Introduction

The fundamental principles to understand charges either positive or negative are

coulomb’s law. If a charge particle moves then it results as current.
Electricity has an important role in modern society. In a span of more than 900 years,
electricity convenient and widely used forms of energy in the world. One of the practical
advantages of electricity as a form of energy is that it can readily transmitted over
considerable distances with relatively small loss in energy.
This makes it possible to supply electricity from a central generating plant to any location.
A type of energy fueled by the transfer of electrons from positive and negative points
within a conductor. Electricity is widely used for providing power to buildings, electric
devices, and even some automobiles.
A number of individuals are responsible for the development of electricity, but the most
notable one is Benjamin Franklin and his flying kite experiment. Franklin was able to
determine that lightning was a form of electrical discharge. Electricity are of two types as
listed here under:

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 • Static Electricity
• Current Electricity
STATIC ELECTRICITY
A Physical phenomenon produced due to charges at rest is known as static electricity.

E.g. When we rub a glass rod with silk the glass rod gets positive charge on it and equal
and opposite charge (i.e. the -ve charge) gets developed on the silk. Similarly, on a
rubbing an ebonite rod with the fur of a cat the ebonite rod gets negative charge on it and
equal and opposite charge (i.e. the +ve charge) gets developed on the fur of a cat.

CURRENT ELECTRICITY:
A Physical phenomenon produced due to charges in motion is known as current
electricity. e.g. electric current we use in our houses is current electricity.

Now we will understand how these charges produced electricity.

Potential difference

• The potential difference between the two conductors equals the work done in
transferring the charging unit from one conductor to the other using a metal wire.
• V=W/q

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 • It is a scalar quantity. Its SI unit is volt (V).
• The potential difference between the two points is 1 volt if the work done on
transferring 1 coulomb of charge from one point to another is 1 joule.

Electrical Resistance
• There are always obstacles to the current flowing in the conductor, like a metal
wire, which is called electrical resistance.
• According to Ohm's law, if the current I flow to a wire where the potential difference
in the ends of the wire is V, then the resistance provided by the wire is.
• Resistance (R) = Potential difference in all wires (V) / Current flow in wire (l)

Frequently Asked Question (FAQs)

Q1. Define electric cell?

Ans. It is an electric device that converts chemical energy into electrical energy when it
sends current in a circuit.

Q2. Name the constituents of a cell?

Ans. A cell constitutes of the following:

1. Two electrodes
2. An electrolyte in a vessel

Q3. What is a secondary cell?

Ans. Secondary cells or accumulators provide current as a result of a chemical reaction.

The chemical reaction is reversible in these cells and can be recharged after use. One
such cell is a Lead accumulator.

Q4. Define the term potential difference?

Ans. The potential difference between two conductors equals the work done in
transferring a positive unit charge from one conductor to the other. It is a scalar quantity.

Q5. State Ohm’s law?

Ans. Ohm’s law states that if a current I flows through a wire when the potential difference
across the ends of the wire is V, the resistance offered by the wire to the flow of current
is the ratio of potential difference across it to the current flowing in it.

Q6. What do you mean by efficient use of energy?

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 Ans. It means reducing the cost and amount of energy used to provide various products
and services.

CONDUCTORS AND INSULATORS

The force between two charges is directly proportional to the product of two
charges q1,q2 and inversely proportional to the square of distance (r) between them

, where K is constant of proportionality.

• Electric charges can neither be destroyed nor be created.

• (Charges are additive i.e. total charge is the algebraic sum of the individual
charges.

Coulomb’s law says that force of attraction between two charged particles includes when
distance between both the charges decreases and both the charge value include force
will increase

PROPERTIES OF ELECTRIC CHARGE

The unit of electric charge is coulomb and 1 coulomb is the charge contained in 6 × 10–
18 electrons. Unlike (opposite) charges attract each and like (similar) charges repel each
other. A law stating that like charges repels and opposite charges attract, with a force
proportional to the product of the charges and inversely proportional to the square of the
distance between them.

CONDUCTORS AND INSULATORS

CONDUCTORS:

The behavior of an object that has been charged is dependent upon whether the object
is made of a conductive or a nonconductive material. Conductors are materials that allow
electrons to flow freely from atom to atom and molecule to molecule. An object made of
a conducting material will permit charge to be transferred across the entire surface of the
object. If charge is transferred to the object at a given location, that charge is quickly
distributed across the entire surface of the object. The distribution of charge is the result
of electron movement. Since conductors allow for electrons to be transported from particle
to particle, a charged object will always distribute its charge until the overall repulsive
forces between excess electrons is minimized. If a charged conductor is touched to
another object, the conductor can even transfer its charge to that object. The transfer of
charge between objects occurs more readily if the second object is made of a conducting
material. Conductors allow for charge transfer through the free movement of electrons.

All the metals like silver, copper and aluminum etc., are conductors. Carbon, in the form
of graphite, is a conductor and the aqueous solutions (water solutions) of salts are also

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 conductors. The human body is a fairly good conductor. All the conductors (like metals)
have some electrons which are loosely held by the nucleus of their atoms. These
electrons are called "free electrons" and can move from one atom to another atom
throughout the conductor. The presence of "free electrons" in a substance makes it a
conductor of electricity.

