0195136047.pdf

1.1 ELECTRICAL QUANTITIES 13

into electric energy as in the case of a battery source, and solar energy converted into electric
energy as in the case of a solar-cell source. On the other hand, when current flows in the direction
of voltage drop, it implies that electric energy is transformed into nonelectric energy. Examples
include electric energy converted into thermal energy as in the case of an electric heater, electric
energy transformed into mechanical energy as in the case of motor load, and electric energy
changed into chemical energy as in the case of a charging battery.
Batteries and ac outlets are the familiar electric sources. These arevoltage sources.Anideal
voltage sourceis one whose terminal voltagevis a specified function of time, regardless of the
currentithrough the source. An ideal battery has a constant voltageVwith respect to time, as
shown in Figure 1.1.5(a). It is known as a dc source, becausei=Iis a direct current. Figure
1.1.5(b) shows the symbol and time variation for asinusoidal voltage sourcewithv=Vmcosωt.
The positive sign on the source symbol indicates instantaneous polarity of the terminal at the
higher potential whenever cosωtis positive. A sinusoidal source is generally termed an ac source
because such a voltage source tends to produce an alternating current.
The concept of anideal current source, although less familiar but useful as we shall see later,
is defined as one whose currentiis a specified function of time, regardless of the voltage across its
terminals. The circuit symbols and the correspondingi–vcurves for the ideal voltage and current
sources are shown in Figure 1.1.6.
Even though ideal sources could theoretically produce infinite energy, one should recognize
that infinite values are physically impossible. Various circuit laws and device representations or
modelsare approximations of physical reality, and significant limitations of the idealized concepts
or models need to be recognized. Simplified representations or models for physical devices are
the most powerful tools in electrical engineering. As for ideal sources, the concept of constantV
or constantIfor dc sources and the general idea ofvoribeing a specified function of time should
be understood.
When the source voltage or current is independent of all other voltages and currents, such
sources are known asindependent sources. There aredependentorcontrolled sources, whose

Source

Node b

Node a

Ground

i

+

−

+

−

Load

Figure 1.1.4Source–load combination.

+

−

0

v

V t

(a)

V

i

+

+

−

−

0

v

t

(b)

v = Vm cos ωt

−Vm

Vm

2 π/ω

i

Figure 1.1.5Voltage sources.(a)Ideal dc source (battery).(b)Ideal sinusoidal ac source.