Node Voltage Analysis Questions

[turpy]

Hopefully it's ok if I post two questions

QUESTION 1

Homework Statement

Homework Equations

Node voltage analysis method

The Attempt at a Solution

First of all is this circuit equivalent?

(combining the 10 ohm and 4 ohm in parallel, and extending the ends of the protruding 10 om to nodes for v1 and v2?)

If so I solve (using the sum of all currents flowing into a node =0)
(1) 3 + ix + (v2-v1)/10 + 4*ix =0
(2) -4*ix + 7 + (v1-v2)/10 - v2 /2.86 = 0
with ix = -v1 /4
(1) -1.35*v1 + 0.1*v2 = -3
(2) 1.1*v1 - 0.45*v2 = -7
v1 = 4.12 V
v2 = 25.63 V


QUESTION 2

Homework Statement

Homework Equations

node voltage analysis method

The Attempt at a Solution

I'm at a loss as to where I should place the reference ( 0V ground) voltage, and where to put the nodes for node voltage analysis.

Typically the ground is at the negative terminal of the voltage source. But if I put it there, would the other junctions along the bottom be 0V? I thought the voltage drops would be the same only if the resistors were in parallel, and with the ladder/steps I'm not so sure.

We're given that there's 0.2V across the 1ohm resistor, so it's 2A of current flowing through it by ohm's law. The 2 ohm resistor above is has the same 2A flowing through since it's in series. But does the 2 ohm resistor in parallel (are they parallel?) to them have 2A flowing through, and then in turn the 4 ohm resistor?
I'm really missing something to understand how currents flow and voltages drop in a circuit

Thanks!

 

[lewando]

It would be less confusing if you did 2 posts. I'm willing to help with the 2nd one, for now. Recheck your calculation for current through the 1Ω. It should be 0.2A. Consider the entire bottom rail to be at 0V if you like. You can solve this problem by working right-to-left. If you know the voltage, you know the current, if you know the current, you know the voltage across the resistor above, etc...

 

[gneill]

As lewando suggested, separate threads for separate problems will help to reduce confusion, otherwise you'll have a lot of interleaved "crosstalk" to sort through. This will be no fun for you or for people wanting to help.

I can help you with the first problem. So far, looking at your equation (1) for the V1 node, it looks as though you've treated the controlled source as a current source. That is incorrect as it is a voltage source. Note that this makes the v1 and v2 potentials into a Supernode, which will actually simplify your calculations somewhat.

Oh, and yes, your second rendering of the circuit is equivalent to the original.