Electric Potential Between Multiple Points

[Mitchtwitchita]

Homework Statement

There are four points. The electric potential difference between points 1 and 2 (V12) is 30V, the electric potential difference between points 2 and three (V23) is 50 V, and the electric potential difference between points 4 and 1 (V41) is 60 V. What is the electric potential difference between points 3 and 4 (V34)?

Homework Equations

V = kq/r

The Attempt at a Solution

I have no idea how to get this one started. Can somebody please help me if you can?

 

[hikaru1221]

The only relevant equation here is potential difference between point A and B $$V_{AB}=V_A - V_B$$

 

[Mitchtwitchita]

How would I go about getting this problem started with that equation?

 

[hikaru1221]

Write down all potential differences provided and asked in the problem in that form, and you will see the miracle.

 

[Mitchtwitchita]

I'm not seeing any miracle.

V1 - V2 = 30V
V2 - V3 = 50V
V4 - V1 = 60V
V3 - V4 = V34?

 

[hikaru1221]

V12 = V1 - V2
V23 = V2 - V3
V41 = V4 - V1
V34 = V3 - V4
And: V12 + V23 + V41 + V34 = ?

 

[Mitchtwitchita]

I want to say the total is 150V and that V34 is 10, but I don't know why?

 

[hikaru1221]

Where do you get that 150V?
Again:
V12 = V1 - V2
V23 = V2 - V3
V41 = V4 - V1
V34 = V3 - V4
If I add these four equations together, I will have V12 + V23 + V41 + V34 = ?

 

[Mitchtwitchita]

I really don't know, nor do I have a guess. We don't know what V34 is, so how would it be possible to know the answer?

 

[kuruman]

If

A=B
C=D

then

A+C=B+D

Does that help?

 

[Mitchtwitchita]

So, V12 + V23 = V41 + V34?

30V + 50V = 60V + x
x = 20V?

 

[kuruman]

So, V12 + V23 = V41 + V34?

No. It doesn't follow from what you have. I just gave you an example with two equations. What works with two also works for three and four and five and so on. Use that fact and try answering hikaru1221's question.

 

[Mitchtwitchita]

I'm really perplexed by this problem, and am not understanding the concepts you are giving me. Is there any other information that you can give me that may enable me to grasp this problem better?

 

[kuruman]

If you have any number of equations, you can together everything on the left side and that will be equal to what you get when you add together everything on the left side.

Example

2 = 1+1
3 = 1+2
-2 = 2-4
4 = 2+2

Then
2+3+(-2)+4 = (1+1)+(1+2)+(2-4)+(2+2)

What works with numbers works with symbols that stand for numbers.

 

[Mitchtwitchita]

So, V12 + V23 + V41 + V34 = 140 V + x ?

 

[kuruman]

So, V12 + V23 + V41 + V34 = 140 V + x ?

Where did you get that? Show me exactly how just like I showed you in the previous example with numbers.

 

[Mitchtwitchita]

O.K. This problem has gotten me totally confused!

Would this be what I'm looking for?...

V12 = V1 - V2
V23 = V2 - V3
V41 = V4 - V1
V34 = V3 - V4

V12 + V23 + V41 + V34 = (V1 - V2) + (V2 - V3) + (V4 - V1) + (V3 - V4)?

 

[xcvxcvvc]

Ok, if you connect two voltages by having each voltage share the same point as their junction, then you've found a new voltage between the two points in the extreme.

$$V_{ab} + V_{bc} = V_{ac}$$
shown here:
$$V_{ab} = V_a - V_b$$
$$V_{bc} = V_b - V_c$$
$$V_{ab} + V_{bc} = V_a - V_b + V_b - V_c = V_a - V_c = V_{ac}$$
also, notice this result:
$$V_{ab} = V_a - V_b$$
then
$$-V_{ab} = -(V_a - V_b) = V_b - V_a = V_{ba}$$

So you basically have to use these results to make a chain of voltages that are properly connected to find v34. These rules apply to any number of voltages, too:
$$V_{12} + V_{23} + V_{34} = V_{14}$$

 

[kuruman]

That's what you are looking for. Now remove the parentheses from all the terms on the right side and add things together. What do you get on the right side?

 

[Mitchtwitchita]

O.K. This problem has gotten me totally confused!

Is this what I should be looking for?:

V12 = V1 - V2
V23 = V2 - V3
V41 = V4 - V1
V34 = V3 - V4

V12 + V23 + V41 + V34 = (V1 - V2) + (V2 - V3) + (V4 - V1) + (V3 - V4)??

 

[Mitchtwitchita]

Disregard the last post. If I remove the brackets, then all of them cancel and I'm left with 0.

 

[kuruman]

So you know that

V12 + V23 + V41 + V34 = 0

Can you find V34?

 

[Mitchtwitchita]

So, I have V12 + V41 = V1 - V2 + V4 - V1 = V42
V42 + V23 = V4 - V2 + V2 - V3 = V43
I don't know where to go from here...

 

[kuruman]

So, I have V12 + V41 = V1 - V2 + V4 - V1 = V42
V42 + V23 = V4 - V2 + V2 - V3 = V43
I don't know where to go from here...

Please explain how you got that from (*** On edit *** actually don't - it is irrelevant to the problem)
V12 + V23 + V41 + V34 = 0.

What do V12, V23, V41 and V34 stand for? Do you have any values for any of them?

 

[Mitchtwitchita]

I guess I'm not getting the rules. I was using what xcvxcvvc posted as a guide. I don't know where to plug the values in.

 

[kuruman]

Homework Statement

There are four points. The electric potential difference between points 1 and 2 (V12) is 30V, the electric potential difference between points 2 and three (V23) is 50 V, and the electric potential difference between points 4 and 1 (V41) is 60 V. What is the electric potential difference between points 3 and 4 (V34)?

Plug the values in the equation
V12 + V23 + V41 + V34 = 0.
What do you get?

 

[Mitchtwitchita]

V34 = 140 v?

 

[kuruman]

If the sum of four terms is zero and three of them are positive can the fourth term also be positive?

 

[Mitchtwitchita]

Sorry, -140V?

 

[kuruman]

Much better. You're done with this.

 

[Mitchtwitchita]

What? That can't be right. And, if it is, WOW do I feel dumb!

 

[kuruman]

A shortcut is to remember that the sum of all potential differences added around a closed loop is zero.

 

[Mitchtwitchita]

Thank you for all your time and patience!