APPLIED ELECTRICITY-I
GET 225
Chapter 5: Capacitors & Inductors
Course Instructor: Ahmad A. Galadima
1 1/3/2023
Outline
1. Introduction
2. Capacitors
3. Inductors
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1. Introduction
So far we have limited our study to resistive circuits
We shall introduce two new and important passive linear
circuit elements: the capacitor and the inductor.
Unlike resistors, which dissipate energy, capacitors and
inductors do not dissipate but store energy, which can be
retrieved at a later time.
The application of resistive circuits is quite limited. With the
introduction of capacitors and inductors in this chapter, we
will be able to analyze more important and practical circuits.
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2. Capacitors
A capacitor is a passive element designed to store energy in
its electric field.
Besides resistors, capacitors are the most common electrical
components.
Capacitors are used extensively in electronics,
communications, computers, and power systems.
For example, they are used in the tuning circuits of radio
receivers and as dynamic memory elements in computer
systems.
Fig 1. Circuit symbols for capacitor (a) Fixed Capacitor (b)
4 1/3/2023 Variable Capacitor
Capacitors (Cont’d)
A capacitor consists of two conducting plates separated by an insulator (or dielectric).
In many practical applications, the plates may be aluminum
foil while the dielectric may be air, ceramic, paper, or mica.
When a voltage source is connected to the capacitor the
source deposits a positive charge q on one plate and a
negative charge on the other.
5 1/3/2023 Fig 2. A typical capacitor Fig 3. A capacitor with
applied voltage v
Dielectric Strength of some
materials
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Capacitors (Cont’d)
The amount of charge stored, represented by q, is directly
proportional to the applied voltage so that:
where C, the constant of proportionality, is
known as the capacitance of the capacitor.
Capacitance is the ratio of the charge on one plate of a capacitor to the voltage
difference between the two plates, measured in farads (F).
where A is the surface area of each plate, d is the
distance between the plates, and ε is the
permittivity of the dielectric material between the
plates.
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Current-voltage relationship
In addition, capacitors are used to block dc, pass ac, shift phase,
store energy, start motors, and suppress noise.
To obtain the current-voltage relationship of the capacitor, we
take the derivative of both sides of q=Cv:
Fig 4 Current-voltage
relationship of a
capacitor
This is the current-voltage relationship for a capacitor,
assuming the passive sign convention.
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Power
The voltage-current relation of the capacitor can be
obtained by integrating both sides:
The instantaneous power delivered to the capacitor is:
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Properties of a Capacitor
The voltage across a capacitor is not changing with time
(i.e., dc voltage), the current through the capacitor is zero.
A capacitor is an open circuit to dc
The voltage on the capacitor must be continuous.
The voltage on a capacitor cannot change abruptly
The ideal capacitor does not dissipate energy. It takes power
from the circuit when storing energy in its field and returns
previously stored energy when delivering power to the
circuit.
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Examples
1.
2.
3.
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Example
4.
5.
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1.
Examples
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Examples
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Examples
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4.
Example
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5.
Example
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5.
Example
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Series and Parallel Capacitors
The equivalent capacitance of N parallel-connected capacitors is the sum of the
individual capacitances.
Fig. 5. Parallel-connected N capacitors Fig 6 Series-connected N capacitors
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Example
5. Find the equivalent capacitance seen at the terminals of the
circuit in:
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3. Inductors
An inductor is a passive element designed to store energy in
its magnetic field.
Inductors find numerous applications in electronic and
power systems. They are used in power supplies,
transformers, radios, TVs, radars, and electric motors.
Any conductor of electric current has inductive properties
and may be regarded as an inductor.
21 1/3/2023 Fig. Circuit symbols for inductors: (a) air-core,
(b) iron-core, (c) variable iron-core
Inductors (Cont’d)
An inductor consists of a coil of conducting wire.
where L is the constant of proportionality called
the inductance of the inductor.
Inductance is the property whereby an inductor exhibits opposition to the
change of current flowing through it, measured in henrys (H).
where N is the number of turns, is the length, A
is the cross-sectional area, and μ is the
permeability of the core.
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Current-voltage relationship
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Properties of an Inductor
The voltage across an inductor is zero when the current is
constant.
An inductor acts like a short circuit to dc.
An important property of the inductor is its opposition to the
change in current flowing through it.
The current through an inductor cannot change instantaneously
Like the ideal capacitor, the ideal inductor does not dissipate
energy. The energy stored in it can be retrieved at a later
time.
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Examples (Inductors)
1.
2.
3. Consider the circuit below. Under dc conditions, find: (a) i, Vc and
iL (b) the energy stored in the capacitor and inductor.
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Series and Parallel Inductors
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Example
Calculate the equivalent inductance for the inductive ladder
network below
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Characteristics of Basic Elements
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Summary
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Summary
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Reference
Fundamentals of electric circuits / Charles K. Alexander, Matthew N.
O. Sadiku. — 4th ed.
Introductory Circuit Analysis 10e (Prentice, 2002) –Boylestad
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