Solved Example Problems [Nodal Analysis]

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