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# Electric Circuit - Lecture 04

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### Electric Circuit - Lecture 04

1. 1. Electric Circuit Analysis Lec4: Nodal analysis Ahsan Khawaja Ahsan_khawaja@comsats.edu.pk Lecturer Room 102 Department of Electrical Engineering
2. 2. Steps of Nodal Analysis 1. 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.
3. 3. Common symbols for indicating a reference node, (a) common ground, (b) ground, (c) chassis.
4. 4. 1. Reference Node The reference node is called the ground node where V = 0 + – V 500 500 1k 500 500 I1 I2
5. 5. Steps of Nodal Analysis 1. 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.
6. 6. 2. Node Voltages V1, V2, and V3 are unknowns for which we solve using KCL 500 500 1k 500 500 I1 I2 1 2 3 V1 V2 V3
7. 7. Steps of Nodal Analysis 1. 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.
8. 8. Currents and Node Voltages 500 V1 500V1 V2 500 21 VV 500 1 V
9. 9. 3. KCL at Node 1 500 500 I1 V1 V2 500500 121 1 VVV I
10. 10. 3. KCL at Node 2 500 1k 500 V2 V3V1 0 500k1500 32212 VVVVV
11. 11. 3. KCL at Node 3 2 323 500500 I VVV500 500 I2 V2 V3
12. 12. Steps of Nodal Analysis 1. 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.
13. 13. Typical circuit for nodal analysis
14. 14. • Find the node voltages in the circuit shown below.
15. 15. • At node 1 2 0 4 5 121 321 vvv iii
16. 16. • At node 2 6 0 4 5 212 5142 vvv iiii
17. 17. Practice
18. 18. • Determine the voltage at the nodes in Fig. below
19. 19. • At node 1, 24 3 3 2131 1 vvvv ii x
20. 20. • At node 2 4 0 82 23221 32 vvvvv iiix
21. 21. • At node 3 2 )(2 84 2 213231 21 vvvvvv iii x
22. 22. • In matrix form: 0 0 3 8 3 8 9 4 3 8 1 8 7 2 1 4 1 2 1 4 3 3 2 1 v v v
23. 23. Spot quiz…
24. 24. Example:Use nodal analysis to find the voltage at each node of this circuit.
25. 25. • 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.
26. 26. 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
27. 27. • 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
28. 28. • 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
29. 29. Example:Use nodal analysis to find the voltage at each node of this circuit.
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