Basic Electrical and Electronics Engineering: Unit I: Electrical Circuits
Solved Example Problems [Nodal Analysis]
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.
Example: 33
Find V1 ,V2 ,V3 by nodal method for the given circuit.
Basic Electrical and Electronics Engineering: Unit I: Electrical Circuits : Tag: : Electrical Circuits - Solved Example Problems [Nodal Analysis]
Basic Electrical and Electronics Engineering: Unit I: Electrical Circuits
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