Single Loop Potential difference -- sign issue

In summary, this person is trying to figure out how to solve a problem, but they are not sure why the results are different depending on the direction they take. They explain that the direction of the current is not important, only the polarity. They also explain that if you go from + to -, you will see a potential drop, and if you go from - to +, you will see a potential increase. Finally, they thank the person for clearing up everything.
  • #1
simphysics
7
0
Homework Statement
Find Va-Vb in the following circuit.
R=3 OHM
Ɛ1=10V
Ɛ2=4V
Relevant Equations
Va-Vb=Ɛ1
Va-Vb=iR-Ɛ2
Hello everyone, I've been struggling with this problem for 1 hour so far.
klvproblem.jpg
Here's how I've tried to solve it. as i supposed, the current flows counterclockwise and i=2A.
it doesn't matter which path i take, cause i should always arrive at the same potential but i actually don't and i can't get why.
If taking Vab clockwise:
Va-Vb=Ɛ1 and i assume it positive since the current flows through it from the negative pole to the positive one. so Va-Vb=10V
If taking Vab counterclockwise
Va-Vb=iR-Ɛ2=6V-4V=2V
I'm assuming Ɛ2 negative since the current flows through it from the positive pole to the negative pole.
The values are different and I can't get why.
Thank you! :)
homework-and-exerciseselectric-cir
 
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  • #2
Current direction is irrelevant for the emfs. All that matters is the polarity. You therefore has the wrong sign for the second emf.
 
  • #3
Got it, so what's the rule for the polarity?Thank you!
 
  • #4
If you go from + to -, potential drops. If you go from - to +, potential increases.
 
  • #5
sorry but i still can't get over it...
when i calculate Vab counterclokwise i go from + to -, so why should i take it positive?
thank you
 
Last edited:
  • #6
Why did you take the other emf positive?
 
  • #7
well...i don't know at this point
 
  • #8
Which direction you go and how you count is conventional. Computing Vab = Va - Vb you can either go from a to b and count potential drops or go from b to a and count potential gains. Since you say you want to go ccw from a to b, you should be counting potential drops. The drop across the resistor is iR because you are going in the direction of the current. The drop across the emf is E2 because going from + to - you get a potential drop.

Same thing happens when you take the other way across the other emf. You get E1 because you get a drop of E1 going from + to -.
 
  • #9
everything's clear now, thank you so much!
 

FAQ: Single Loop Potential difference -- sign issue

What is single loop potential difference?

Single loop potential difference refers to the difference in electric potential between two points in a circuit that are connected by a single loop of wire. It is also known as voltage and is measured in volts (V).

Why is there a sign issue in single loop potential difference?

The sign issue in single loop potential difference arises because the direction of current flow in a circuit is arbitrary. This means that the direction of the loop can be chosen in either clockwise or counterclockwise direction, resulting in a positive or negative potential difference, respectively.

How do you determine the sign of single loop potential difference?

The sign of single loop potential difference can be determined by using the right-hand rule. This rule states that if you point your thumb in the direction of current flow, the fingers of your right hand will curl in the direction of the loop. The potential difference will be positive if the loop is in the same direction as the current flow and negative if it is in the opposite direction.

Can the sign of single loop potential difference change?

Yes, the sign of single loop potential difference can change if the direction of the loop or the current flow is reversed. This is because the potential difference is dependent on the direction of the loop and the direction of current flow.

How does single loop potential difference affect the overall circuit?

Single loop potential difference is an important concept in understanding the behavior of electric circuits. It affects the flow of current and the distribution of energy in the circuit. It is also used to calculate the power and resistance in a circuit. Understanding the sign issue is crucial in accurately analyzing and predicting the behavior of circuits.

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