Module No. 30

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Module # 30
Capacitor, Eddy Current & Lenz’s Law
Capacitor
The device which is used to store charge and electrical energy is
called capacitor. Thus, capacitors are devices commonly used in
electrical and electronic circuits because of their ability to store
energy in the form of electrostatic field.
A capacitor consists of two conducting plates, parallel to each
other. The two plates are separated by an insulating material such
as paper, mica, ceramic, plastic film or foil, glass, air etc. which is
called the dielectric. A dielectric is an insulating medium
separating charged surfaces. When a capacitor is connected to a
voltage source, electrons flow from the negative terminal to the
positive terminal. One plate acquires positive charge and the
other acquires negative charge. The electron flow in connecting
wire stops as soon as the plates have been charged to the same
voltage as the voltage source.
Construction
Fix two metallic plates A and B on insulated stands. Charge the
plate A positively in small steps. This can be done by rubbing a
glass rod against silk cloth and then touching it with the plate.

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This process may be repeated many times to increase the
amount of charge on the plate.
Fig: Parallel Plate Capacitor
This increases the potential of the plate A but cannot be
continued indefinitely. It will be noticed after a while that plate A
cannot be charged any more. The plate B is connected to the
earth. The amount of work done in carrying positive charge to the
plate A is converted into electrical potential energy. The other
plate will have negative charge due to induction. The positive and
negative charges hold each other. The system of these two plates
is called a capacitor. It is used to store charge and electric
energy. This capacitor is called a parallel plate capacitor as the
charge is stored on parallel plates. If an insulator such as glass,
mica etc. is introduced between the plates, then, its capacity to
store charge increases. It has also been observed that the
increase in the area of the plates of the capacitor or decrease in
the distance between the plates also increases its capacity to

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store charge. Thus, the capacity to store charge depends upon
the following factors.
(1) Nature of medium between the plates,
(2) Size of the plates, and
(3) Separation of the plates.
The stored electric energy in a capacitor can be utilized according
to the need. A capacitor is a very important component of
electrical appliances.
Capacitors in Parallel
When capacitors are connected in parallel, their equivalent
capacitance (Ce) is equal to the sum of their individual
capacitances.
Ce = C1 + C2 + C3
Capacitors in Series
When capacitors are connected in series, then reciprocal of the
equivalent capacitance is equal to the sum of the reciprocals of
individual capacitances.
1/Ce = 1/C1 + 1/C2 + 1/C3

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Capacity or Capacitance of a Capacitor and its Unit
When charge q is transferred to one of the plates of a capacitor,
then, the potential difference V between the plates also increases.
The charge q on the plate of the capacitor is directly proportional
to the electric potential difference V between them i.e.
q  V
OR
q = CV
Where, C is a constant, called capacity or capacitance of the
capacitor. Its value depends upon the area of the plates, the
distance between the plates and the medium between them.
If
V = 1 Volt
then
q = CV
becomes
q = C

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If the potential difference between the plates of a capacitor is 1
volt, then, the quantity of charge stored on its plates is equal to its
capacity or capacitance.
When a voltage is applied across the plates of a capacitor, it does
work on the capacitor in charging it thus providing energy to the
capacitor. Energy is released when the capacitor is discharged.
Let us assume that across the plates of a capacitor, the p.d.
increases from zero to V uniformly. Then, the charge on the
plates also increases uniformly from zero to Q coulombs. The
energy stored is equal to the work done by the applied p.d. As the
whole energy is not delivered at a p.d. of V volts, therefore, we
take the average p.d. during charge equal to V/2, so the work
done is
W = ½ V x Q= ½ V x CV = ½ CV2
Where, W is the work done in joules or energy stored, C is the
capacitance in farad.
Units for Capacitance
The unit of capacitance is called Farad. One farad is the
capacitance of a system in which one coulomb of charge is stored
when the potential difference is one volt.

