Potential difference of an electric circuit

In summary, the figure shows two potentials and the line of intensities that is given by the statement.
  • #1
Guillem_dlc
184
15
Homework Statement
Consider the circuit section of the figure. Determine the potential difference ##V_a-V_b##.

Data: ##\varepsilon_1=6\, \textrm{V}##; ##\varepsilon_2=7\, \textrm{V}##; ##R_1=2\, \textrm{k}\Omega##; ##R_2=4\, \textrm{k}\Omega##.

Sol.: ##11\, \textrm{V}##
Relevant Equations
Ohm's law
The figure is:
062AD319-1DF8-44E6-8593-15C440364258.jpeg

I have the solution to this problem:
We have two distinct branches
$$V_a-V_b=\overbrace{(V_a-V_c)}^{\textrm{INI}-\textrm{FIN}}+\overbrace{(V_c-V_b)}^{\textrm{FIN}-\textrm{INI}}$$
They have different intensities: ##3\, \textrm{mA}## and ##2\, \textrm{mA}##
##V_A-V_C\rightarrow## We have battery and resistor
$$V_A-V_C=+\overbrace{R_1I_1}^{V_1}+\varepsilon_1$$
##V_C-V_B\rightarrow## High potential ##\rightarrow V_B##
$$V_C-V_B=-\overbrace{R_2I_2}^{V_2}+\varepsilon_2$$The question that I have is: If they tell me the potential ##V_a-V_b## the green arrow it should not go the other way. Like the blue one I have drawn. So I would make ##V_a-V_b=(V_c-V_b)+(V_a-V_c)##.
 
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  • #2
The equation ##V_a-V_b=(V_c-V_b)+(V_a-V_c)## is always true if you add and subtract ##V_a## on the left side and is not saying anything new. My question to you is. "Are the 3 mA and 2 mA currents and their directions given to you by the problem?" If so, then you have charge accumulating somewhere between ##a## and ##b## unless the line I see extending down from C is a piece of wire carrying 1 mA down. Please clarify.

Also, please rephrase your question because I do not understand what you are really asking. Maybe my eyes are deceiving me but the arrow I see is blue, not green. Whatever its color, what is it supposed to indicate?
 
  • #3
Yes, the line of intensities is given by the statement.

The blue line is the route I think we should do, and the green line is the one the teacher put when solving the exercise.
 
  • #4
Guillem_dlc said:
Yes, the line of intensities is given by the statement.

The blue line is the route I think we should do, and the green line is the one the teacher put when solving the exercise.
As far as I can make out, the question is the meaning of an arrow in a diagram between two potentials: should it point from the higher voltage to the lower (green) or the other way around (blue).
Higher to lower seems more natural to me, but it's just a convention; if there is no agreed standard, do whichever you like as long as you state it.
 
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  • #5
kuruman said:
you have charge accumulating somewhere between a and b
I read the diagram as being only part of a circuit. The unterminated lines above a, below c and to the right of b (and maybe some more in the upper right) go who knows where.
 
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  • #6
haruspex said:
As far as I can make out, the question is the meaning of an arrow in a diagram between two potentials: should it point from the higher voltage to the lower (green) or the other way around (blue).
Higher to lower seems more natural to me, but it's just a convention; if there is no agreed standard, do whichever you like as long as you state it.
Thanks! All understood!
 

What is potential difference?

Potential difference, also known as voltage, is the difference in electric potential between two points in an electric circuit. It is measured in volts (V) and is represented by the symbol "ΔV".

How is potential difference measured?

Potential difference is measured using a voltmeter, which is connected in parallel to the circuit element or components being measured. The voltmeter measures the difference in electric potential between two points in the circuit.

What causes potential difference in an electric circuit?

Potential difference is caused by the presence of an electric field in the circuit. This electric field is created by the movement of electric charges, typically electrons, through the circuit.

What is the relationship between potential difference and current?

There is a direct relationship between potential difference and current in an electric circuit. As potential difference increases, the current flowing through the circuit also increases. This relationship is described by Ohm's Law, which states that current is equal to the potential difference divided by the resistance of the circuit.

Can potential difference be negative?

Yes, potential difference can be negative. This occurs when the direction of current flow is opposite to the direction of the electric field. In this case, the potential difference is negative, indicating that energy is being used to move the charges against the direction of the electric field.

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