1. ELECTRIC CIRCUIT ANALYSIS - I
Chapter 15 – Series & Parallel ac Circuits
Chapter 16 – Series–Parallel ac Networks
Lecture 22
by Moeen Ghiyas
20/04/2017

2. Chapter 15 – Series & Parallel ac Circuits
TODAY’S lesson – Part I

3. Today’s Lesson Contents
Chapter 15 - Series & Parallel ac Circuits
Equivalent Circuits
Chapter Series-Parallel ac Networks
Reduction Methods
Ladder Networks
Assignment # 4 - Submission by 10:30 am 23 Apr
20/04/2017

4. EQUIVALENT CIRCUITS
The term equivalent refers only to the fact that for the same applied potential, the same impedance and input current will result (in the equivalent circuit).
Whether a series or parallel ac circuit, the total impedance of two or more elements in series is often equivalent to an impedance that can be achieved with fewer elements of different values
However, the equivalent elements and their values are determined by the frequency applied.

5. EQUIVALENT CIRCUITS For example, for circuit of fig
The total impedance at the frequency applied is equivalent to a capacitor with a reactance of 10Ω , as shown

6. EQUIVALENT CIRCUITS
Always keep in mind that this equivalence is true only at the applied frequency. If the frequency changes, the reactance of each element changes, and the equivalent circuit will change — perhaps from capacitive to inductive in the above example

7. EQUIVALENT CIRCUITS Another interesting example,
which is the impedance of a series circuit with a resistor of 1.92Ω and an inductive reactance of 1.44Ω , as shown

8. EQUIVALENT CIRCUITS
Current I will be same in equivalent circuit for same input voltage E
For a parallel circuit of one resistive element and one reactive element, the series circuit with the same input impedance will always be composed of one resistive and one reactive element.
The impedance of each element of the series circuit will be different from that of the parallel circuit, but the reactive elements will always be of the same type; i.e., an R-L circuit and an R-C parallel circuit will have an equivalent R-L and R-C series circuit respectively
The same is true when converting from a series to a parallel circuit.

9. EQUIVALENT CIRCUITS
The equivalent series circuit for a resistor and reactance in parallel can be found by determining total impedance in rectangular form;
The equivalent parallel circuit for a resistor and reactance in series can be found by determining total admittance in rectangular form;
See proof in book

10. EXAMPLE - For the network of Fig
Determine YT.

11. EXAMPLE - For the network of Fig
Determine YT. - Network is redrawn with phasor notation

12. EXAMPLE - For the network of Fig
Determine YT. - The admittance Y is

13. EXAMPLE - For the network of Fig
Sketch the admittance diagram.

14. EXAMPLE - For the network of Fig
Find E and IL.

15. EXAMPLE - For the network of Fig
Compute the power factor of the network and the power delivered.

16. EXAMPLE - For the network of Fig
Determine the equivalent series circuit as far as the terminal characteristics of the network are concerned.

17. EXAMPLE - For the network of Fig
Determine the equivalent series circuit as far as the terminal characteristics of the network are concerned.

18. EXAMPLE - For the network of Fig
Determine the equivalent parallel network from the equivalent series circuit, and calculate the total admittance YT

19. EXAMPLE - For the network of Fig
Determine YT for the equivalent parallel circuit.

20. TODAY’S lesson – Part II
Chapter 16 – Series–Parallel ac Networks
TODAY’S lesson – Part II

21. Series-Parallel ac Networks - Approach
Reduce the network to the fundamental structure preferably towards source to determine the total impedance of the network and redraw network by combining series and parallel elements.
The source current and voltages can then be determined.
Later work back (Expand) from the source through the network to find specific quantities.
When you have arrived at a solution, check to see that it is reasonable by considering the magnitudes. If not, either solve the network using another approach, or check over your work very carefully

22. Series-Parallel ac Networks - Approach
EXAMPLE - For Fig :
a. Calculate the current Is
b. Find the voltage Vab
Solution
Simplify the circuit and redraw
In this case the voltage Vab is lost in the redrawn network, which will be worked backwards later

23. Series-Parallel ac Networks - Approach
Now we know Z1 = 5Ω /53.130
and Z2 = 10Ω /
Determine ZT
Calculate I or IS

24. Series-Parallel ac Networks - Approach
Now we know Z1 = 5Ω /53.130
and Z2 = 10Ω /
and IS = A /
Determine branch currents using ohms law

25. Series-Parallel ac Networks - Approach
Now I1 and I2 known
Working backwards to original cct

26. Series-Parallel ac Networks - Approach
To find Vab apply KVL,

27. Series-Parallel ac Networks - Approach
EXAMPLE - For the network of Fig
a. Compute I.
b. Find I1, I2, and I3.
c. Verify KCL by showing that I = I1 + I2 + I3
d. Find the total impedance of the circuit.

28. Series-Parallel ac Networks - Approach
EXAMPLE - For the network of Fig
Redrawing the circuit reveals a parallel circuit

29. Series-Parallel ac Networks - Approach
Calculate Impedances to determine currents

30. Series-Parallel ac Networks - Approach
The total admittance is
The current I becomes

31. Series-Parallel ac Networks - Approach
Since the voltage is same across parallel branches

32. Series-Parallel ac Networks - Approach
c. Verify by KCL
d. Find the total impedance of the circuit

33. LADDER NETWORKS
A general sinusoidal ac ladder network is as shown. The current I6 is desired.
ac ladder network with ZT, ZT’, ZT” and currents I, I3 defined.

34. LADDER NETWORKS
Determining impedances and then working backwards calculating currents to finally know the current I6 as desired.

35. Assignment # 4
Ch 15 - Q. 17, 23, 31
Ch 16 - Q. 11, 13
Submission by 09:00 am 23 Apr 2012
20/04/2017

36. Summary / Conclusion Chapter 15 - Series & Parallel ac Circuits
Equivalent Circuits
Chapter Series-Parallel ac Networks
Reduction Methods
Ladder Networks
Assignment # 4 - Submission by 10:30 am 23 Apr

37. 20/04/2017