# Homework Help: Electric Potential Between Multiple Points

1. Jun 17, 2010

### Mitchtwitchita

1. The problem statement, all variables and given/known data

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)?

2. Relevant equations

V = kq/r

3. The attempt at a solution

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

2. Jun 17, 2010

### hikaru1221

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

3. Jun 17, 2010

### Mitchtwitchita

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

4. Jun 17, 2010

### hikaru1221

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

5. Jun 17, 2010

### Mitchtwitchita

I'm not seeing any miracle.

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

6. Jun 17, 2010

### hikaru1221

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

7. Jun 17, 2010

### Mitchtwitchita

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

8. Jun 17, 2010

### 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 = ???

9. Jun 17, 2010

### 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?

10. Jun 17, 2010

### kuruman

If

A=B
C=D

then

A+C=B+D

Does that help?

11. Jun 17, 2010

### Mitchtwitchita

So, V12 + V23 = V41 + V34?

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

12. Jun 17, 2010

### kuruman

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.

13. Jun 17, 2010

### 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?

14. Jun 17, 2010

### 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.

15. Jun 17, 2010

### Mitchtwitchita

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

16. Jun 17, 2010

### kuruman

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

17. Jun 17, 2010

### 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)?

18. Jun 17, 2010

### 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:
$$V_{12} + V_{23} + V_{34} = V_{14}$$

19. Jun 17, 2010

### 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?

20. Jun 17, 2010

### 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)??