivered by: Dr. Irfan Ahmad Pindoo
3
Quick Quiz
An inductor with a reactance of 120 Ω, a capacitor with a reactance of
120 Ω and a 24 Ω resistor are in series across a 60 V source. The circuit
is at resonance. The voltage across the inductor is
A. 60 V
B. 660 V
C. 30 V
D. 300 V
Delivered by: Dr. Irfan Ahmad Pindoo
4
Quality Factor
• The sharpness of the peak is measured quantitatively and is called the
Quality factor, Q of the circuit.
• The Q, or quality, factor of a resonant circuit is a measure of the
“goodness” or quality of a resonant circuit. A higher value for this
figure of merit corresponds to a more narrow bandwidth, which is
desirable in many applications. More formally, Q is the ratio of power
stored to power dissipated in the circuit reactance and resistance,
respectively:
• Mathematically,
𝑃𝑜𝑤𝑒𝑟 𝑆𝑡𝑜𝑟𝑒𝑑
𝐼2 𝑋 𝑋
𝑄=
= 2 =
𝑃𝑜𝑤𝑒𝑟 𝐷𝑖𝑠𝑠𝑝𝑎𝑡𝑒𝑑 𝐼 𝑅 𝑅
Therefore, 𝑄 =
𝐿𝜔
𝑅
=
1
𝜔𝑅𝐶
=
1
𝑅
𝐿
𝑓𝑟
=
𝐶Delivered𝐵𝑊
by: Dr. Irfan Ahmad Pindoo
5
THREE PHASE CIRCUITS
Delivered by: Dr. Irfan Ahmad Pindoo
6
Three Phase Circuits
Delivered by: Dr. Irfan Ahmad Pindoo
7
Three Phase Circuits
Why?
1. Requires lesser number of conductors
2. Power in a single phase circuit is pulsating, while as the
power in the three phase circuit remains constant.
3. Due to the constant power, a uniform torque is generated in
three phase motors.
4. Provides higher output voltage as compared to a 1-Phase.
5. Serves the purpose of domestic as well as industrial use.
6. Better Voltage Regulation.
Delivered by: Dr. Irfan Ahmad Pindoo
8
Three Phase Voltages
• Has three single phase emfs with same amplitude and frequency but
phase displaced by 120.
• Considering Ea as the reference voltage, then (rotating anticlockwise)
phase b lags phase a by 120 and phase c lags phase b by 120.
Delivered by: Dr. Irfan Ahmad Pindoo
9
Types of Load
1. Star Connection
2. Delta Connection
𝑖𝑓 𝑍1 = 𝑍2 = 𝑍3 , then the load is said to be BALANCED.
Delivered by: Dr. Irfan Ahmad Pindoo
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