Analysis of AC electrical circuits

1. Sinusoidal Steady-State
Analysis
1
Unit – 3

2. Steps to Analyze AC Circuits:
1. Transform the circuit to the phasor or frequency
domain.
2. Solve the problem using circuit techniques (nodal
analysis, mesh analysis, superposition, etc.).
3. Transform the resulting phasor to the time domain.
2
Time to Freq
Solve variables in
Freq
Freq to Time

3. Impedances of the following passive elements
Resistor
Inductor
Capacitor
R
ZR 
L
j
ZL 

C
j
C
j
ZC





1
3

4. Admittance
-is the ratio of phasor current to phasor voltage
V
I
Y 
Z
Y
1

jX
R
Z
jB
G
Y





1
1
G(conductance)= is the real part of the admittance
B(susceptance)= is the imaginary part of the admittance
4

5. Problem 1:
By Mesh Analysis, find the current I2 in Figure 1.
Figure 1
5

6. Problem 2:
Find I1 and I2 by Mesh Analysis.

6 0 A

12 0 V

I1
I2
AC AC

j1
-j1
+ +
- -
6

7. Nodal Analysis
7

8. Problem 3:
Determine the voltages 𝑉1 and 𝑉2 for the circuit in figure, using Nodal analysis
8

9. Problem 4:
By nodal analysis, calculate the current I2 and voltage V1.
9
2 Ω j2 Ω
- j4 Ω

10. Superposition theorem:
The superposition theorem states that the response in a circuit with
multiple sources is given by algebraic sum of responses due to individual
sources acting alone.
Thevenin’s theorem:
It states that a circuit with two terminals can be replaced by an
equivalent circuit consisting of a voltage source in series with an impedance.
Norton’s theorem:
It states that a circuit with two terminals can be replaced by an
equivalent circuit consisting of a current source in parallel with an impedance.
Network Theorems
10

11. Problem 5:
Using the superposition principle, find ix in the circuit of Fig.
11

12. Problem 6:
Using the superposition theorem, determine the voltage for the circuit of
Figure.
12

13. Circuit with
sources and
impedance
s
A
B
ZL
A
B
Zth
ZL
Vth
+
-
+
-
A
B
ZL
Zth
Is
Thevenin’s equivalent
Norton’s equivalent
Original Circuit
13

14. Procedure:
1. Remove that portion of the network across which the Thévenin equivalent
circuit is to be found.
2. Mark (О, ●, and so on) the terminals of the remaining two-terminal
network.
3. Calculate ZTh by first setting all voltage and current sources to zero (short
circuit and open circuit, respectively) and then finding the resulting
impedance between the two marked terminals.
4. Calculate VTh by first replacing the voltage and current sources and then
finding the open-circuit voltage between the marked terminals.
5. Draw the Thévenin equivalent circuit with the portion of the circuit
previously removed replaced between the terminals of the Thévenin
equivalent circuit.
14

15. 15
Problem 7:
The sinusoidal voltage source in the circuit in figure is 247.49 cos 1000𝑡 + 45° 𝑉.
Determine the following:
a) the Thevenin voltage with respect to the terminals a,b.
b) The Thevenin’s impedance with respect to the terminals a, b
c) Draw the Thevenin equivalent circuit.

16. 16
Problem 8:
For the circuit in figure .Determine the following:
a) the Thevenin voltage (𝑣𝑡ℎ) with respect to the terminals a,b.
b) The Thevenin’s impedance(𝑍𝑡ℎ ) with respect to the terminals a, b
c) Draw the Thevenin equivalent circuit.

17. 17
Problem 9:
Use source transformation, find the vo voltage for the circuit given below.

18. 18
Problem 10:
For the circuit in figure, 𝑣𝑠1 = 8 cos 4𝑡 − 9° 𝑉 and 𝑣𝑠2 = 5 cos 4𝑡 𝑉. Using
a series of source transformations reduce the given circuit into a single
voltage source and determine the current 𝑖 𝑡 .