Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22...
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Transcript of Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22...
![Page 1: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/1.jpg)
Chapter 15 – Series & Parallel ac Circuits
Chapter 16 – Series–Parallel ac Networks
Lecture 22
by Moeen Ghiyas
19/04/23 1
![Page 2: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/2.jpg)
Chapter 15 – Series & Parallel ac Circuits
![Page 3: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/3.jpg)
Chapter 15 - Series & Parallel ac Circuits
Equivalent Circuits
Chapter 16 - Series-Parallel ac Networks
Reduction Methods
Ladder Networks
Assignment # 4 - Submission by 10:30 am 23 Apr
19/04/23 3
![Page 4: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/4.jpg)
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.
![Page 5: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/5.jpg)
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
![Page 6: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/6.jpg)
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
![Page 7: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/7.jpg)
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
![Page 8: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/8.jpg)
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.
![Page 9: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/9.jpg)
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
![Page 10: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/10.jpg)
Determine YT.
![Page 11: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/11.jpg)
Determine YT. - Network is redrawn with phasor notation
![Page 12: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/12.jpg)
Determine YT. - The admittance Y is
![Page 13: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/13.jpg)
Sketch the admittance
diagram.
![Page 14: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/14.jpg)
Find E and IL.
![Page 15: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/15.jpg)
Compute the power factor of the network and the power delivered.
![Page 16: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/16.jpg)
Determine the equivalent series circuit as far as the terminal
characteristics of the network are concerned.
![Page 17: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/17.jpg)
Determine the equivalent series circuit as far as the terminal
characteristics of the network are concerned.
![Page 18: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/18.jpg)
Determine the equivalent parallel network from the equivalent
series circuit, and calculate the total admittance YT
![Page 19: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/19.jpg)
Determine YT for the equivalent parallel circuit.
![Page 20: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/20.jpg)
Chapter 16 – Series–Parallel ac Networks
![Page 21: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/21.jpg)
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
![Page 22: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/22.jpg)
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
![Page 23: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/23.jpg)
Now we know Z1 = 5Ω /53.130
and Z2 = 10Ω / -36.870
Determine ZT
Calculate I or IS
![Page 24: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/24.jpg)
Now we know Z1 = 5Ω /53.130
and Z2 = 10Ω / -36.870
and IS = 22.36 A /-26.560
Determine branch currents using ohms law
![Page 25: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/25.jpg)
Now I1 and I2 known
Working backwards to original cct
![Page 26: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/26.jpg)
To find Vab apply KVL,
![Page 27: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/27.jpg)
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.
![Page 28: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/28.jpg)
EXAMPLE - For the network of Fig
Redrawing the circuit reveals a parallel circuit
![Page 29: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/29.jpg)
Calculate Impedances to determine currents
![Page 30: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/30.jpg)
The total admittance is
The current I becomes
![Page 31: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/31.jpg)
Since the voltage is same across parallel branches
![Page 32: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/32.jpg)
c. Verify by KCL
d. Find the total impedance of the circuit
![Page 33: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/33.jpg)
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.
![Page 34: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/34.jpg)
Determining impedances and then working backwards calculating
currents to finally know the current I6 as desired.
![Page 35: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/35.jpg)
Ch 15 - Q. 17, 23, 31
Ch 16 - Q. 11, 13
Submission by 09:00 am 23 Apr 2012
19/04/23 35
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Chapter 15 - Series & Parallel ac Circuits
Equivalent Circuits
Chapter 16 - Series-Parallel ac Networks
Reduction Methods
Ladder Networks
Assignment # 4 - Submission by 10:30 am 23 Apr
![Page 37: Chapter 15 – Series & Parallel ac Circuits Chapter 16 – Series–Parallel ac Networks Lecture 22 by Moeen Ghiyas 21/08/2015 1.](https://reader033.fdocuments.net/reader033/viewer/2022061404/56649dd15503460f94ac7513/html5/thumbnails/37.jpg)
19/04/23 37