INSULATORS:

Substances through which electric charges cannot flow, are called insulators. In other
words, those substances through which electricity cannot flow, are called insulators.
Glass, ebonite, rubber, most of the plastics, paper, dry wood„ cotton, mica, bakelite, and
dry air, are all insulators because they do not allow electric charges (or electricity) to flow
through them. In the case of charged insulators like glass, ebonite etc., The electrons
present in insulators are strongly held by the nuclei of their atoms. Since there are "no
free electron" in an insulator which can move from one atom to another, so an insulator
does not allow electric charges (or electricity) to flow through it.

Insulators are materials that impede the free flow of electrons from atom to atom and
molecule to molecule. If charge is transferred to an insulator at a given location, the
excess charge will remain at the initial location of charging. The particles of the insulator
do not permit the free flow of electrons; subsequently charge is seldom distributed evenly
across the surface of an insulator.

While insulators are not useful for transferring charge, they do serve a critical role in
electrostatic experiments and demonstrations. Conductive objects are often mounted
upon insulating objects. This arrangement of a conductor on top of an insulator prevents
charge from being transferred from the conductive object to its surroundings. The
insulator serves as a handle for moving the conductor around on top of a lab table. If
charging experiments are performed with aluminum pop cans, then the cans should be
mounted on top of Styrofoam cups. The cups serve as insulators, preventing the pop cans
from discharging their charge. The cups also serve as handles when it becomes
necessary to move the cans around on the table.

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 SEMICONDUCTORS:

Those substances whose conductivity lies in between that of the conductors and
insulators are called semi-conductors.

For eg : Silicon, germanium are semi-conductors.

We have already learnt about flow of charges that produce electricity.

ELECTRIC CIRCUIT AND ITS COMPONENTS

All electrical appliances like lamps, heaters and air-conditioners, which work on electricity,
are called Loads.
To pass electric current through any 'Load', it has to be connected to a source of electric
power through wires called conductors.

A source of electric power (battery), loads and switches connected together through wires
form an Electric Circuit.

There are many components or elements of an electric circuit:

Connecting wires: They are also called conductors.

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 Resistors, Rheostats: It consists of wires made of Manganin and constantan alloys.
Resistors provide fixed resistance whereas rheostats provide variable resistance.

Resistor Rheostat
Battery: It is a combination of two or more cells.

Galvanometer: It is a device used for detecting flow of current.

Ammeter: Also called as ampere-meter, it is used to measure current. It is always placed

in series with the circuit.

Voltmeter: Used for measuring potential difference. It is always connected in parallel

across the circuit.

Closed electric circuit: In this, key is closed and current flows in the circuit continuously.

Open electric circuit: In this, key is open and no current flows in the circuit.

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 Wires crossing without joining

An electric cell

Electric bulb

EARTHING

Earthing means to connect the metal case of electrical appliance to the earth (at zero
potential) by means of a metal wire called "earth wire". In household circuits, we have
three wires, the live wire, the neutral wire and the earth wire. One end of the earth wire is
buried in the earth. We connect the earth wire to the metal case of the electrical appliance
by using a three-pin plug. The metal casing of the appliance will now always remain at
the zero potential of the earth. We say that the appliance has been earthed or grounded.

If, by chance, the live wire touches the metal case of the electric iron (or any other
appliance) which has been earthed, then the current passes directly to the earth through
the earth wire. It does not need our body to pass the current and therefore, we do not get
an electric shock. Actually, a very heavy current flows through the earth wire and the fuse
of household wiring blows out or melts. And it cuts off the power supply. In this way,
earthing also saves the electrical appliance from damage due to excessive current.

COLOUR CODING OF WIRES:

An electric appliance is provided with a three-core flexible cable. The insulation on the
three wires is of different colours. The old convention is red for live, black for neutral and
green for earth.
The new International convention is brown for live, light blue for neutral and green (or
yellow) for earth.

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 Function Wire Color
Line Brown or Coax
Ground Black (Violet in SIE)
+300 Volts (Downhole Power) Red
-300 volts (Downhole Power) Blue
+12 Volts Orange
-12 Volts Yellow
+24 Volts Red
-24 Volts Violet
120 Vac Line Voltage, "Hot" Grey
120 Vac Line Voltage, "Neutral" White
Less Standardized Wire Color
Plate Leads, FET Drain Blue
Transistor Base, Diodes Green
Transistor Base 2 Orange
Emitters, Cathode Yellow
Bias Supply White

GALVANOMETER:
A galvanometer is an instrument that can detect the presence of current in a circuit. The
pointer remains at zero (the center of the scale) for zero current flowing through it. It can
deflect either to the left or to the right of the zero-mark depending on the direction of
current.

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 Galvanometers are of two types:
• Moving coil galvanometer
• Moving magnet galvanometer

It is used to make ammeter and voltmeter as follows:

(A) Ammeter:

Ammeter is an electrical instrument which measures the strength of current in 'ampere' in

a circuit which is always connected in series in circuit so that total current (to be
measured) may pass through it. The resistance of an ideal ammeter is zero (practically it
should be minimum).

