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1
Basic Circuit Elements and Waveforms
1.1
INTRODUCTION
The phenomenon of transferring charge from one point in a circuit to another is termed as
“electric current”. An electric current may be defined as the rate of net motion of electric
charge q across a cross-sectional boundary. Random motion
of electrons in a metal does not constitute a current unless
there is a net transfer of charge. Since the electron has a
charge of 1.6021 × 10–19 coulomb, it follows that a current of 1
ampere corresponds to the motion of 1/(1.6021 × 10–19) = 6.24
× 1018 electrons per second in any cross-section of a path.
In terms of the atomic theory concept, an electric
current in an element is the time rate of flow of free electrons
in the element. The materials may be classified as
(i) conductors, where availability of free electrons is very large,
as in the case of metals; (ii) insulators, where the availability
of free electrons is rare, as in the case of glass, mica, plastics,
etc. Other materials, such as germanium and silicon, called
semiconductors, play a significant role in electronics.
Thermally generated electrons are available as free electrons
at room temperature, and act as conductors, but at 0 Kelvin
they act as insulator. Therefore, conductivity is the ability or
easiness of the path or element to transfer electrons. The
resistivity of the path is the resistance offerred to the passage
of electrons, i.e., resistance (resistivity) is the inverse of
conductance (conductivity).
1
Andrè-Marie Ampère (1775–
1836), a French mathematician and
physicist, was born in Lyon, France.
At that time the best mathematical
works were in Latin and Ampere
was keenly interested in mathematics, so he at the age of 12
mastered in Latin in a few weeks.
He was a brilliant scientist and a
prolific writer. He formulated the
laws of electromagnetics. He
invented the electromagnet and
ammeter. The unit of electric
current, was named in his honour,
the ampere.
2
NETWORKS AND SYSTEMS
In circuit analysis, we are concerned with the four basic manifestations of electricity,
namely, electric charge q(t), magnetic flux φ(t), electric potential v(t) and electric current i(t).
We assume that the reader is familiar with these concepts. There are four fundamental
equations of circuit analysis.
The current1 through a circuit element is the time
derivative of the electric charge q(t) i.e.,
i(t) =
d
q(t)
dt
(1.1)
The unit of charge is coulomb. The unit of current
i(t) is coulomb per second, which is termed ampere
(abbreviated A) in honour of the French physicist AndrèMarie Ampère (1775–1836).
The potential difference between the terminals of
a circuit element in a magnetic field is equal to the time
derivative of the flux φ(t), i.e.,
v(t) =
d
φ (t )
dt
(1.2)
The unit of potential is webers per second, which
is called volts in honour of the Italian physicist Alessandro
Volta (1745–1827).
Alessandro Giuseppe Antonio
Anastasio Volta (1745–1827), an
Italian physicist, was born in a noble
family in Como, Italy. Volta was
engaged himself in performing
electrical experiments at the age of 18.
His invention of the electric cell
(battery) in 1796 revolutionised the use
of electricity. Volta received many
honours during his lifetime. The unit
of voltage or potential difference, was
named in his honour, the volt.
Voltage is the energy required to move 1 coulomb of charge through an element, i.e.,
v(t) =
dw
dq
(1.3)
The instantaneous power p(t) delivered to a circuit element is the product of the
instantaneous value of voltage v(t) and current i(t) of the element.
p(t) = v(t) i(t)
(1.4)
The unit of power is watt in honour of the British inventor James Watt (1738–1819).
The energy delivered to a circuit element over the time interval (t0, t) is given by
E(t0, t) =
z
t
t0
p(x) dx =
z
t
t0