Draw a Circuit based on the info and find the voltage values

[yaro99]

Homework Statement

Consider a circuit containing four nodes
labeled a, b, c, and d. Also, we know that
v_ab= 12V,v_cb=−4V,and v_da= 8V. Deter-
mine the values of v_ac and v_cd. (Hint: Draw
a picture showing the nodes and the known
voltages.)

Homework Equations

∑ voltages in a loop = 0

The Attempt at a Solution

I had no idea how to approach the problem, just a couple ideas. I tried sketching this out:

This one didn't make much sense to me since applying the loop rule, I get differing answers for $v_{ac}$

So I tried a few other ways to draw it and this was the closest I could get:

This seems like it makes more sense, but I'm not entirely sure. Am I on the right track?

 

[collinsmark]

I recommend the first thing to change is you need to change your voltage symbol to indicate some sort of polarity. They blue squares alone are not sufficient. Either use a symbol with obvious polarity such as a battery symbol, or (and this is just as good too) label the '+' and '-' signs.

What I mean by that is if you look at the 8 V element in the upper left. Imagine, hypothetically, flipping the polarity of that element, making it V_AD = 8 V. If you did so, it wouldn't look any different than the way it is now with V_DA = 8 V. You need some way of indicating the polarity. You need to know by looking at your picture that if V_DA = 8 V, then V_AD = -8 V

Secondly, don't draw that stuff in the middle. It's not necessary. Just keep it as a square if you wish (or even three sides of a square), with nothing in the center. Note that V_AC = V_AB + V_BC

 

[ehild]

It is easier to work with potentials. If Vab means the potential of b with respect to a : Vab=Vb-Va=12 V. Write 0 at point a and 12 V at point b. Draw a battery between the nodes to ensure the given potential difference.
Draw the batteries and determine the potential of each node. Calculate the potential differences Vac=Vc-Va and Vcd=Vd-Vc.

You can connect a resistor between two nodes and an other one between the other two nodes, the potential differences would not change.

ehild