Conversion of Galvanometer into Ammeter

(B) Voltmeter:

It is an electrical instrument which measures the potential difference in 'volt' between two
points of electric circuit. The only difference between ammeter and voltmeter is that

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 ammeter has a negligible (approximately zero) resistance so that it may measure current
of circuit passing through it more accurately giving the deflection accordingly, while the
voltmeter passes negligible current through itself so that potential difference developed
due to maximum current passing through circuit may be measured.

Voltmeter has a very high resistance and the resistance of an ideal voltmeter is infinite. A
voltmeter is always connected in parallel.

ELECTRIC CHARGE

Electric charge, basic property of matter carried by some elementary particles. Electric
charge, which can be positive or negative, occurs in discrete natural units and is neither
created nor destroyed.

When we rub our shoes across a carpet and reach for a metal doorknob, we can be
zapped by a spark of electricity. The answers to this lies in the branch of Physics called
Electrostatics. The word electricity comes from the Greek word electron, which means
"amber." Amber is petrified tree resin, and it was well known to the ancients that if we rub
an amber rod with a piece of cloth, the amber attracts small pieces of dry leaves or paper.
A piece of hard rubber, a glass rod or a plastic comb rubbed with cloth also display this
"amber effect" or static electricity or frictional electricity as we call it today.

Experiments show that there are exactly two kinds of electric charges:

• Negative charge
• Positive charge

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 These also show that unlike charges attract each other while like charges repel each
other. The S.I. unit of electric charge is coulomb. It is denoted by symbol C.

Electrons
Electrons are the smallest and lightest of the particles in an atom. Electrons are in
constant motion as they circle around the nucleus of that atom. Electrons are said to have
a negative charge, which means that they seem to be surrounded by a kind of invisible
force field. This is called an electrostatic field.

Protons
Protons are much larger and heavier than electrons. Protons have a positive electrical
charge. This positively charged electrostatic field is exactly the same strength as the
electrostatic field in an electron, but it is opposite in polarity. Notice the negative electron
(pictured at the top left) and the positive proton (pictured at the right) have the same
number of force field lines in each of the diagrams. In other words, the proton is exactly
as positive as the electron is negative.

Like charges repel, unlike charges attract

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 Two electrons will tend to repel each other because both have a negative electrical
charge. Two protons will also tend to repel each other because they both have a positive
charge. On the other hand, electrons and protons will be attracted to each other because
of their unlike charges.

Since the electron is much smaller and lighter than a proton, when they are attracted to
each other due to their unlike charges, the electron usually does most of the moving. This
is because the protons have more mass and are harder to get moving. Although electrons
are very small, their negative electrical charges are still quite strong. Remember, the
negative charge of an electron is the same as the positive electrical charge of the much
larger in size proton. This way the atom stays electrically balanced.

Another important fact about the electrical charges of protons and electrons is that the
farther away they are from each other, the less force their electric fields have on each
other. Similarly, the closer they are to each other, the more force they will experience
from each other due to this invisible force field called an electric field.

PROPERTIES OF ELECTRIC CHARGE

The unit of electric charge is coulomb and 1 coulomb is the charge contained in 6 × 10–
18 electrons. Unlike (opposite) charges attract each and like (similar) charges repel each
other. A law stating that like charges repels and opposite charges attract, with a force
proportional to the product of the charges and inversely proportional to the square of the
distance between them.

ELECTRIC CURRENT
The electric current is a flow of electric charges (called electrons) in a conductor. The
magnitude of electric current in a conductor is the amount of electric charge passing
through a given point of the conductor in one second. If a charge of Q coulombs flows
through a conductor in time t seconds, then the magnitude of the electric current I flowing
through it is given by:

The unit of charge, in S.I. system is coulomb, which is equivalent to the charge of nearly
6.25 × 1018 electrons. If charge is measured in coulomb, then the flow of 1
coulomb/second gives us the unit of current, which is called Ampere named in the honor
French scientist, Andre - Marie Ampere (1775 – 1836).

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 UNIT OF ELECTRIC CURRENT
SI unit of current is Ampere (A)

1 Ampere =

Therefore, 1 ampere of current is said to be flowing through the conductor if one coulomb
of charge flows through it in one second.

1 mA (milliampere) = A

1μA (microampere) = A

DIRECTION OF ELECTRIC CURRENT:

When electricity was invented, it was known that there are two types of charges: positive
charges and negative charges, but the electron had not been discovered at that time. So,
electric current was considered to be a flow of positive charges and the direction of flow
of the positive charges was taken to be the direction of electric current. Thus, the
conventional direction of electric current is from positive terminal of a cell (or battery) to
the negative terminal through the circuit.

Figure showing direction of flow of conventional current

Ben Franklin, who conducted extensive scientific studies in both static and current
electricity, envisioned positive charges as the carriers of charge. As such, an early
convention for the direction of an electric current was established to be in the direction
that positive charges would move. The convention has stuck and is still used today.
The direction of an electric current is by convention the direction in which a positive
charge would move. Thus, the current in the external circuit is directed away from the
positive terminal and toward the negative terminal of the battery. Electrons would actually

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 move through the wires in the opposite direction. Knowing that the actual charge carriers
in wires are negatively charged electrons may make this convention seem a bit odd
and outdated. Nonetheless, it is the convention that is used worldwide and one that a
student of physics can easily become accustomed to.

