Voltage Calculations for Simple Circuit with Switches - VA and VB

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Homework Statement

I'm going to try drawing the circuit. Numbers are added to it for reference. I apologize for the formatting. I'm not sure how to do white space. Edit: for V_B the + is on top.

V_A and V_B are switches.

I need to figure out the voltage across V_A and VB_B when they are:
1. open, open
2. open, closed
3. closed, open
4. closed, closed

1-------(+ V_A -)-------(+ 8 V -)-------2--------------3
|_______________________________|___________|
12Ω____________________________15Ω_______(+ V_B -)
|_______________________________|___________|
6-----------------------------------------5--------------4

Homework Equations

V = IR
Kirchhoff's Laws

The Attempt at a Solution

1. When they are both open there isn't a circuit. So, V_A = 0 V and V_B = 0 V.
2. Again, no circuit.
3. There is a circuit. It has a total resistance of 27 Ω (I don't know if this matters). V_A = -8 V and V_B = 0 V.
4. I'm not sure about this one. There are two loops, but loop 1256 has a total resistance of 27 Ω and loop 1346 has a total resistance of 12 Ω. So 1256 gets 27/39 = 9/13 of the current and voltage and 1346 gets 12/39 = 4/13 of the current and voltage? So V_A = -8*9/13 V and V_B = -8*4/13 V?

 

[NascentOxygen]

1. When they are both open there isn't a circuit. So, V_A = 0 V and V_B = 0 V.

Circuit or no circuit, does not give the answer. If a voltmeter (or any device) were to be connected between the 2 terminals of the switch in question, would that form a path for current to flow through the meter? If so, what voltage would it register? That's the question you must address.

 

[NascentOxygen]

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[CWatters]

1. When they are both open there isn't a circuit. So, VA = 0 V and VB = 0 V.

You need a circuit for current to flow. You don't need a circuit for a voltage to be present. For example a 9V battery still produces 9V even when it's disconnected from the circuit.