Solve Node Voltages Problem Homework

[k_squared]

Homework Statement

We are told to analyse the circuit in the diagram (ignore the texts) with the method of node voltages.

Here is the answer:

Homework Equations

Kirchhoff's Current Law
Kirchhoff's Voltage Law

The Attempt at a Solution

So far, all I have been able to get is the equation described by the top line of the matrix relation. However, there is no 0 by the resistance!

Worse, the bottom equation looks to me like (1-alpha)*v_2. And I have no idea where v_2 is even defined, or how this is a valid KCL equation without the value or R_2 anywhere...

Thank you in advance for any help!

 

[gneill]

Your diagram has labelled the nodes 1 and 2. So it is reasonable to assume that v1 corresponds to node 1's voltage and that v2 corresponds to node 2's voltage.

It could be that when you are trying to recover the individual node voltage expressions that you are not correctly carrying out the matrix times vector operation?

I do see one typo in the text's solution though. The resistor in the matrix's first term should be R₁, not R.

Why don't you try writing out the nodal analysis equations from scratch. They can always be be wedged into matrix form afterwards.