# CIRCUIT ANALYSIS: 3 Resistors, 3 Voltage Src, 1 Current Src - Find v1, v2, v3

1. Jan 23, 2007

### VinnyCee

1. The problem statement, all variables and given/known data

Find the node voltages $V_1$ through $V_3$ in the circuit below.

2. Relevant equations

KCL, KVL, V = i R, super-node

3. The attempt at a solution

I added 5 currents and 2 KVL loops.

$$V_2\,=\,42\,V$$ <----- Right?

Now I do KVL loop 1

$$(-12\,V)\,+\,(20\,V)\,+\,V_3\,=\,0\,\,\longrightarrow\,\,V_3\,=\,-8\,V$$

And KVL at loop 2

$$(-20\,V)\,+\,(10\,V)\,+\,(V_1\,-\,V_3)\,=\,0\,\,\longrightarrow\,\,V_1\,-\,V_3\,=\,10\,V$$

$$V_1\,-\,(-8\,V)\,=\,10\,\,\longrightarrow\,\,V_1\,=\,2\,V$$

Does that seem right?

Last edited: Jan 23, 2007
2. Jan 23, 2007

### mjsd

i think you meant V2=12V. otherwise correct

3. Jan 23, 2007

### VinnyCee

What about the 10 V and the 20 V that are also connected to node $V_2$?

4. Jan 23, 2007

### mjsd

your statement represents a common mistake/misconception about circuit theory.... when we talk about V2 we actually mean V2 with respect to (w.r.t.) the ground we are chosen (that's why I say this all the time), because if you choose a different ref node, value of V2 can change. For example, if you choose V3 to be your ref node (ie. ground), then V2 will have the value of 20V.
you get V2=12V for this daigram because, you see that the potential difference between V2 and ref node is V2-0 = 12 so V2 =12.
Now, you could also say
V2-V3=20 => V2 = 20+V3 (with V3 still unknown as this stage)
or
V2-V1=10 => V2 = 10+V1 (V1 too is unknown)

note that they never quite "add together", in fact if V1 and V3 are connected directed to ground, you have an inconsistent circuit...because all sources in circuit theory are assumed to be ideal.

anyway, if you sub V1, V3 you calculated into those equations above, you will find that all gives V2=12