The Laws of Circuit - you can learn and practice by just reading

Copyright. Charles Kim 2006

A Convention where Talks Are All About Polarity and Flow Direction
What is the "passive convention" and how do we apply that in circuit problem solving? First, as the name implies the passive convention is a norm we use for voltage polarity and current flow direction in a passive element (i.e., resistor). What it says is, basically, you have only one degree of freedom.
In other words, if you choose the direction of current (you used the freedom in current direction), you do not have freedom in voltage polarity (instead, you have to follow your voltage polarity according to the direction of current.) That means your voltage polarity should satisfy so that current flows from positive polarity of voltage to the negative polarity of the voltage. If you use your freedom on voltage polarity and placed + polarity at one side of your resistor and - polarity of the other side of the resistor, you have no freedom in the current direction but to follow the convention so that current flows from + voltage polarity to - polarity of the voltage. What about on active element like a voltage source or current source. Let's kake a voltage source first. A voltage source has polarities already determined. Therefore you do not have freedom on voltage, but you have full freedom on current flow direction so that you can assume current flows out of the + polarity or into the + polarity side of the source. For a current source, the current flow direction is given with the source, so you have full freedom in voltage polarity across the current source. So you can assign + at the arrow of the current source or - polarity there.