HOW THE CURRENT FLOWS IN A WIRE:

As electric current is the flow of electrons in a metal wire (or conductor) when a cell or
battery is connected across its ends. A metal wire has plenty of free electrons in it. When
the metal wire has not been connected to a source of electricity like a cell or a battery,
then the electrons present in it move at random in all the directions between the atoms of
the metal wire as shown in figure.

When a source of electricity like a cell or a battery is connected between the ends of the
metal wire, then an electric force acts on the electrons present in the wire. Since the
electrons are negatively charged, they start moving from negative end to the positive end
of the wire and this flow of electrons constitutes the electric current in the wire.

HOW TO GET A CONTINUOUS FLOW OF ELECTRIC CURRENT:

It is due to the potential difference between two points that an electric current flow
between them. The simplest way to maintain a potential difference between the two ends
of a conductor so as to get a continuous flow of current is to connect the conductor
between the terminals of a cell or a battery.

Due to the chemical reactions going on inside the cell or battery, a potential difference is
maintained between its terminals and this potential difference drives the current in a
circuit.

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 ELECTRIC FIELD AND ELECTRIC POTENTIAL
Electric field due to a given charge is defined as the space around the charge in which
electrostatic force of attraction or repulsion due to charge can be experienced by any
other charge. If a test charge experiences no force at a point, the electric field at that point
must be zero.
Electric field intensity at any point is the strength of electric field at that point. It is defined
as the force experienced by a unit positive charge placed at that point.

If is the force acting on a test charge +q0 at any point r, then electric field intensity at
this point is given by

Electric field is a vector quantity and its S.I. unit is Newton per coulomb or N/C.

ELECTRIC POTENTIAL:
The work done in charging a body is stored in it as its electric potential energy. The electric
potential energy per unit charge is called electric potential.

Electric Potential = Electric Potential Energy/Charge

Mathematically,

V = W/q

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 Since work is measured in joule and charge in coulomb, therefore electric potential is
measured in joule per coulomb (J/C). This unit occurs so often in our study of electricity,
so it has been named as volt, in honors of the scientist Alessandra Volta (the inventor of
the voltaic cell).
1 Volt = 1Joule/1Coulomb

Potential is a scalar quantity; therefore, it is added algebraically. For a positively charged

body potential is positive and for a negatively charged body potential is negative.

ELECTRIC POTENTIAL DIFFERENCE:

Consider a charge Q placed at a point P. Let A and B be two other points (B being closer
to A) as shown in figure.

PAB

If a charge q is brought from infinity to A, a work WA will be done.

The potential at A will then be, VA = W A/q

If charge q is brought from infinity to B, the work done will be WB.

The potential at B will then be, VB = W B/q

The quantity VB-VA is called the potential difference between points A & B in the electric
field of charge Q.

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 Mathematically we have, VB - VA = W B/q - W A/q

Electric potential difference is measured in volt.

OHM’S LAW
The law stating that the direct current flowing in a conductor is directly proportional to the
potential difference between its ends. It is usually formulated as V = IR, where V is the
potential difference, or voltage, I is the current, and R is the resistance of the conductor
or the flow of electric current through a conductor depends on the potential difference
across its ends. At a particular temperature, the strength of current flowing through it is
directly proportional to the potential difference across its ends.
This is known as Ohm's Law.

I∝V
or V ∝ I V = Potential difference

V = RI, Where R = Resistance

or where I = Current

Here, R is the constant of proportionality, which depends on size, nature of material and
temperature. R is called the electrical resistance or resistance of the conductor.

EXPERIMENTAL VERIFICATION OF OHM'S LAW

• Set up a circuit as shown in figure consisting of a nichrome wire XY of length, say

0.5 m, an ammeter, a voltmeter and four cells of 1.5 V each. (Nichrome is an alloy
of nickel, chromium, manganese, and iron metal.)
• First use only one cell as the source in the circuit. Note the reading in the ammeter
I, for the current and reading of the voltmeter V for the potential difference across
the nichrome wire XY in the circuit. Tabulate them.
• Next connect two cells in the circuit and note the respective readings of the
ammeter and voltmeter for the values of current through the nichrome wire and
potential difference across the nichrome wire.
• Repeat the above steps using three cells and then four cells in the circuit
separately.
• Calculate the ratio of V to I for each pair of potential difference (V) and current (I).
• Plot a graph between V and I, and observe the nature of the graph.

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 Thus, is a constant ratio which is called resistance (R). It is known as Ohm’s Law.

RESISTANCE OF A CONDUCTOR:

There are three external factors that influence the resistance in a conductor.

• Thickness (cross sectional area of the wire),

• Length
• Temperature

All have some effect on the amount of resistance created in a conductor. The fourth factor
is the conductivity of the material we are using. Some metals are just more electrically
conductive than others. This however, is considered an internal factor rather than an
external one.

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 The electric current is a flow of electrons through a conductor. When the electrons move
from one part of the conductor to the other part, they collide with other electrons and with
the atoms and ions present in the body of the conductor. Due to these collisions, there is
some obstruction or opposition to the flow of electrons through the conductor.

