# Passive Sign Convention Misconception?

1. Mar 14, 2015

### vintageplayer

The Passive Sign Convention from Wiki:

"In electrical engineering, the passive sign convention (PSC) is a sign convention or arbitrary standard rule adopted universally by the electrical engineering community for defining the sign of electric power in an electric circuit. The convention defines electric power flowing out of the circuit intoan electrical component as positive, and power flowing into the circuit out of a component as negative"

All well and good. What I don't understand is what voltages and currents have to do with it. The page goes on to say:

"To comply with the convention, the direction of the voltage and current variables used to calculate power and resistance in the component must have a certain relationship: the current variable must be defined so positive current enters the positive voltage terminal of the device."

I understand the sign of power can be arbitrarily defined depending on what system you're interested in; however, how can currents and voltages be arbitrarily defined? In a conductor, the actual current will always "flow" in the direction of the Electric Field, from a greater voltage potential. You can't just define the directions of the voltages and currents arbitrarily, unless you also want to rewrite Maxwell's Equations.

What am I missing here?

2. Mar 15, 2015

### axmls

Simple. Take a circuit. Now assume a current. It doesn't matter what direction the current goes. Just assume the current is flowing in a circuit direction. Now say, write Kirchoff's voltage law around a loop. Now, assuming you're talking about resistors, passive convention means that the current will always flow DOWNWARD from high voltage to low voltage. In other words, you pick your current direction, and as that current passes through a resistor in its path, it enters at the + voltage and exits at the - voltage.

What happens if the current direction you picked is wrong? Then your answer will be negative.

This basically means that when you pick a current, you will always assume a voltage DROP across a resistor for your loop equations.

3. Mar 15, 2015

### vintageplayer

If you assume the current is going one way in a resistor, you immediately know which way the voltage is. You don't have to assume its a voltage drop. It must be a voltage drop, otherwise you're violating the definition of current flow direction. The direction of the current is an assumption, but this then implies the direction of the voltage. In a resistor, the current will always flow from a greater voltage potential. As an analogy, if you assume the earth is down, then you must assume gravity points down also. It is not called a "convention" with gravity?

4. Mar 15, 2015

### milesyoung

You're confusing reference polarities/directions with the actual polarities and directions of the voltages and currents in the circuit, respectively.

Take this two-terminal element:

where the references are assigned according to the active sign convention, which is perfectly valid.

If the element is a resistor with resistance $R$, then to calculate $i$, you have to use its v-i relationship for the active sign convention, which is $v = -Ri$. If $v$ is positive, then $i$ is negative, so the actual current flows in the direction it should.

The power delivered to the element is $p = vi$, which is negative for a resistor, since $v$ and $i$ have opposite signs. It would be positive for the passive sign convention.

5. Mar 15, 2015

### vintageplayer

OK I think I got it!

In the active sign convention, we define the power delivered to the resistor as negative. We then say in order to calculate the power, we use P = VI, but we must take I as the current going into the negative voltage terminal. This "reference current" will always be negative for a resistor because we know the "actual current" is going the other way. Hence we will always calculate a negative power as desired.

In the passive sign convention, we defined the power delivered to the resistor as positive. We then say in order to calculate the power, we use P=VI, but we must take I as the current going into the positive voltage terminal. This is the "actual current" and will be positive. Hence we will always calculate a positive power as desired.

The direction of the actual current flows from a greater voltage potential in both conventions. It's just when it comes to calculating the power, we don't necessarily have to use the actual current depending on what sign we want for the power.

6. Mar 15, 2015

### milesyoung

The passive/active sign convention is a definition of what sign of the power corresponds to what direction of power flow. It doesn't involve any specific type of element or what the actual polarity and direction is of the voltage and current, respectively.

The passive sign convention states that the power $p$ is a positive quantity for power flowing into the element, which makes $p$ positive for passive elements.
The active sign convention states that the power $p$ is a positive quantity for power flowing out of the element, which makes $p$ positive for active elements.

Yes, since, for instance, if $v$ and $i$ are positive, then power is flowing out of the element, and $p = vi$ is indeed positive, so the references have been assigned according to the active sign convention.

For a resistor, but you should try to view it more abstractly. Convince yourself that the references are assigned correctly regardless of what the element is and what the values for $v$ and $i$ are.

Nature doesn't care about our conventions.

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