Engineering Voltage Calculations for Simple Circuit with Switches - VA and VB

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The discussion focuses on calculating the voltages across switches VA and VB in various open and closed configurations. When both switches are open, the voltage across each is 0 V due to the lack of a complete circuit. In the scenario where VA is closed and VB is open, VA measures -8 V while VB remains at 0 V. When both switches are closed, the circuit has two loops with different resistances, leading to a division of voltage based on the total resistance. The key point is that voltage can exist even without a complete circuit, as demonstrated by the example of a disconnected battery still producing a voltage.
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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 VB the + is on top.

VA and VB are switches.

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

1-------(+ VA -)-------(+ 8 V -)-------2--------------3
|_______________________________|___________|
12Ω____________________________15Ω_______(+ VB -)
|_______________________________|___________|
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, VA = 0 V and VB = 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). VA = -8 V and VB = 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 VA = -8*9/13 V and VB = -8*4/13 V?
 
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ƒ(x) said:
1. When they are both open there isn't a circuit. So, VA = 0 V and VB = 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.
 
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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.
 

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