Calculation with this electric circuit (battery and resistors)

[AnneX]

Homework Statement

This is not homework, but a problem I came across while studying

Relevant Equations

None, as you have to find the wrong statement

Hey,

I am struggling a bit, als I try to solve this problem - I‘d say all five statements are correct, but it is said, that one must be incorrect

 

[TSny]

Welcome to PF.

Please explain your reasoning for obtaining values for $\varphi_A$, $\varphi_B$, etc.

 

[AnneX]

I marked it in the image

this is all I got for this problem

 

[TSny]

Why do you think that $\varphi_A = -4$ V? What is your thought process for deducing this?

 

[AnneX]

That was my train of thought:

 

[TSny]

How did you get from a resistance of 4 $\Omega$ to a voltage drop of -4 V? Does a resistance of 4 $\Omega$ always correspond to a voltage drop of -4 V?

 

[AnneX]

No, it does not, but this is multiple choice and I am trying to find the incorrect statement while being very clueless... :(

 

[TSny]

We need to identify why you are having trouble with this problem.

Suppose you have 2 A of current through a 5 $\Omega$ resistor as shown below

The potential at point $b$ is given to be 12 V. Can you figure out the potential at point $a$?

 

[AnneX]

7V?

 

[AnneX]

Wait I think I got it, is that correct:

 

[TSny]

7V?

7 V is incorrect. Does the current play a role in determining the voltage at $a$?

Hint: Ohm's law

 

[AnneX]

This is the point I got to

to

 

[TSny]

You correctly applied Ohm's law to find that there is a 10 V drop across the resistor. But how did you arrive at a value of 17 V for the potential at point $a$?

 

[AnneX]

12+5... I am still not sure if a is 2V or 22V

 

[TSny]

I am still not sure if a is 2V or 22V

This is where the direction of the current is important. Whenever current flows through a resistor, the voltage is higher on the side of the resistor where the current enters the resistor. That is, voltage drops as you go through a resistor in the direction of the current.

An analogy might help (but, beware of analogies!). If you have a horizontal pipe full of water and you want the water to flow from left to right through the pipe, then you need a higher pressure at the left end of the pipe compared to the right end.

Likewise, in order for the current to flow from left to right in the 5 $\Omega$ resistor, the potential must be higher at the left side of the resistor compared to the right side.

 

[AnneX]

So it is 22V

 

[TSny]

So ist is 22V

Yes. Good. You can see that you had to know the current going through the resistor.

So, going back to the original question, what are you going to need to find first before you can determine the voltage drop across each resistor? And, how are you going to do that?

 

[AnneX]

The current, to calculate the voltage drop

 

[TSny]

Good. You're almost home.

Yes, the potential is given to be 0 at point E.

Note: We prefer posters to type their work rather than post pictures, if possible. This makes it easier for helpers to quote specific parts of a post. On the toolbar there are various tools for typing superscripts, subscripts, math symbols, etc.

 

[AnneX]

That is what I got: potential a is -4V potential b -3V and potential c +6V, as the flow of current goes from the positive pole to the negative pole - at least that is what I read about it, but I find it kinda confusing

 

[cnh1995]

That is what I got: potential a is -4V potential b -3V and potential c +6V

Looks correct. Now you can tell which option is incorrect.

as the flow of current goes from the positive pole to the negative pole - at least that is what I read about it, but I find it kinda confusing

Look up "conventional current" vs "electron current".

 

[AnneX]

So c is incorrect. But how do I know which one of these two currents applies to a problem?

 

[cnh1995]

But how do I know which one of these two currents applies to a problem?

You can use any. Conventional current is just opposite to the electron current. As long as you are consistent with polarities and sign conventions in circuit laws, you will be okay.
I will suggest you stick to the conventional current approach, as the electon-current approach is now almost non-existent in circuit analysis.
(..though I remember some standard textbooks explicitly mentioning "conventional current edition" on their cover, so I am not sure).