Is passive sign convention the exact oposite of active sign convention?

Question

I'm currently studying the fundamentals of electrical circuits. For my studies, I'm using the book "Fundamentals of Electric Circuits 5th ed."

In the introduction chapter, section 1.5 Power and Energy, the author discusses the "passive sign convention" as defined in the image below. However, in a side note, the author mentions the "active sign convention," which has left me quite confused.

It seems to me that both conventions can be used, but one considers the opposite of the other, or did I misunderstand?

Answer 1

It seems to me that both conventions can be used,

Both conventions are equally valid.

But you should only use one of them when solving a given problem.

but one considers the opposite of the other, or did I misunderstand?

They opposite in the sense that in the passive sign convention, the power (\$I\times V\$) of a branch is positive when the branch is absorbing electrical power and negative when it is delivering electrical power; but in the active convention it is the opposite: power is positive when the branch is delivering electrical power and negative when the branch is absorbing electrical power.

If you solve the problem once using the active convention and then with the passive convention you will get "opposite" results for the power of each branch.

Answer 2

It is the same thing. In the figure (b) the current flow is reversed.

But, if you would calculate P = UxI -> P < 0 and |P| > 0

Therefore, you use P = Ux(-I) -> P > 0 and |P| > 0

As the sign is used to represent the flow of power (+ = in, - = out), the second option makes more sense, as there is no such thing as "negative power" in a Resistor - as it can not source power ( - )!.

Or in more detail:

The active sign convention is used to define voltage and current in a way that aligns with the behavior of active circuit elements like power sources. It considers voltage positive when the current enters the positive terminal of a device and current positive when it flows into the positive terminal, representing power sources as positive voltage and load elements as positive current sources.

In contrast, the passive sign convention focuses on power dissipation in circuit elements. It defines voltage as positive when the current flows from the positive terminal to the negative terminal, and current is positive when it flows out of the device's positive terminal. This convention is typically used in physics and emphasizes the consumption or absorption of power by circuit elements.

The choice between these conventions depends on the context and the desired perspective for analyzing electrical circuits.