Passive sign convention

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 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; it is used for example in computer circuit simulation programs such as SPICE. 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.

The convention The passive sign convention states that in components in which the conventional current variable i is defined as entering the device through the terminal which is positive as defined by the voltage variable v, the power p and resistance r are given by

p = v i {\displaystyle p=vi\,} and r = v i {\displaystyle r={v \over i}\,}

In components in which the current i is defined such that positive current enters the device through the negative voltage terminal, power and resistance are given by

p = − v i {\displaystyle p=-vi\,} and r = − v i {\displaystyle r=-{v \over i}\qquad \,}

With these definitions, passive components (loads) will have p > 0 and r > 0, and active components (power sources) will have p < 0 and r < 0.

Explanation

Active and passive components In electrical engineering, power represents the rate of electrical energy flowing into or out of a given device (electrical component) or control volume. Power is a signed quantity; negative power represents power flowing in the opposite direction from positive power. A simple component (shown in these diagrams as a rectangle) is connected to the circuit by two wires, through which electric current passes through the device. From the standpoint of power flow, electrical components in a circuit can be divided into two types:

In a source or active component, such as a battery or electric generator, electric current (conventional current, flow of positive charges) is forced to move through the device in the direction of greater electric potential, from the negative to the positive voltage terminal. This is opposite to the direction of the force on the charges from the electric field. This increases the potential energy of the electric charges, so electric power flows out of the component into the circuit. Work must be done on the moving charges by some source of energy in the component, to make them move in this direction against the opposing force of the electric field E. In a load or passive component, such as a light bulb, resistor, or electric motor, the current moves through the device under the influence of the electric field E in the direction of lower electric potential, from the positive terminal to the negative. So work is done by the charges on the component; potential energy flows out of the charges; and electric power flows from the circuit into the component, where it is converted to some other form of energy such as heat or mechanical work. Some components can be either a source or a load, depending on the voltage or current through them. For example, a rechargeable battery acts as a source when used to supply energy but as a load when it is being recharged. A capacitor or an inductor acts as a load when it is storing energy in its electric or magnetic field from the external circuit, respectively, but as a source when it is releasing into the external circuit the stored energy from the electric or magnetic field. Since it can flow in either direction, there are two possible ways to define electric power; two possible reference directions: either power flowing into an electrical component or power flowing out of the component, which can be defined as positive. Whichever is defined as positive, the other will be negative. The passive sign convention arbitrarily defines power flowing into the component (out of the circuit) as positive, so passive components have "positive" power flow. In an AC (alternating current) circuit, the current and voltage switch direction with each half-cycle of the current, but the definitions above still apply. At any given instant, in nonreactive passive components, the current flows from the positive terminal to the negative, while in nonreactive active components, it flows the other direction. In addition, components with reactance (capacitance or inductance) store energy temporarily, so they act as sources or sinks in different parts of the AC cycle. For example, in a capacitor, when the voltage across it is increasing, the current is directed into the positive terminal, so the component is storing energy from the circuit in its electric field, while when the voltage is decreasing, the current is directed out of the positive terminal, so it is acting as a source, returning stored energy to the circuit. In a steady-state AC circuit, all the energy stored in reactances is returned within the AC cycle, so a pure reactance, a capacitor or inductor, neither consumes nor produces net power, neither a source nor a load.

Reference directions The power flow p and resistance r of an electrical component are related to the voltage v and current i variables by the defining equation for power and Ohm's law:

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