ground - How to find Voltage based on reference nodes?

I came across this problem and I'm trying to really understand it.

1. 
   
   

   VB is the voltage drop across a particular element, it is the change in voltage from node a to node b. Find the value of VB in volts and enter it in the box below.

   
   


2. 
   

   The expression Vab indicates the voltage referenced from node b to node a. In other words, imagine Vab being identified in the diagram as having a "-" at node b and a "+" at node a. For the circuit above, find Vab and enter it into the space below without units.

   
   


3. 
   

   For the same circuit above, find VC and enter it into the space below without units. (VC is the voltage across the top element, not the voltage at the point c in the circuit.)

   
   

The answers are:

• 1) 3


• 2) -3


• 3) -2

Now, I know that since VA is 3V so do VB because they are in parallel. but why is not VC + VD= 3V since they are also in parallel to VA

what is throwing me off is that if VA=3V that means the voltage at node b is 3V now the voltage at node a is 1V, that would mean that the voltage at node b minus the voltage at node a is equal to 2, (i.e. Vb-Va=3V-1V=2V=VB) but it is 3 instead.

The way I solved for VC is just intuitive, subtracted VA-VD and then multiplied by a negative sign because the negative sign is first (assuming that my current flows clockwise through the whole circuit), why can I do this fro VB?

Also why is Vab negative if voltage is dropping and not raising?

Answer

Voltage is the difference in electric potencial between two points.

The electric potencial of point a is 1V. Your mistake was to assume that the electric potencial in point b must be 3V because of the voltage drop of 3V. Actually the electric potencial in point b is 4V.

VA = Vb - Va
3V = Vb - 1V
Vb = 3V + 1V
Vb = 4V

In words: The electric potencial in point b is 3V higher than the electric potencial in point a. Resulting in a voltage drop over the Resistor VA of 3V.

In the same way you can calculate the electric potencial in point c.

VD = Vc - Va

1V = Vc - 1V
Vc = 1V + 1V
Vc = 2V

And last the voltage drop VC:

VC = Vc - Vb
VC = 2V - 4V
VC = -2V

Quick Scetch:

Hope that helps.