Solve Node Voltages Problem Homework

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In summary, the conversation is about analyzing a circuit using the method of node voltages and applying Kirchhoff's Current Law and Kirchhoff's Voltage Law. The attempted solution involves using a matrix relation, but there are some discrepancies with the equations and a possible typo. The suggestion is to write out the nodal analysis equations and then convert them into matrix form.
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k_squared
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Homework Statement


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

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Here is the answer:

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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!
 
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  • #2
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.
 

What is a node voltage problem?

A node voltage problem is a type of electrical circuit analysis problem where the goal is to find the voltage at each node (connection point) in a circuit. This is done by applying Kirchhoff's Voltage Law and Ohm's Law to the circuit.

What are the steps to solve a node voltage problem?

The steps to solve a node voltage problem are:

  1. Identify the nodes in the circuit
  2. Assign a variable for the voltage at each node
  3. Write Kirchhoff's Voltage Law equations for each closed loop in the circuit
  4. Apply Ohm's Law and Kirchhoff's Current Law to determine the relationships between node voltages
  5. Solve the resulting system of equations to find the voltage at each node

What is Kirchhoff's Voltage Law?

Kirchhoff's Voltage Law states that the sum of all voltages around a closed loop in a circuit must equal zero. This law is based on the principle of conservation of energy.

What is Ohm's Law?

Ohm's Law states that the voltage across a resistor is equal to the current through the resistor multiplied by the resistance of the resistor. This relationship is represented by the equation V=IR.

What are the applications of solving node voltage problems?

Solving node voltage problems is an important skill for electrical engineers and scientists. It can be used to analyze and design circuits in a variety of applications, such as electronic devices, power systems, and communication systems.

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