network theory current voltage resistance

all topics are cover

1. Topic :- Discussion of Node Analysis concept of electrical circuits with examples Name :- Bisweswar Mahato Department :- Electronics And Communication Engineering Subject :- Network Theory Subject Code :- EC 304 Roll no. :- 35000323013 College :- Ramkrishna Mahato Government Engineering College 1

2. Outline Objective Steps in Nodal Analysis To solve DC circuits using Nodal analysis. AC circuits using Nodal analysis. 2

3. Objective 3 To introduce Nodal analysis technique (Nodal Voltage method) To formulate Node equations To solve circuits using Nodal analysis To introduce nodal analysis by inspection method

4. Nodal Analysis 4 An analysis technique to solve electrical circuit where the node voltages are used as the circuit variables It involves systematic steps with an objective to solve the node voltages Nodal Analysis method applies KCL to find the unknown voltages With node voltages known, current in every branch can be calculated 6 2 7 1A 4A Reference node v 1 , v 2 : node voltages If v 1 and v 2 are known, current in all branches can be calculated

5. Nodal Analysis Steps: Step 1. Determine the reference node: typically the one with the most branches (or ) bottom node Step 2. Assign the rest of the nodes with node voltages (referred to the reference node) Step 3. Write down equations using KCL for every non-reference node in terms of node voltages. Step 4. Obtain the node voltages by solving the simultaneous equations in step 3 5

6. Nodal Analysis- Example 1 Step 1. Determine the reference node: typically the one with the most branches (or ) bottom node 6 6 2 7 1A 4A

7. Nodal Analysis- Example 1 Step 2. Assign the rest of the nodes with node voltages (referred to the reference node) 7 6 2 7 1A 4A v 1 v 2

8. Nodal Analysis- Example 1 Step 3. Write down equations using KCL for every non-reference node in terms of node voltages  if there are N nodes, there should be (N-1) equations 8 6 2 7 1A 4A v 1 v 2

9. Nodal Analysis- Example 1 Step 3. Write down equations using KCL for every non-reference node in terms of node voltages  if there are N nodes, there should be (N-1) equations 9 6 2 7 1A 4A v 1 v 2 i1 i2 i3 i3 i4 i5

10. Nodal Analysis- Example 1 Step 3. Apply KCL to Node 1 i 1 = i 2 + i 3 ---- (1)   10 6 2 7 1A 4A v 1 v 2 i1 i2 i3 i3 i4 i5

11. Nodal Analysis- Example 1 Step 3. Apply KCL to Node 2 i 3 + i 5 = i 4 ---- (2)   11 6 2 7 1A 4A v 1 v 2 i1 i2 i3 i3 i4 i5

12. Nodal Analysis- Example 1 Step 4. Obtain the node voltages by solving the simultaneous equations in step 3 ---- (1) ---- (2) Rearrange and solve the equations, V1=-2v & V2 = -14 V   12

13. Nodal Analysis for AC circuits - Example 1 If Z L = – j 2Ω, find VL in the circuit using nodal analysis. 13

14. Nodal Analysis for AC circuits - Example 1 Step 1: Let us mark nodes along with the node voltages V 1 and V 2 in the given figure. Step 2: At node (1): At node (2): i.e. 14

15. Nodal Analysis for AC circuits - Example 1 Comparing: 15

16. Nodal Analysis for AC circuits - Example 1 To calculate V 2 Load voltage 16

17. 17 THANK YOU