The property of a conductor due to which it opposes the flow of current through it, is called
resistance. The resistance of a conductor is numerically equal to the ratio of potential
difference across its ends to the current flowing through it.

Resistance = Or R =

Cross Sectional Area

The cross-sectional area of a conductor (thickness) is similar to the cross section of a

hallway. If the hall is very wide, it will allow a high current through it, while a narrow hall
would be difficult to get through due to its restriction to a high rate of flow. The animation
at the left demonstrates the comparison between a wire with a small cross-sectional area
(A) and a larger one (A). Notice that the electrons seem to be moving at the same speed
in each one but there are many more electrons in the larger wire. This results in a larger
current which leads us to say that the resistance is less in a wire with a larger cross-
sectional area.

• Length of the Conductor: The length of a conductor is similar to the length of a

hallway. A shorter hallway would allow people to move through at a higher rate
than a longer one.

• Temperature: The temperature of a conductor has a less obvious effect on the

resistance of the conductor. It would be as hard to apply the hallway analogy as it
is hard to say whether a hot hallway would make us move faster or slower than a
cold hallway. To truly understand the effect, you must picture what happens in a
conductor as it is heated. Heat on the atomic or molecular scale is a direct
representation of the vibration of the atoms or molecules. Higher temperature
means more vibrations. Since the wire is cold the protons are not vibrating much

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 so the electrons can run between them fairly rapidly. As the conductor heats up,
the protons start vibrating and moving slightly out of position. As their motion
becomes more erratic they are more likely to get in the way and disrupt the flow of
the electrons. As a result, the higher the temperature, the higher the resistance. A
prime example of this is when you turn on a light bulb. The first instant, the wire
(filament) is cold and has a low resistance but as the wire heats up and gives off
light it increases in resistance. As a result, we can say that Ohm's law holds true
unless temperature changes. At extremely low temperatures, some materials have
no measurable resistance. This is called superconductivity. The materials are
known as superconductors. We are creating materials that become
superconductors at higher temperatures and the race is on to find or create
materials that superconduct at room temperature. We are painfully far away from
the finish line.

UNIT OF RESISTANCE
The S.I. unit of resistance is Ohm (Ω)

1 Ohm (Ω) =

The resistance of a conductor is said to be one ohm if a current of one ampere flows
through it when a potential difference of one volt is applied across its ends.

CONDUCTORS, RESISTORS AND INSULATORS:

We have already study this in flow of charge form. But in different sense in terms of
electricity we know this.
On the basis of their electrical resistance, all the substances can be divided into three
groups: conductors, resistors and insulators.

• Conductors: Those substances which have very low electrical resistance are
called conductors. A conductor allows the electricity to flow through it easily. Silver
metal is the best conductor of electricity Copper and Aluminium metals are also
good conductors. Electric wires are made of Copper or Aluminium because they
have very low electrical resistance.

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 • Resistors: Those substances which have comparatively high electrical
` resistance, are called resistors. The alloys like nichrome, managing and
constantan (or eureka), all have quite high resistances, so they are used to make
those electrical devices where high resistance is required. A resistor reduces the
current in the circuit.

• Insulators: Those substances which have infinitely high electrical resistance are
called insulators. An insulator does not allow electricity to flow through it. Rubber
is an excellent insulator. Electricians wear rubber hand gloves while working with
electricity because rubber is an insulator and protects them from electric shocks.
Wood is also a good insulator.

Activity to show that the amount of current through an electric component depends upon
its resistance:

• Take a nichrome wire, a torch bulb, a 10 W bulb and an ammeter (0-5 A range), a
plug key and some connecting wires.
• Set up the circuit by connecting four dry cells of 1.5 V each in series with the
ammeter leaving a gap XY in the circuit, as shown in figure.

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 • Complete the circuit by connecting the nichrome wire in the gap XY. Plug the key.
Note down the ammeter reading. Take out the key from the plug. [Note: Always
take out the key from the plug after measuring the current through the circuit.]
• Replace the nichrome wire with the torch bulb in the circuit and find the current
through it by measuring the reading of the ammeter.
• Now repeat the above step with 10 W bulb in the gap XY.
• You will notice that the ammeter readings differ for different components
connected in the gap XY.
• You may repeat this Activity by keeping any material component in the gap.
Observe the ammeter readings in each case. Annalise the observations.
• Thus, we come to a conclusion that current through an electric component
depends upon its resistance.

FACTORS AFFECTING RESISTANCE OF A CONDUCTOR

Resistance depends upon the following factors: -

• Length of the conductor.

• Area of cross-section of the conductor (or thickness of the conductor).
• Nature of the material of the conductor.
• Temperature of the conductor.

This same factor we have to see mathematically: It has been found by experiments that:

(i) The resistance of a given conductor is directly proportional to its length i.e.

R ∝ l …. (i)

(ii) The resistance of a given conductor is inversely proportional to its area of cross-section
i.e.

…. (ii)

From (i) and (ii), we have

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 …(iii)

Where ρ (rho) is a constant known as resistivity of the material of the conductor.

Resistivity is also known as specific resistance.

Experiment to show that resistance of a conductor depends on its length, cross section
area and nature of its material.

