# Defining Reference Directions for Voltage and Power (sign convention)

My professor decided to use the above reference directions when calculating power in circuits. He says that when power > 0, power is consumed. When p < 0, power is generated.

This definition is counter intuitive to what I would have assigned--I would have said negative means power is consumed and positive power means power is generated.

So my question is this: Are these sign conventions actually what is happening physically? In other words, when you look at the diagrams above, what determines (or what are the formal conditions based on the parameters above) that a system is generating or consuming power?

Do we understand it like this: On the left diagram, charge is flowing from "high" to "low" potential so charge is being used. And on the right, charge is flowing in its "opposite" direction so power is being generated?

• "[...] so charge is being used" Charge is not used/wasted in a series connection (although it can be stored temporarily in capacitors)! Don't confuse charge with energy. They are different properties, and are measured in different units. A given object has a certain charge, energy, mass... – Alejandro Nava Feb 6 at 18:26

Consider a resistor. Label one terminal "+" and the other one "-".

When current flows in to the + terminal (like in your left-hand diagram), Ohm's law tells us that the voltage at the + terminal is higher than at the - terminal and the value is given by $V=IR$.

And we know that in this situation, electrical power is consumed by the resistor and turned into thermal power.

Conversely, when a battery turns chemical energy into electrial energy and delivers it to the rest of the circuit, current flows out of the more positive terminal of the battery.

Of course this is just a convention. We could have defined current with the opposite sign (for example, we could have defined current in the direction of negative charge flow), and then we'd have the opposite result: When negative charge flows from + to - in a resistor, the voltage would be negative, giving a negative product of voltage and "current", but the resistor would still be consuming electrical power.

Assuming $i_1$ and $v_1$ are both positive or negative (such that their product is positive) then positive charge enters the more positive terminal and exits the the more negative terminal; the charge exits the device at a lower potential

Thus, the charge has less potential energy after passing through the device and so energy is delivered to the device.

If, on the other hand, either $i_1$ or $v_1$ is negative (such that their product is negative), the charge exits the device at a higher potential and so, the device is supplying energy.

For further reading, see the Wikipedia article "Passive Sign Convention".

The convention defines electric power flowing out of the circuit into an electrical component as positive, and power flowing into the circuit out of a component as negative. So a passive component which consumes power, such as an appliance or light bulb, will have positive power dissipation, while an active component, a source of power such as an electric generator or battery, will have negative power dissipation. This is the standard definition of power in electric circuits.

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. These directions may be different from the directions of the actual current flow and voltage.

When we discuss power in the general physics sense, we mean the rate at which energy is transferred from one system to another, or possibly one form to another. The sign convention your professor specified is very common, and yields the power consumed by the device, taking energy out of the charge flow system and putting it somewhere else at a certain rate. This somewhere else might be internal energy of a resistor, or energy of the EM field of a transformer or capacitor or inductor, etc. In this convention, a negative number for the power means that energy is being transferred into the charge flow system.

The nice thing about allowing for negative power consumption is that for closed circuit systems (i.e., all sources and sinks are shown in the circuit diagram), the total power consumed is zero, so you can check your solutions of voltages and currents.