circuit analysis
I am looking at the problem in page 5 of this document.
It is an example of KVL (Kirchoffs voltage law).
The circuit is as shown below –
.
I have 2 questions –
1) Why is the voltage -5V ? Is it because the polarities reversed ?
2) The sign convention in the 8 Ohms resistor is wrong as I assumed the current loop as shown below and the sign convention as stated in the diagram. The voltage across 8 Ohms is -12V. Is the minus sign because of wrong convention ?
This is how i think i would solve the problem:
I don't see it necessary to add a 1V excitation source since there already a 9v in the circuit. The trick when analyzing circuit with dependent sources is to avoid the Short circuiting you would normally do when having a circuit with independent sources alone:
_Things to note that may help
Focus on node A:
define a current from the 9v source direction to node A and also define a current from 6ohm to A
_not Vx =Va
9 - Vx = I1
Vx/6 = I2
and i reckon Vab = 2Vx..
Hope this helps you!
Positive current (conventional current/positive charge) flows into the + terminal comes out through the - terminal in a resistor. That's why Ohm's law will yield a positive result for the current when going from a higher potential to a lower potential:
$$I=\dfrac{V_{higher}-V_{lower}}{R} $$
Since the numerator is \$\geq\$ 0, current is positive.
Positive sign convention is used so that you don't have to deal with the signs as you do in the first example you showed, where you 'manually' had to place a minus sign in Ohm's law. Now, what is higher or lower potential is an assumption that could turn out to be wrong in the end, but it helps to keep the math consistent.
So if in your analysis you assume that the current flows into the positive terminal and flows out of the negative terminal (which is the same as from higher to lower potential), the ohm's law relationship is positive, otherwise you need to add a negative sign to the relationship (like you did in your first example).
This is an excerpt from the Nilsson-Riedel electric circuit textboot
I think what they want to emphasize with that statement is that if you're better off assuming the current to be in the direction of the voltage drop, from + to -, as it'll make things less confusing with the signs
Best Answer
1) Yes, you could also reverse the polarity of the voltage source and write +5V instead. It makes the schematic easier to read. Both variants are equivalent.
2) If the polarity of a voltage across a resistor is not known, it is required to make an assumption. A minus sign indicates that the actual polarity of the voltage is against the assumed direction. But this is not "wrong" because the result is just with respect to an assumed polarity.