Basic Electrical and Electronics Engineering: Unit I: Electrical Circuits
Nodal Analysis - Solved Example Problems
Electrical Circuits
The nodal method is used to analyze multisource circuits. In this method, Kirchoff's current law is applied at various nodes in an electric circuit.
NODAL ANALYSIS
Example: 29
Using nodal analysis determine the current in the 20 Ω resistor.
Convert all the voltage sources into their equivalent current sources.
I1= 10/10 = 1A
I2= 20/10 = 2A
Apply KCL to node 1
Example: 30
Write the node voltage equations and determine the currents in each branch for the network shown in fig
Applying Kirchoff's current law at node 1
5 = i10+ i3
5 = V1/10 + V1-V2/3
5 = V1/10 + V1/3 - V2/3
5 = V1(1/10 +1/3) -V2(1/3)
…………(1)
At node 2
0 = i3 + i5 + i1
………….(2)
Solving equ (1) and (2)
equ (1) ⇒ 5 = V1(0.43) - V2(0.33)
equ (2) ⇒ 10 = -V1(0.33) + V2(2.65)
V1 = 19.85 V, V2 = 10.9 V
I10 = V1/10 = 1.985A
I3 = V1 –V2/3 = 1.985-10.9/3 = 2.98A
I5 = V2/5 = 10.9/5 = 2.18A
I1 = V2-10/1 = 10.9 - 10 = 2.18A
Example: 31
Determine the node voltages for the network shown in fig
Apply KCL, at node (1)
V1/2 + V1-V2/12 = 4
0.5 V1 + 0.083 V1 - 0.083 V2 = 4
0.583V1 - 0.083V2 = 4 ………….(1)
At node (2)
V2/6 + V2-V1/12 + 2 = 0
0.167 V2 + 0.083 V2 -0.083 V1 = -2
-0.083V1 + 0.25V2 = -2
By solving the above two equations
V1 = 6V, V2 = -6V
Example: 32
Find V1 and V2 in the circuit given below using nodal analysis.
Find V1 and V2 in the circuit given below using nodal analysis.
Example: 33
Find V1 ,V2 ,V3 by nodal method for the given circuit.
Find V1 ,V2 ,V3 by nodal method for the given circuit.
Basic Electrical and Electronics Engineering: Unit I: Electrical Circuits : Tag: : Electrical Circuits - Nodal Analysis - Solved Example Problems
Basic Electrical and Electronics Engineering: Unit I: Electrical Circuits
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