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The unit most commonly used is the microfarad which is equal to
one-millionth of a farad.
I  F (1 micro farad) = 10-6
farad
Similarly,
I n F (1 nano farad) = 10-9
farad
A still smaller unit of capacitance is pico farad which is equal to
one millionth-millionth of a farad
I  F (1 micro micro farad) = 1 p F (1 pico farad) = 10-12
farad
Troubles in Capacitors
There are some troubles with capacitor i.e. it may open or short. In
both cases, it is useless because cannot store energy. Some other
causes to failure are
1 Leakage Current
2 Dielectric Loss
3 Mechanical or Thermal Shocks
4 High Humidity
5 Poor Assembly Technique

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Different Types of Capacitors
Capacitors may be divided into the following main types according
to the nature of the dielectric (insulating material between plates)
used.
Air Capacitors
This type generally consists of one set of fixed plates and another
set of movable plates. It is mainly used for radio work where it is
required to vary the capacitance.
Paper Capacitors
The electrodes consist of metal foils inter leaved with paper
impregnated with wax or oil and rolled into a compact form.
Mica Capacitors
This type consists either of alternate layers of mica and metal foil
clomped tightly together or of thin films of silver sputtered on the
two sides of a mica sheet. Due to its relatively high cost, this type
is mainly used in high frequency circuits when it is necessary to
reduce to a minimum the loss in the dielectric.
Ceramic Capacitors
The electrodes consist of metallic coatings on the opposite faces
of a thin disc or plate of ceramic material such as talc. This type of

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capacitor is mainly used in high frequency circuits subject to wide
variation of temperature.
Electrolytic Capacitors
The type most commonly used consists of two aluminum foils,
one with an oxide film and one without, the foils being interleaved
with a material such as paper saturated with a suitable electrolyte,
for example, ammonium borate. The aluminum oxide film is
formed on the one foil by passing it through an electrolytic bath of
which the foil forms the positive electrode. The finished unit is
assembled in a container, usually of aluminum, and sealed. The
oxide film acts as the dielectric. Electrolytic capacitors are mainly
used where very large capacitances are required.
Polycarbonate Capacitors
Polycarbonate is a development in the field of plastic insulating
materials. A film of polycarbonate is metallized with aluminum and
wound to form the capacitor elements. Such a capacitor has low
dielectric loss.
Charging of a Capacitor
When a capacitor is directly connected to a d.c. supply, its
charging current may be regarded as instantaneous. But if a
resistor of high value is joined in series, the charging rate is

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slowed down. Similarly, if a charged capacitor is joined to a
resistor, the time required to discharge it is prolonged.
Combinations of capacitors and resistors are often used where
time delay is required, as in the operation of traffic signals. We
can say that the flow of alternating current in the circuit is due to
charging and discharging of the capacitor.
Note that the power delivered by the source to the capacitor is
equal to the power returned to the source by the capacitor over a
cycle. When the capacitor voltage increases, energy is stored in
the dielectric field. When the capacitor voltage decreases, this
energy is released by the dielectric field. Thus, no energy is lost
during charging and discharging of capacitor.
Eddy Current & Eddy Current Loss
When alternating current flows through an inductance with an iron
core, a voltage is induced in the core also. The core is generally
made of iron which itself is a conductor. The induced voltage in
the core establishes a current in the core, known as eddy current.
The eddy current circulates in the core, and causes an I2
R loss in
the core, known as eddy-current loss, where I represents the
current and R is the core resistance. Eddy currents are produced in
iron core and thus it becomes hot. The losses are minimized by
using thin iron sheets insulated from one another. These are called

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laminations or stampings.
Thus, eddy currents heat the core and cause energy consumption
in the core. Therefore, it is necessary to reduce these currents to
a possible minimum value. To reduce eddy currents the magnetic
core is made up of thin sheets of iron, called the laminations.
These laminations are insulated from each other. It is to be noted
that the higher the frequency of the alternating current in the
inductance the greater the eddy current loss.
Core Loss
When hysteresis loss and eddy current loss are taken together,
they are called core loss. The core loss is present in dc as well as
in ac machines. Thus, eddy current loss and hysteresis loss
together are called core losses.
Copper Loss
Copper loss is due to the resistance of wire of which the coils are
made.
Magnetic Leakage Loss
The voltage drop due to magnetic leakage in a transformer is
minimized by winding the coils one upon the other.

