very basic circuit analysis problem

[omg]

Hi
I have to "find voltages \[v_1\]\[v_2\]" in the following circuit:
**broken link removed**

I'm trying to use "node method", but I got problems with currents flowing in/out of my nodes. I'm not sure what the marked elemets are.
Element between \[v_1\] and gnd looks like voltage source, and element between \[v_1\] and \[v_2\] looks like a current source, but it's got value 0.5 \[v_a\], how do I calculate current through it?

I think KCL for \[v_1\] would be:
\[-\frac{v_a}{10}+0.4i_b\]+how do i get current through the element between \[v_1\] and \[v_2\]?


This is my first attempt ever to solve circuit so I might be mixing things up.
Could someone point out what am I missing here, and elaborate a bit on how to solve this for \[v_1\] and \[v_2\]

Thanks.

 

[BradtheRad]

I have been trying a simulation.

From what I can tell, you are supposed to adjust the voltage coming out of the diamond with a + and - inside it (icon for a voltage source), so that:

a) current from V1 to V2 is 0.5 x that through the resistor marked Va.

b) current from V1 to ground (or ground to V1) is 0.4 x that through the 5 ohm resistor.

It is confusing because the diamond containing an arrow could indicate either a theoretical current source, or it could indicate a measure of current flowing in a PLAIN WIRE from V1 to V2.

It does not appear as though we can put resistors at the icons in question, so that current will flow from V1 to V2 in a way that satisfies the readings on the icons.

 

[omg]

Hey, thanks for reply.

I tried to do it as per a) and b):
KCL for node \[v_1\]:
\[-v_a+0.4i_b+0.5v_a = 0\]
By ohm's law current through \[v_a\] is \[\frac{14V}{10ohm}=1.4A\]
So it becomes:
\[-1.4A+0.4i_b+0.7A=0\]
\[i_b = 1.75A\]

But it doesn't match KCL for node \[v_2\]:
\[-\frac{14V}{1ohm}-0.5v_a+i_b = 0\]

\[-14A-0.7A+1.75A = 0\] <= fail

What did I miss?

 

[BradtheRad]

By ohm's law current through \[v_a\] is \[\frac{14V}{10ohm}=1.4A\]

This assumes V1 is at 0V, but we cannot assume that. However we can construct one equation:

Current_through_v_a = (14 - V1) / 10

and we can construct another equation:

Total current through the 1 ohm and 10 ohm = 1.4_I_B

and more equations after that.

Another thing. Notice that V1 will be = V2 if there is just a plain wire between them. Or do you know for sure that V1 is supposed to be different from V2? If so then there must be something intervening between them, either in the form of a component, or a voltage/current source.

Although it could be a resistor, I seem to remember trying a resistor, and found there was no value high or low which I could install, that would not result in wrong current flow somewhere.

Whatever the component is, some other equation can be constructed.

When you have enough simultaneous equations, it may automatically generate the necessary node levels, or else it will lead you to an 'aha' moment, when you discover there is a certain relationship between the various current flows that allows you to solve the problem.

 

[Ratch]

omg,

You should not have any problems identifying the elements in the diagram. The diamond with an arrow is a current source, specifically a dependent voltage controlled current source (VCCS). The diamond with the polarity signs is a voltage source, specifically a dependent current controlled voltage source (CCVS).

Now to solve it. V1 is a "gimme", in that the voltage source output is right on top of the node V1, so you know the voltage 0.4*ib. So we only have to solve for one node, V2, and a couple of unknown circuit values.

Writing out the equations for node analysis, we get from equating the currents into V2:

-0.5Va + (V2-14)/1 + ib = 0 , Va = 14 - 0.4*ib , ib = V2/5

Three equations and three unknowns are V2 = 16.93548, Va = 12.64516, ib = 3.387097

Now, can you solve the network by the loop method?

Ratch