• Complete an electric circuit consisting of a cell, an ammeter, a nichrome wire of

length  [marked (1)] and a plug key, as shown in figure.
• Now, plug the key. Note the current in the ammeter.

• Replace the nichrome wire by another nichrome wire of same thickness but twice
the length, that is 2 [marked (2) in the figure]. Note the ammeter reading.
• Now replace the wire by a thicker nichrome wire, of the same length  [marked
(3)]. A thicker wire has a larger cross-sectional area. Again, note down the current
through the circuit.
• Instead of taking a nichrome wire, connect a copper wire [marked (4) in figure] in
the circuit. Let the wire be of the same length and same area of cross-section as
that of the first nichrome wire [marked (1)]. Note the value of the current.
• Notice the difference in the current in all cases.
• We notice that the current depends on the length of the conductor.
• We also observed that the current depends on the area of cross-section of the
wire used.

RESISTIVITY:
We will define resistivity by the help of its formula as

Resistivity, …. (iv)

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 By using this formula, we will now obtain the definition of resistivity.By using this
formula, we will now obtain the definition of resistivity. Let us take a conductor
having a unit area of cross-section of 1 m2 and a unit length of 1 m. So, putting A= 1 and l
= 1 in equation (iv), we get:
Resistivity, ρ = R

The resistivity of a substance is numerically equal to the resistance of a rod of that

substance which is 1 meter long and 1-meter square in cross-section.

Unit of resistivity,

The S.I. unit of resistivity is ohm-meter which is written in symbols as Ω - m.

Material Resistivity /Ωm

Copper 1.7 × 10-8
Aluminum 2.7 × 10-8
Graphite 8.0 × 10-6
Silicon 2.3 × 103
Quartz 8.0 × 1016
Resistivity of a substance does not depend on its length or thickness. It depends only on
the nature of the substance. The resistivity of a substance is its characteristic property.
So, we can use the resistivity values to compare the resistances of two or more
substances.

• Resistivity is a measure of the resistance to electrical conduction for a given size

of material. Its opposite is electrical conductivity (=1/resistivity).
• Metals are good electrical conductors (high conductivity and low resistivity), while
non-metals are mostly poor conductors (low conductivity and high resistivity).
• The more familiar term electrical resistance measures how difficult it is for a piece
of material to conduct electricity - this depends on the size of the piece: the
resistance is higher for a longer or narrower section of material.
• To remove the effect of size from resistance, resistivity is used - this is a
material property which does not depend on size.
• Resistivity is affected by temperature - for most materials the resistivity increases
with temperature. An exception is semiconductors (e.g. silicon) in which the
resistivity decreases with temperature.
• The ease with which a material conducts heat is measured by thermal conductivity.
As a first estimate, good electrical conductors are also good thermal conductors.

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 SPECIFIC USE OF SOME CONDUCTING MATERIALS:
Tungsten: It has high melting point of 3380ºC and emits light at 2127ºC. It is thus used
as a filament in bulbs.

Nichrome: It has high resistivity and melting point. It is used as an element in heating
devices.
Constantan and Manganin: They have modulated resistivity. Thus, they are used for
making resistances and rheostats.

Tin-lead Alloy: It has low resistivity and melting point. Thus, it is used as fuse wire.

Ex. When a 12 V battery is connected across an unknown resistor, there is a current of

2.5 mA in the circuit. Find the value of the resistance of the resistor.

Solution: Given that voltage of battery V = 12 V

Circuit current I = 2.5 mA = 2.5 ×

∴ Value of resistance R = = 4800 Ω

COMBINATION OF RESISTORS

Many times, we have to join two or more resistances to get the desirable resistance.
There are two ways in which resistances be joined:

• Resistances in series
• Resistances in Parallel

RESISTANCES IN SERIES

A number of resistances are said to be connected in series if they are joined end to end
and the same current flows through each one of them, when a potential difference is
applied across the combination.

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 R1, R2, R3 – Resistances in series.

V – Total potential difference across XY.

V1, V2, V3 – Potential difference across R1, R2, R3 respectively.

I – Current flowing through combination.

So, V = V1 + V2 + V3 ... (i) [Potential difference gets divided among resistances joined in
series]

According to Ohm's Law:

V1 = IR1 ... (ii)

V2 = IR2 ... (iii)

V3 = IR3 ... (iv)

Let R is the resultant or equivalent resistance of the combination. Then

V = IR ... (v)

From (i), (ii), (iii), (iv) and (v) we get that:

IR = IR1 + IR2 + IR3

IR = I(R1 + R2 + R3)

∴ R = R1 + R2 + R3

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 THINGS TO REMEMBER IN SERIES CONNECTION:

• When a number of resistances are connected in series, the equivalent or resultant

resistance is equal to the sum of individual resistances and resultant resistance is
greater than any individual resistance.
• If n resistances each of value R are connected in series, the equivalent resistance
Re is given by:

𝑒 𝑅𝑒 = R + R + R .......... n times
𝑅 = nR
Re = Number of resistors × resistance of each resistor

• Equal current flows through each resistance and it is also equal to the total current
in the circuit. This is because there is no other path along which the current can
flow.
• The potential difference across the ends of the combination is distributed across
the ends of each of the resistances. The potential difference across any one of the
resistances is directly proportional to its resistance.
• The equivalent resistance when used in place of the combination of resistances
produces the same current with the same potential difference applied across its
ends.
• When two or more resistances are joined in series, the result is the same as
increasing the length of the conductor. In both cases the resultant resistance is
higher.
• In a series combination, the equivalent resistance is greater than the greatest
resistance in the combination.

