Hi everyone. I really would appreciate some help. I'm a first year engineering student. I need to find the voltage at V1 on the circuit I have attached via nodal analysis. However, the 20ia is confusing me, stopping me in my tracks after applying Kirchoff's current law at V1. Please help!

 

Hello tesla, good luck with your studies.

Please tell us what you found when you applied KCL to V1.

 

I have attached my work so far. I haven't found a value for v1 yet at I am unsure as to how to include 20ia into my working.

 

What sign convention are you using for your node currents?
Edit sorry I should have said branch currents.

As written they all seem to indicate that current only flows into or out of nodes V1 and V2.

It is a good idea to assume directions and label the diagram accordingly so that no node has all current flowing in (or out).

 

The sign convention I am using is:
1) if current is flowing into a node, designate it as a negative current.
2) if current is flowing out of a node, designate it as a positive current.

 

Presumably the 20ia source is a current controlled voltage source rather than a current controlled current source.

The second KCL equation at the node designated V2 is therefore incorrect. V2 would simply be noted as -20*ia volts.

Hopefully the OP is familiar with controlled sources and the means of dealing with them in circuit analysis.

 

Presumably the 20ia source is a current controlled voltage source rather than a current controlled current source.

Why do you say this?

It seems to be labelled as a current controlled current source in the diagram, but the direction is important.

 

Yep - my mistake. Thanks.

 

Tesla you are going in the right direction to obtain two simultaneous equations in two unknowns (V1 and V2), but you need to pay attention to your signs, which is why I suggest you label the branch currents at each node and asign each a direction, and therefore a sign. The correct directions and signs will come out in the wash.

 

Then again maybe not my mistake. Some clarification of the symbols might be in order.

Check : http://en.m.wikipedia.org/wiki/Current_source

 

If you prefer arrows in the diamonds, conventional current flows from + to - so an arrow can be asigned to replace the +/- signs in the diamond. The controlling equation of current is definitely related to another current, however.

 

The 20ia is a dependent voltage source. If v2 is just -20ia V, why is the 30 ohm resistor not included in any of the nodal analysis via a v2 equation?

 

If you prefer arrows in the diamonds, conventional current flows from + to - so an arrow can be asigned to replace the +/- signs in the diamond. The controlling equation of current is definitely related to another current, however.

Did you check the convention shown in Table 2 of the link to Wikipedia?

Hence my comment about needing some clarification - preferably from the OP.

 

Attached are the symbols used in my lecture slides.

 

I am getting confused here.

Let us examine your second equation.


\(\frac{{{V_2} - 10}}{{30}} + \frac{{{V_2} - {V_1}}}{{20}} + 20{I_a} = 0\)

The first two terms are currents.

You now tell me tht you meant the dependent source to be a voltage source so the 20Ia is a voltage?

How is that equation consistent?

Further your equation contains the current through the 30Ω resistor in the first term does it not?

 

Sorry studiot, I don't mean to confuse you. The 20ia in the second equation is definately incorrect, i see that now. You're also right about the 30 ohm resistor (i lose a few iq points when I'm tired. It's 1:14am here.) So how would I find the current across the dependent voltage source so I could include it into the KCL equation for node v2?

Thanks

 

You need some voltage equations since you know the voltage, not the current. (these of course include the currents in another way)

Can you think of any?

Yes it's GMT here as well.

 

Presumably the 20ia source is a current controlled voltage source rather than a current controlled current source.

The second KCL equation at the node designated V2 is therefore incorrect. V2 would simply be noted as -20*ia volts.

Hopefully the OP is familiar with controlled sources and the means of dealing with them in circuit analysis.

So if ia is 2mA, V2 is -40 volts? Saying "-20*ia volts" is saying, "let's ignore units and just use the number part of a value."

The designation of the supply should (probably) be "(20 V/A)*ia". Then it is unambiguous and no one has to read someone else's mind. Engineering is not about guessing.

Also, if ia=2A, we don't know that V2 is -40V, only that V2 is 40V lower than the bottom node, whatever voltage that happens to be. If we (i.e., the OP) wants to declare that as his 0V reference node, great. It's certainly a very reasonable choice. But I don't see where the OP did that (but maybe I missed it).

 

I think this could be one \(i{a}=\frac{V{1}-10}{10}\) and then somehow link that to the dependent voltage source.

 

Hi WBahn, the bottom line is my 0V reference node. I didn't include it or the 20 V/A*ia simply because it didn't include it in the problems sheet I was given by my lecturer (attached to my first post).