# Potential difference of an electric circuit

• Guillem_dlc
In summary, the figure shows two potentials and the line of intensities that is given by the statement.

#### Guillem_dlc

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:

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)##.

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?

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.

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.

Guillem_dlc
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.

Guillem_dlc
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!