Homework Solutions for Electric Circuits, 7^th edition, by Nilsson and Riedel

PROBLEM 4.9

Use the node voltage method to find v₁ and v₂.

Note that I labeled the bottom node as the reference node. This allows us to use v₁ and v₂ (the predefined voltages on the 40 W and 120 W resistors) as the two node voltages since they are the differences in voltages from the two top nodes to the bottom node. If one of the top nodes had been chosen as a reference node, we would need to use different variable names for the node voltages to avoid confusion.

If you do not understand the paragraph above, you are almost certainly missing a key concept and you should do whatever is necessary to understand this.

Writing KCL at the two nodes gives

Node 1

Simplifying gives

240 + 5 v₂ - 5 v₁ - v₁ = 0
5 v₂ - 6 v₁ = - 240 (equation A)

Node 2

Simplifying gives

240 + 3 v₂ + 2 v₂ + 30 v₂ - 30 v₁ = 0
35 v₂ - 30 v_{1 =} - 240 (equation B)

Solving Equations A and B gives

v₁ = 120 V
v₂ = 96 V

This page last updated at 12:48 PM on Thu, Sep 8, 2005