Fundamentals of Electric Circuits Lecture 2 Basic circuit elements and concepts.
Electric Circuit - Lecture 04
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Transcript of Electric Circuit - Lecture 04
![Page 1: Electric Circuit - Lecture 04](https://reader038.fdocuments.in/reader038/viewer/2022110119/555e3620d8b42a63048b4947/html5/thumbnails/1.jpg)
Electric Circuit Analysis
Lec4: Nodal analysis
Ahsan [email protected] 102Department of Electrical Engineering
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Steps of Nodal Analysis1. Choose a reference (ground) node.2. Assign node voltages to the other nodes.3. Apply KCL to each node other than the reference
node; express currents in terms of node voltages.4. Solve the resulting system of linear equations for
the nodal voltages.
![Page 3: Electric Circuit - Lecture 04](https://reader038.fdocuments.in/reader038/viewer/2022110119/555e3620d8b42a63048b4947/html5/thumbnails/3.jpg)
Common symbols for indicating a reference node, (a) common ground, (b) ground, (c) chassis.
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1. Reference Node
The reference node is called the ground node where V = 0
+
–
V 500W
500W
1kW
500W
500WI1 I2
![Page 5: Electric Circuit - Lecture 04](https://reader038.fdocuments.in/reader038/viewer/2022110119/555e3620d8b42a63048b4947/html5/thumbnails/5.jpg)
Steps of Nodal Analysis1. Choose a reference (ground) node.2. Assign node voltages to the other nodes.3. Apply KCL to each node other than the reference
node; express currents in terms of node voltages.4. Solve the resulting system of linear equations for
the nodal voltages.
![Page 6: Electric Circuit - Lecture 04](https://reader038.fdocuments.in/reader038/viewer/2022110119/555e3620d8b42a63048b4947/html5/thumbnails/6.jpg)
2. Node Voltages
V1, V2, and V3 are unknowns for which we solve using KCL
500W
500W
1kW
500W
500WI1 I2
1 2 3
V1 V2 V3
![Page 7: Electric Circuit - Lecture 04](https://reader038.fdocuments.in/reader038/viewer/2022110119/555e3620d8b42a63048b4947/html5/thumbnails/7.jpg)
Steps of Nodal Analysis1. Choose a reference (ground) node.2. Assign node voltages to the other nodes.3. Apply KCL to each node other than the reference
node; express currents in terms of node voltages.4. Solve the resulting system of linear equations for
the nodal voltages.
![Page 8: Electric Circuit - Lecture 04](https://reader038.fdocuments.in/reader038/viewer/2022110119/555e3620d8b42a63048b4947/html5/thumbnails/8.jpg)
Currents and Node Voltages
500W
V1
500WV1 V2
50021 VV
5001V
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3. KCL at Node 1
500W
500WI1
V1 V2
500500
1211
VVVI
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3. KCL at Node 2
500W
1kW
500W V2 V3V1
0500k1500
32212
VVVVV
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3. KCL at Node 3
2323
500500I
VVV
500W
500W
I2
V2 V3
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Steps of Nodal Analysis1. Choose a reference (ground) node.2. Assign node voltages to the other nodes.3. Apply KCL to each node other than the reference
node; express currents in terms of node voltages.4. Solve the resulting system of linear equations for
the nodal voltages.
![Page 13: Electric Circuit - Lecture 04](https://reader038.fdocuments.in/reader038/viewer/2022110119/555e3620d8b42a63048b4947/html5/thumbnails/13.jpg)
Typical circuit for nodal analysis
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• Find the node voltages in the circuit shown below.
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• At node 1
2
0
45 121
321
vvv
iii
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• At node 2
6
0
45 212
5142
vvv
iiii
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Practice
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• Determine the voltage at the nodes in Fig. below
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• At node 1,
243
3
2131
1
vvvv
ii x
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• At node 2
4
0
8223221
32
vvvvv
iiix
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• At node 3
2
)(2
84
2
213231
21
vvvvvv
iii x
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• In matrix form:
0
0
3
8
3
8
9
4
38
1
8
7
2
14
1
2
1
4
3
3
2
1
v
v
v
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Spot quiz…
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Example:Use nodal analysis to find the voltage at each node of this circuit.
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• Step 1:Identify and label, each node in the circuit. Ground has been chosen for you.
• Step 2:Write the Nodal equation for each node identified in Step 1. • Node 1:Because the voltage at node 1 is known with respect to our
reference point, the equation is:V1 = 71 volt
• Node 2:At node 2, assume all currents are leaving the node as shown in Figure 5.
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All currents are assumed to be leaving node V2,
so all terms are positive.
Node 2 I (1) + I (2) + I (3) = 0
Ohm's Law I (1) = (V2 - V1)/2
I (2) = (V2 – 0)/11
I (3) = (V2 - V3)/10
Substituting: (V2 - V1)/2 + V2/11 + (V2 - V3)/10 = 0
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• I (4) and I (5) are assumed to be leaving node V3, so these terms are positive. But Is (the 2A source) is entering, so it is assigned a negative sign.
Node 3 -Is + I (4) + I (5) = 0
Ohm's Law I (4) = (V3 - V2)/10
I (5) = V3/5
Substituting:-2 + (V3 - V2)/10 + V3/5 = 0
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• The three equations are shown below:
Node 1: V1 = 71v
Node 2 : (V2 - V1)/2 + V2/11 + (V2 - V3)/10 = 0
Node 3: -2 + (V3 - V2)/10 + V3/5 = 0
• After solving we find that the node voltages are:
V1 = 71v
V2 = 55v
V3 = 25v
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Example:Use nodal analysis to find the voltage at each node of this circuit.