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Transformer Losses
The losses in a transformer may be of various types, such as
copper loss, Eddy current loss, hysteresis loss and magnetic
leakage loss.
Hysteresis
Hysteresis is delay in the movement of the magnetic domains.
The domains encounter mechanical resistance (friction) as
they change position. As a result, they lag behind the changing
electrical field and produce heat loss.
Hysteresis Loss
As soft iron has smaller hysteresis loss than hard steel, hence the
cores of the transformers are generally made of soft iron (pure or
alloyed). It requires an expenditure of certain amount of energy to
reverse the magnetism, or realign the domains, in a piece of
ferromagnetic material. The energy lost due to hysteresis appears
as heat in magnetic material. For this reason, when transformers
using a.c in them are made with iron core, it is necessary to select
metals having narrow hysteresis loops and with little hysteric loss.
So, the core of transformer always heats a little because of
hysteresis loss.

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Superposition Theorem
The superposition theorem is useful in the analysis of linear
circuits with more than one source. It provides a method of
determining the current in any branch of a multi-source circuit. It
states that in a linear bilateral multi-source network, the current in
any branch is the sum of the currents produced by each source
acting alone, with all other sources replaced by their internal
resistances. The total current in any branch of the network is the
algebraic sum of the currents produced independently by each
source.
In a two-source network, if the current produced by one source is
in one direction, while that produced by the other is in the
opposite direction in the same branch, the resulting current is the
difference of the two and has the direction of the larger. If both the
currents are in the same direction, the resulting current is equal to
the sum of the two in the direction of either current.
The steps in applying the superposition theorem are as follows:
1 Leave one of the sources in the circuit and replace all others
by their internal resistances.
2. Find the current due to the one remaining source.
3. Repeat steps 1 and 2 for each source.

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4. Add all of the currents algebraically. If the currents are in the
same direction, add them. If the currents are in opposite
directions, subtract them.
Thevenin’s Theorem
Thevenin's theorem gives a method for reducing any circuit to an
equivalent circuit consisting of an equivalent voltage source in
series with an equivalent resistance. Thevenin's theorem states
that any two-terminal linear bilateral network can be replaced by
an equivalent circuit consisting of a voltage source and a series
resistor. This series combination is called the Thevenin equivalent
circuit.
The Thevenin's theorem states that any two terminal linear
bilateral network can be replaced by a single voltage source in
series with a single resistance. The source voltage is the voltage
between the two terminals with all the emf sources replaced by
their internal resistances and the series resistance is the
resistance of the network between the terminals.
Maximum power is transferred when Thevenin equivalent
resistance becomes equal to the load resistance.
Maximum Power Transfer Theorem
Maximum power transfer theorem states that the maximum power

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is transferred by a source when the load resistance equals the
internal resistance of the source.
OR
Maximum power transfer theorem states that a source delivers
maximum power to a load when the resistance of source is equal
to the resistance of the load.
Lenz’s Law
We now come to the question of determining the sign or direction
of the induced emf or current. H. E. F. Lenz, a German scientist,
enunciated a law which is known after his name. This law states:
“The direction of an induced current is such as to oppose the
cause producing it”.
The “cause” of the current may be the motion of a conductor in a
magnetic field, or it may be the change of flux through a stationary
conductor.
Lenz’s law is also directly related to energy conservation. When
we drag the loop of wire across the magnetic field, we do work
against the magnetic force arising from the inter-action of the
original magnetic field and that of the induced current and in doing
so we impart energy to the loop. This energy is the source of

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induced current. Thus, electromagnetic induction is exactly
according to the law of conservation of energy.
Inverse Square Law
The electromagnetic wave intensity from a point source in free
space is inversely proportional to the square of the distance from
the source.
Kirchhoff’s Current and Voltage Law
Kirchhoff’s current law states that current entering a junction is
equal to current leaving the junction or the algebraic sum of
currents directed toward and away from a node equals zero.
Kirchhoff’s voltage law states that the algebraic sum of voltages
around a closed loop equals zero or the sum of voltage drops
must equal the source voltage.
GAUSS'S LAW
The Gauss's Law may be stated as "The flux through any closed
surface is 1/εo time the total charge enclosed in it”.
Faraday (1791-1867)
In the later part of classical physics period (1700-1890 AD),
Faraday contributed a lot to the field of electricity. Faraday was

