INTRODUCTION
Electric circuit theory and electromagnetic theory are the two fundamental
theories upon which all branches of electrical engineering are built.
Many branches of electrical engineering, such as power, electric machines,
control, electronics, communications, and instrumentation, are
based on electric circuit theory. Therefore, the basic electric circuit theory
course is the most important course for an electrical engineering
student, and always an excellent starting point for a beginning student
in electrical engineering education. Circuit theory is also valuable to
students specializing in other branches of the physical sciences because
circuits are a good model for the study of energy systems in general, and
because of the applied mathematics, physics, and topology involved.
In electrical engineering, we are often interested in communicating
or transferring energy from one point to another. To do this requires an
interconnection of electrical devices. Such interconnection is referred to
as an electric circuit, and each component of the circuit is known as an
element.
An electric circuit is an interconnection of electrical elements.
Our goal in this text is to learn various analytical techniques and computer
software applications for describing the behavior of a circuit like this.
Electric circuits are used in numerous electrical systems to accomplish
different tasks. Our objective in this book is not the study of various
uses and applications of circuits. Rather our major concern is the analysis
of the circuits. By the analysis of a circuit, we mean a study of the
behavior of the circuit: How does it respond to a given input? How do
the interconnected elements and devices in the circuit interact?
We commence our study by defining some basic concepts. These
concepts include charge, current, voltage, circuit elements, power, and
energy. Before defining these concepts, we must first establish a system
of units that we will use throughout the Aritcle
CHARGE AND CURRENT
The concept of electric charge is the underlying principle for explaining
all electrical phenomena. Also, the most basic quantity in an electric
circuit is the electric charge. We all experience the effect of electric
charge when we try to remove our wool sweater and have it stick to our
body or walk across a carpet and receive a shock.
Charge is an electrical property of the atomic particles of which
matter consists, measured in coulombs (C).
We know from elementary physics that all matter is made of fundamental
building blocks known as atoms and that each atom consists of electrons,
protons, and neutrons. We also know that the charge e on an electron is
negative and equal in magnitude to 1.602×10−19 C, while a proton carries
a positive charge of the same magnitude as the electron. The presence of
equal numbers of protons and electrons leaves an atom neutrally charged.
The following points should be noted about electric charge:
- 1. The coulomb is a large unit for charges. In 1 C of charge, there are 1/(1.602 × 10−19) = 6.24 × 1018 electrons. Thus realistic or laboratory values of charges are on the order of pC, nC, or μC.
- 2. According to experimental observations, the only charges that occur in nature are integral multiples of the electronic charge e = −1.602 × 10−19 C.
- 3. The law of conservation of charge states that charge can neither be created nor destroyed, only transferred. Thus the algebraic sum of the electric charges in a system does not change.We now consider the flow of electric charges. A unique feature of electric charge or electricity is the fact that it is mobile; that is, it can be transferred from one place to another, where it can be converted to another form of energy.
When a conducting wire (consisting of several atoms) is connected
to a battery (a source of electromotive force), the charges are compelled
to move; positive charges move in one direction while negative charges
move in the opposite direction. This motion of charges creates electric
current. It is conventional to take the current flow as the movement of
positive charges, that is, opposite to the flow of negative charges, Although we now
know that current in metallic conductors is due to negatively charged
electrons, we will follow the universally accepted convention that current
is the net flow of positive charges.
CURRENT
Electric current is the time rate of change of charge, measured in amperes (A).
Electric current is the time rate of change of charge, measured in amperes (A).
Mathematically, the relationship between current i, charge q, and time t
is
i = dq/dt
where current is measured in amperes (A), and
1 ampere = 1 coulomb/second
The charge transferred between time t0 and t is obtained by integrating
both sides of Eq. (1.1). We obtain
Theway we define current as i in Eq. (1.1) suggests that current need not
be a constant-valued function. As many of the examples and problems in
this chapter and subsequent chapters suggest, there can be several types
of current; that is, charge can vary with time in several ways that may be
represented by different kinds of mathematical functions.
If the current does not change with time, but remains constant, we
call it a direct current (dc).
A direct current (dc) is a current that remains constant with time.
By convention the symbol I is used to represent such a constant current.
A time-varying current is represented by the symbol i. A common
form of time-varying current is the sinusoidal current or alternating
current (ac).
An alternating current (ac) is a current that varies sinusoidally with time.
Such current is used in your household, to run the air conditioner, refrigerator,
washing machine
Example:
The total charge entering a terminal is given by q = 5t sin 4πt mC. Calculate
the current at t = 0.5 s.
Solution:
i = dq/dt
= d/dt{(5t sin 4πt) mC/s = (5 sin 4πt + 20πt cos 4πt) }mA
At t = 0.5,
i = 5 sin 2π + 10π cos 2π = 0 + 10π = 31.42 mA
VOLTAGE:
To move the electron in a conductor in a particular direction requires some work or energy transfer.
This work is performed by an
external electromotive force (emf),
The voltage vab between two points a and b in
an electric circuit is the energy (or work) needed to move a unit charge
from a to b; mathematically,
V = dw/dq
where w is energy in joules (J) and q is charge in coulombs (C). The
voltage vab or simply v is measured in volts (V), named in honor of the
Italian physicist Alessandro Antonio Volta (1745–1827), who invented
the first voltaic battery. it is evident that
1 volt = 1 joule/coulomb = 1 newton meter/coulomb
Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V).
POWER & ENERGY
Although current and voltage are the two basic variables in an electric circuit, they are not sufficient by themselves. For practical purposes, we need to know how much power an electric device can handle
Power is the time rate of expending or absorbing energy, measured in watts (W).
p = dw/dt
p = dw/dt = (dw/dq)*(dq/dt)
P=VI watts
- Passive sign convention is satisfied when the current enters through the positive terminal of an element and p = +vi.
- If the current enters through the negative terminal, p = −vi.
Energy
Energy is the capacity to do work, measured in joules ( J).
The electric power utility companies measure energy in watt-hours (Wh),
where
1 Wh = 3,600 J
E = I^2Rt
Example
How much energy does a 100-W electric bulb consume in two hours?
Solution:
w = pt = 100 (W) × 2 (h) × 60 (min/h) × 60 (s/min)
= 720,000 J = 720 kJ
This is the same as
w = pt = 100 W× 2 h = 200 Wh