## Introduction to Electric power | Electric Power and sign Convention

The definition of voltage as work per unit charge lends itself very conveniently to the introduction of power. As we know power is defined as the work done per unit time. Thus, the power, P, either generated or dissipated by a circuit element can be represented by the following relationship:

Thus,

P = V I

The electrical power generated by an active element, or that dissipated or stored by a passive element, is equal to the product of the voltage across the element and the current flowing through it.

It is easy to verify that the units of voltage (joules/coulomb) times current (coulombs/second) are indeed those of power (joules/second, or watts). It is important to understand that, just like voltage, power is a signed quantity, and that it is necessary to make a distinction between positive and negative power.

This distinction can be understood with reference to Figure .1, in which a source and a load are shown side by side. The polarity of the voltage across the source and the direction of the current through it indicate that the voltage source is doing work in moving charge from a lower potential to a higher potential. On the other hand, the load is dissipating energy, because the direction of the current indicates that charge is being displaced from a higher potential to a lower potential. To avoid confusion with regard to the sign of power, the electrical engineering community uniformly adopts the passive sign convention, which simply states that the power dissipated by a load is a positive quantity (or, conversely, that the power generated by a source is a positive quantity).

Another way of phrasing the same concept is to state that if current flows from a higher to a lower voltage (+ to −), the power is dissipated and will be a positive quantity.

Fig.1 The passive sign convention

It is important to note also that the actual numerical values of voltages and currents do not matter: once the proper reference directions have been established and the passive sign convention has been applied consistently, the answer will be correct regardless of the reference direction chosen.