Page 198 - The Mechatronics Handbook

FIGURE 11.4 Sources and loads in an electrical circuit.

One may think of the work done in moving a charge from point a to point b and the work done
moving it back from b to a as corresponding directly to the voltages across individual circuit elements. Let
Q be the total charge that moves around the circuit per unit time, giving rise to the current i. Then the
work done in moving Q from b to a (i.e., across the battery) is

W ba = Q × 1.5 V (11.7)
Similarly, work is done in moving Q from a to b, that is, across the light bulb. Note that the word potential
is quite appropriate as a synonym of voltage, in that voltage represents the potential energy between two
points in a circuit: if we remove the light bulb from its connections to the battery, there still exists a
voltage across the (now disconnected) terminals b and a.
A moment’s reflection upon the significance of voltage should suggest that it must be necessary to
specify a sign for this quantity. Consider, again, the same dry-cell or alkaline battery, where, by virtue of
an electrochemically induced separation of charge, a 1.5-V potential difference is generated. The potential
generated by the battery may be used to move charge in a circuit. The rate at which charge is moved
once a closed circuit is established (i.e., the current drawn by the circuit connected to the battery) depends
now on the circuit element we choose to connect to the battery. Thus, while the voltage across the battery
represents the potential for providing energy to a circuit, the voltage across the light bulb indicates the
amount of work done in dissipating energy. In the first case, energy is generated; in the second, it is
consumed (note that energy may also be stored, by suitable circuit elements yet to be introduced). This
fundamental distinction required attention in defining the sign (or polarity) of voltages.
We shall, in general, refer to elements that provide energy as sources, and to elements that dissipate
energy as loads. Standard symbols for a generalized source-and-load circuit are shown in Fig. 11.4.
Formal definitions will be given in a later section.

Electric Power and Sign Convention

The definition of voltage as work per unit charge lends itself very conveniently to the introduction of
power. Recall that 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:
work work charge
Power = ------------ = ------------------------------------------ = voltage × current (11.8)
time unit charge time
Thus, 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.
P = VI (11.9)
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).

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