RESISTANCES IN PARALLEL:
A number of resistors are said to be in a parallel connection if one end of each resistance
is connected to one point and the other is connected to another point. The potential
difference across each resistor is the same and is equal to the applied potential difference
between the two points.

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 R1, R2, R3 – Three resistances in parallel connection.

V – Potential difference across A and B.

I – Total current flowing between A and B.

I1, I2, I3 – Current flowing through R1, R2, R3 respectively.

I = I1 + I2 + I3 ... (i) [In parallel connection, the current gets divided among the resistances]

The potential difference across R1, R2 and R3 is same, therefore, according to Ohm's law:

... (ii)

Let Re be the equivalent resistance. Thus

... (iii)

From equation (i), (ii) and (iii) we get

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 THINGS TO REMEMBER IN PARALLEL CONNECTION:
• When a number of resistances are connected in parallel, the reciprocal of the
equivalent or resultant resistance is equal to the sum of reciprocals of the individual
resistances and is always smaller than the individual resistances. This is because
there are a number of paths for the flow of electrons.
• If there are n resistances connected in parallel and each resistance has a value
of R

times

• The potential difference across each resistance is the same and is equal to the
total potential difference across the combination.
• The total current divides itself and different current flows through each resistor.
The maximum current flows through the resistor having minimum resistance and
vice versa.
• If an equivalent resistance Re is connected in place of combination, it produces
the same current for the same potential difference applied across its ends.
• In a parallel combination, the equivalent resistance is lesser than the least of all
the resistances.
• If two resistances R1 and R2 are connected in parallel then

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 • If there are n resistors each of resistance R – Let RS be the resultant resistance
of series combination and Rp be the resultant resistance of parallel combination.
Then, RS = nR

𝑅𝑝 =

∴ .

HEATING EFFECT OF ELECTRIC CURRENT:

Energy exists in various forms such as mechanical energy, heat energy, chemical energy,
electrical energy, light energy and nuclear energy. According to the law of conservation
of energy, energy can be transformed from one form to another.

In our daily life we use many devices where the electrical energy is converted into heat
energy, light energy, chemical energy or mechanical energy. When an electric current is
passed through a metallic wire like filament of an electric heater, oven or water heater,
the filament gets heated up and here electrical energy is converted into heat energy. This
is known as 'heating effect of current'.

It is a matter of common experience that a wire gets heated up when electric current flows
through it. Why does this happen? A metallic conductor has a large number of free
electrons in it. When a potential difference is applied across the ends of a metallic wire,
the free electrons begin to drift from the low potential to the high potential region. These
electrons collide with the positive ions (the atoms which have lost their electrons). In these
collisions, energy of the electrons is transferred to the positive ions and they begin to
vibrate more violently. As a result, heat is produced. Greater the number of electrons
flowing per second, greater will be the rate of collisions and hence more heat is produced.

When the ends of a conductor are connected to a battery, then free electrons move with
drift velocity and electric current flows through the wire. These electrons collide
continuously with the positive ions of the wire and thus the energy taken from the battery
is dissipated. To maintain the electric current in the wire, energy is taken continuously
from the battery. This energy is transferred to the ions of the wire by the electrons. This
increases the thermal motion of the ions, as a result the temperature of the wire rises.
The effect of electric current due to which heat is produced in a wire when current is
passed through it is called heating effect of current or Joule heating. In 1841 Joule found
that when current is passed through a conductor the heat produced across it is:

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 • Heat is directly proportional to the square of the current through the conductor i.e.

H ∝ I2

• Heat is directly proportional to the resistance of the conductor i.e. H ∝ R

• Heat is directly proportional to the time for which the current is passed i.e. H ∝ t

Combining the above three equations we have H ∝ I2 Rt

Where J is called Joule's mechanical equivalent of heat and has a value of J = 4.18 J cal - 1.
The above equation is called Joule's law of heating.

In some cases, heating is desirable, while in many cases, such as electric motors,
generators or transformers, it is highly undesirable. Some of the devices in which heating
effect of an electric current is desirable, are incandescent lamps, toasters, electric irons
and stoves. The tungsten filament of an incandescent lamp operates at a temperature of
2700°C. Here, we see electrical energy being converted into both heat and light energy.

