Analyzing a circuit with a current dependent voltage source

[Evales]

Hey guys,

I'm trying the analyze a circuit, I have the answers I should be getting but they're way off what I'm getting when I'm trying to work it out.

I think I might be approaching it from the wrong angle, does anyone have any suggestions as to where I might start.

I'm trying to find v₃ and v₂ (the 2nd and 3rd nodes).

At the moment I'm doing the KCL for each node, and getting three equations with all the node voltages as well as the currents through the voltage source and the current dependant voltage source as variables.

I then do the mesh analysis which I substitute into the original equations, which has given me some pretty crazy answers. The latest being:
v₃=696V

v₃ is supposed to be 80V!

It's driving me insane, and the way I'm doing it means it takes me an hour to redo it everytime.

Any help would be much appreciated.

 

[Jony130]

Hi
All you need to solve this circuit is two equation.
Have you notice that we have a one supernode ? And also also know V1 = 50V

http://www.wolframalpha.com/input/?...++V_2/50+++(V_2+-+50)/5+solve+for+V_2+and+V_3

 

[Evales]

Thanks! I thought it would have something to do with a supernode but we've only done them in parallel, I wasn't sure it would still apply.

Also in my last three tries I let v₁= 50V, but this time I didn't. Clearly time to head to bed lol.

Thanks again.

 

[Jony130]

Look at my solution.
We have a one supernode, and this means that we treat V2 and V3 as a one supernode.
We short CCVS and use nodal analysis.

Now we write KCL for our supernode, 4A current source entering node and remaining currents leaving the node.

4A = V3/100Ω + V2/50Ω + (V2 - 50V)/5Ω (1)

And one additional equation

V3 - V2 = 10*Ia (2)

And that's the only think we need to solve this circuit.

 

[DeeNos]

I understand the frustration of getting unexpected results when analyzing a circuit. It sounds like you are on the right track by using KCL and mesh analysis to solve for the node voltages. However, it is possible that you may have made a mistake in your calculations or have not fully considered the effects of the current dependent voltage source.

One suggestion would be to double check your equations and calculations to ensure they are correct. It may also be helpful to redraw the circuit and label all the node voltages and currents to make sure you are not missing anything.

Additionally, you may want to consider using a simulation software or circuit analysis tool to verify your results and make the process less time consuming. This can also help you identify any potential errors in your approach.

In terms of approaching the circuit from a different angle, you could try using Thevenin's or Norton's equivalent circuits to simplify the circuit and make it easier to solve. You could also try using superposition to analyze the circuit by considering the effects of each voltage source separately.

Overall, my advice would be to carefully review your calculations and equations and consider using different analysis methods to verify your results. Don't get discouraged, circuit analysis can be tricky but with persistence and attention to detail, you will be able to solve it. Good luck!