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the outstanding experimentalist of his time and Maxwell was the
most outstanding theoretical physicist of this period.
Faraday's Laws of Electromagnetic Induction
First Law
An EMF is induced in a circuit whenever we change the magnetic
flux passing through the circuit but the induced EMF remains only
of the time during which the flux is changed.
Second Law
The magnitude of the induced EMF is directly proportional to the
rate of change of magnetic flux passing through the circuit.
Explanation
Whenever there is a change in the magnetic flux linked with a
circuit, an electromotive force is induced, the strength of which is
proportional to the rate of change of the flux linked with the circuit.
Faraday’s law applies to any method for changing the flux through
a coil (i.e. mutual induction). It also tells us that any change in flux
through a coil will induce an emf in the coil. This means that when
a current through a coil changes, the coil induces an emf in itself
(i.e. self-induction).
We know that whenever the magnetic flux through a coil is

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changed, an induced emf is produced in it. This induced emf lasts
so long as the flux keeps changing. The moment the flux ceases
to change, the induced emf vanishes. It has also been observed
that the magnitude of the induced emf depends upon the rate of
change of flux through the coil. It was Michael Faraday who first
came to this conclusion. He found a mathematical relation
concerning the induced emf in the coil.
Faraday’s laws of electromagnetic induction state that when an
electric conductor cuts or moves across magnetic field, an emf is
induced in the conductor proportional to the rate of cutting.
If an amount of flux ΔΦ changes in time Δt through a coil of N
turns, then the average induced emf during this time is
E = -N (ΔΦ/Δt)
The negative sign indicates that the direction of induced emf is
such that it opposes the change in flux. This is known as
Faraday's law.
Following are the Faraday’s observations, known as Faraday's
laws of electromagnetic induction:
1. The amount of voltage induced in a coil is directly proportional
to the amount of flux change with respect to the coil.
2. The amount of voltage induced in a coil is directly proportional

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to the number of turns of the coil.
3. The voltage induced across a coil is proportional to the rate of
change of the magnetic flux.
James Clerk Maxwell (1831-1879)
In the later part of classical physics period (1700-1890 AD), the
most remarkable event is the resolution of the controversies about
the nature of light. Maxwell proposed his famous electromagnetic
wave theory of light which satisfied all parties to the controversy.
Maxwell was the outstanding theoretical Physicist of his time.
In the later part of classical physics period, people thought that
the science of physics was fully organized and well integrated
especially by the work of Maxwell, so that nothing was left to be
discovered by future physicists.
Thus, the most important development during nineteenth century
concerning the nature of light was the work of Maxwell, who, in
1873, showed that the light was a form of high frequency
electromagnetic waves. The theory predicts that these waves
should have a velocity of about 3 X108 ms-1. Within experimental
error, this value turned out to be equal to the velocity of light.

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Joule (1818-1889)
During the classical physics period (1700-1890 AD), in the field of
heat, Joule established that heat was merely a form of energy
which fitted very well into the Newtonian mechanics.
Joule (Unit of Energy)
A joule (J) is defined as the amount of work done, when a force of
one Newton acting on a body displaces it through a distance of 1
meter along the direction of force.
1 Joule= 1 newton x 1 meter
1 Kilo Joule =1000 joule = 103
J
1 mega joule = 1000000 joule = 106
J
1 ft-lb = 1.356 Joules or
1 Joule = 0.7375 ft-lb
As the unit of electric power is joule per second called the watt
(W), so, another name of the joule is the watt seconds.
The joule or watt-second is a very small unit of electrical energy
and for commercial purposes energy is measured in watt-hours
(Wh) or kilowatt-hours (kWh).
The kWh is also called a Board of Trade Unit (BOTU).
1 B.O.T. Unit =1kWh=1000Wh = 360000 Joules

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B.O.T Unit is a commercial unit and the same is being used for
electricity bills charging now-a-days by WAPDA / PEPCO / KESC,
etc. in Pakistan.
Joule's Law and Electric Energy
When a current passes through a resistance for a certain time,
then, the heat dissipated in the resistance is equal to the product
of the square of the current, resistance and time
It is commonly known as Joule's Law. This work is then changed
into heat energy.
Formula for Heat Dissipated
If the potential difference between two ends of a conductor is I
volt and charge of one coulomb flows between them, then, one
joule of energy in the form of work done is obtained, i.e.
1 Joule = 1 Volt x 1 Coulomb
This electrical energy is dissipated as heat. This relation is called
Joule's Law.
Factors for Dissipation of Heat
(1) In a conductor, the work done by electric current is
converted into energy. Due to this, the temperature of the
conductor increases and heat energy is released.

