Circuit +/-: Find Potential Difference b/w Point A & B

[pyroknife]

Homework Statement

I attached the pic of the problem. Note: I left half the diagram off because this part of the question only concerns this part. It wants me to find the potential difference between point a and point b. The answer is supposed to be 1V, but I don't get why. The current was for the 3 ohm resistor was given to be 2A (you won't get this answer if you try to solve for it because I left out half the diagram). When you move down the wire you gain 5V then drop (3)(2) which gives -1V. Am I misunderstandingthis question?

Homework Equations

The Attempt at a Solution

 

[lewando]

the potential difference between point a and point b.

This alone could be ambiguous. You should pick a reference terminal. How about "b" for this circuit. You want to know the voltage at "a" relative to "b" (v_a - v_b).

When you consider the 2A current moving through the loop, it will move in a counterclockwise manner (agree?). 2A encountering a 3-ohm resistor will result in a 6V drop with respect to the terminal that the current enters (teminal b).

Does this bring you closer to an understanding?

 

[PeterO]

Homework Statement

I attached the pic of the problem. Note: I left half the diagram off because this part of the question only concerns this part. It wants me to find the potential difference between point a and point b. The answer is supposed to be 1V, but I don't get why. The current was for the 3 ohm resistor was given to be 2A (you won't get this answer if you try to solve for it because I left out half the diagram). When you move down the wire you gain 5V then drop (3)(2) which gives -1V. Am I misunderstandingthis question?

Homework Equations

The Attempt at a Solution

The current of 2A in the 3 ohm resistor means the voltage drops 6 V across it. You then gain 5V across the battery, so the net drop is 1 Volt, so your reasoning is understandable if not correct.

The difference between two numbers is always positive, so the difference is 1V, never -1V

Subtraction can give a negative answer, difference never gives a negative answer.

 

[pyroknife]

This alone could be ambiguous. You should pick a reference terminal. How about "b" for this circuit. You want to know the voltage at "a" relative to "b" (v_a - v_b).

When you consider the 2A current moving through the loop, it will move in a counterclockwise manner (agree?). 2A encountering a 3-ohm resistor will result in a 6V drop with respect to the terminal that the current enters (teminal b).

Does this bring you closer to an understanding?

Yeah I think so, I wasn't thinking about the CCW and CW thing.

The difference between two numbers is always positive, so the difference is 1V, never -1V

I think this makes more sense to me from a non physics major point of view. Is this absolute that the difference between 2 #s is always positive?

 

[lewando]

"1V" is the absolute value of the potential difference. Since the original question did not specify a reference terminal, this could be a valid answer. I personally think you should always designate a reference terminal and stipulate this when you submit your answer.

 

[pyroknife]

wait so if I picked B as my reference terminal that means I drop 6V after current goes thru the resistor. then gain 5V after going thru the battery. Wouldn't that give me -1V?

 

[lewando]

Yes.

 

[PeterO]

Yeah I think so, I wasn't thinking about the CCW and CW thing.


I think this makes more sense to me from a non physics major point of view. Is this absolute that the difference between 2 #s is always positive?

Try buying a -9V battery at the electronics shop!

dif·fer·ence (dfr-ns, dfrns)
n.
1. The quality or condition of being unlike or dissimilar.
2.
a. An instance of disparity or unlikeness.
b. A degree or amount by which things differ.
c. A specific point or element that distinguishes one thing from another.
3. A noticeable change or effect: Exercise has made a difference in her health.
4.
a. A disagreement or controversy.
b. A cause of a disagreement or controversy.
5. Discrimination in taste or choice; distinction.
6. Mathematics
a. The amount by which one quantity is greater or less than another.
b. The amount that remains after one quantity is subtracted from another.

The word amount means we are looking at the magnitude only.

 

[PeterO]

wait so if I picked B as my reference terminal that means I drop 6V after current goes thru the resistor. then gain 5V after going thru the battery. Wouldn't that give me -1V?

A relative potential of -1V , yes. So a potential difference of 1V. Potential can be negative, Potential difference cannot.

eg suppose the potential of b was 17 Volts [and it can be made that].
After the resistor we are down to 11V, then after the Battery we are back to 16. A potential difference of 1V.

 

[lewando]

In many applications, exactitude of language is critical. I think that this question has some room for interpretation--it doesn't make it a bad question, just that it requires you to state your answer using terms that express exactly how you mean it to be.

 

[phinds]

Is this absolute that the difference between 2 #s is always positive?

Yes, that's what "difference" means in this case ... the MAGNITUDE of what you get from one minus the other, not a signed value.