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(2) Quantity of heat is directly proportional to the square of the
current.
(3) Quantity of heat produced is directly proportional to the
resistance.
(4) Heat produced is directly proportional to the time.
Electrical Generators
A generator is a device, which converts mechanical energy into
electrical energy.
The principle of producing a voltage and a current by relative
motion of coil and magnetic field is the basis for electrical
generators.
Simple Loop Generator
A simple loop generator consisting of a single loop of wire placed
in a permanent magnetic field indicates a basic A.C. Generator.
The two end leads of copper coils are brought on separate solid
conductive rings called slip rings.
After one complete revolution of the loop, one full cycle of the sine
wave voltage is produced. As the loop continues to rotate,
repetitive cycles of the sine wave are generated.

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Electric Motor
An electric motor is a device which converts electrical energy into
mechanical energy. It is essentially a generator run backward.
Like a generator, a simple motor consists of a coil rotating in the
field produced by a magnet. This magnet is an electromagnet and
not a permanent magnet. The coil itself is wound on a soft iron
core to intensify the magnetic field resulting from the current
(passing) through it. The current carrying coil itself acts as a bar
magnet. Its strength increases many fold due to iron core.
When current is supplied to the coil by a battery, the torque acting
on the current carrying coil causes it to rotate. The commutators
reverse the current in the coil at the proper instant to produce a
continuous torque and as a result rotation continues.
We know that a current carrying conductor experiences a
mechanical force when placed in a magnetic field. This was a key
to convert electrical energy into mechanical energy and the
devices which convert electric energy into mechanical energy are
called electric motors.
The portion which rotates in a motor is called a rotor or Armature.
The speed of rotation of a magnet depends on the following
factors.
(1) The magnitude of current through the rotor.

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(2) The magnetic field strength of the magnet
(3) Number of turns in the coil of the rotor.
(4) Permeability of its armature.
Transformer
Basically a transformer depends for its proper functioning upon
the principle that energy may be transferred by electromagnetic
induction from one set of coils called primary to another set of
coils called secondary by means of a changing magnetism
provided that both sets of coils are linked magnetically by a
common magnetic path.
A transformer is a device which steps up or steps down ac
voltage. For example, in power transmission high voltage is
stepped down to 220 volts for domestic use with the help of the
transformer. The common door-bell requires a voltage of about 9
V, and a transformer is used to obtain this voltage from the usual
supply of 220 V.
Electrolytic Cell or Voltammeter
The apparatus consisting of vessel, electrolyte, electrodes, and so
on in which the electrolysis is carried out is called an electrolytic
cell or voltameter.

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Electrodes
The two wires or plates at which the current enters and leaves the
electrolyte are called electrodes.
Electrolysis
The process by which a substance is decomposed by the
passage of an electric current is called electrolysis.
Electrical Force
An electron revolves around the nucleus of an atom due to the
"electrical force". Matter is held together by the electrical forces.
Electron Volt (eV)
“One electron volt (eV) is the amount of energy acquired or lost by
an electron when it is displaced across two points between which
potential difference is one volt".
1eV = 1.60 x 10-19
J
However, this is a small unit of energy. The following bigger units
are in frequent use:
1 Million Electron Volt =1 Mega Electron Volt = 1MeV=106
eV
1 Billion Electron Volt = 1 Giga Electron Volt = 1GeV = 109
eV

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The unit of energy used in particle physics is the electronvolt (eV),
which is defined as the energy acquired by an electron (or a
proton) in moving through a potential difference of 1 volt.
Electric Polarization
When a dielectric is placed in an electric field in such a way that
the field is directed from up to downward direction, then under the
influence of this external field, negative charges appear on the
upper face (side) and positive charges on the lower side (face) of
the dielectric. The phenomenon is known as electric polarization
and dielectric is said to be polarized.

Module No. 30

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Module No. 30