DERIVATION OF WORK DONE AND ELECTRIC ENERGY

Now we know that:

Current (I) = or Q = IT ... (i)

Also, potential difference is the work done in bringing a charge Q from one end to the
other end of the conductor. Thus

(Potential Difference)

W = VQ ... (ii)

From (i) and (ii), we get that

W = V(It)

W = VIt ... (iii)

But according to Ohm's law

V = IR ... (iv)

From equation (iii) and (iv), we get that

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 W = (IR)(It)

W=

But and by putting this value in equation (iii), we get

W=

W=

This work done (W) by the current, measures the Electric Energy. Thus

W∝

W∝R

W∝t

Thus,

(i) Commercial unit of electrical energy (Kilowatt - hour):

The S.I. unit of electrical energy is Joule and we know that for commercial purposes we
use a bigger unit of electrical energy which is called "Kilowatt - hour". One Kilowatt - hour
is the amount of electrical energy consumed when an electrical appliance having a power
rating of 1 Kilowatt and is used for 1 Hour.

(ii) Relation between Kilowatt hour and Joule:

Kilowatt-hour is the energy supplied by a rate of working of 1000 watts for 1 hour.

1 kilowatt-hour= 3600000 joules

⇒ 1kWh=3.6 × 106J

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 ELECTRIC POWER:
The rate at which electric energy is dissipated or consumed, is termed as electric power.
The power P is given by, P = W/t = I2 R

The unit of electric power is watt, which is the power consumed when 1 A of current flows
at a potential difference of 1V.

(i) Unit of power:

The SI unit of electric power is ‘watt' which is denoted by the letter W. The power of 1 watt
is a rate of working of 1 joule per second.

A bigger unit of electric power is kilowatt.

1 kilowatt (kW) = 1000 watt.

Power of an agent is also expressed in horse power (hp).

1 hp = 746 watt.

(ii) Formula for calculating electric power:

We know, Power, P =

And Work, W = V × I × t Joules

P=V×I

P=V×I
Power P in terms of I and R :Now from Ohm's law we have,

V= I × R

P= I × R × I

P= I2 × R

Power P in terms of V and R: We know, P = V × I

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 From Ohm's law I =

P=

P=

Power - Voltage Rating of Electrical Appliances:

Every electrical appliance like an electric bulb, radio or fan has a label or engraved plate
on it which tells us the voltage (to be applied) and the electrical power consumed by it.
For example, if we look at a particular bulb in our home, it may have the figures 220V,
100W written on it. Now, 220V means that this bulb is to be used on a voltage of 220 volts
and 100W which means it has a power consumption of 100 watts or 100 joules per
second.

ELECTRIC FUSE:
An electric fuse is an easily fusible wire of short length put into an electrical circuit for
protection purposes. It is arranged to melt ("blow") at a definite current. It is an alloy of
lead and tin (37% lead + 63% tin). It has a low resistivity and low melting point. As soon
as the safe limit of current exceeds, the fuse "blows" and the electric circuit is cut off.

Consider a wire of length L, radius r and resistivity ρ . Let I be the current flowing through
the wire. Now rate at which heat is produced in the wire is,

This heat increases the temperature of the wire. Due to radiation some heat is lost. The
temperature of the fuse becomes constant when the heat lost due to the radiation
becomes equal to the heat produced due to the passage of current. This gives the value
of current which can safely pass through the fuse.

In other words, we have,

Ex. 15 bulbs of 60W each, run for 6 hours daily and a refrigerator of 300 W runs for 5
hours daily. Work out per day bill at 3 rupees per unit.

Solution: Total wattage of 15 bulbs = 15 × 60W = 900W

∴ Electrical energy consumed by bulbs per day = P × t = 900 × 6 = 5400Wh

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 And electrical energy consumed by refrigerator per day = 300 × 5 = 1500 h

Total electrical energy consumed per day = (5400 + 1500) Wh = 6900Wh

∴ Electrical energy consumed per day = KWh = 6.9 KWh

Here, per day bill = Rs. 6.9 × 3 = Rs. 20.7

Example: Two lamps, one rated 100W at 220V and other 60W at 220V are connected in
parallel to a 220V supply. What is current drawn from the supply line?

Solution: Given that V = 220V

P1 = 100W and P2 = 60W

∴ Current

Similarly,

Current

Hence, total current drawn from the supply line = .

HOUSE-HOLD ELECTRICAL CIRCUIT:

Electric power is usually generated at places which are very far from the places where it
is consumed. At the generating station, the electric power is generated at 11,000 volts
(because voltage higher than this causes insulation difficulties, while the voltage lower
than this involves high current). This voltage is alternating of frequency 50 Hz (i.e.
changing its polarity 50 times in a second). The power is transmitted over long distances
at high voltage to minimize the loss of energy in the transmission line wires. For a given
electric power, the current becomes low at a high voltage and therefore the loss of energy
due to heating (=I2 Rt) becomes less. Thus, the alternating voltage is stepped up from 11
kV to 132 kV at the generating station (or called grid sub-station). It is then transmitted to
the main sub-station. At the main sub-station, this voltage is stepped down to 33 kV and
is transmitted to the switching transformer station or the city sub-station. At the city sub-
station, it is further stepped down to 220 V for supply to the consumer as shown in figure.

To supply power to a house either the overhead wires on poles are used or an
underground cable is used. Before the electric line is connected to the meter in a house,
a fuse of high rating (≈ 50 A) is connected at the pole or before the meter. This is called

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 the company fuse. The cable used for connection has three wires: (i) live (or phase) wire,
(ii) neutral wire and (iii) earth wire. The neutral and the earth wires are connected together
at the local sub-station, so the neutral wire is at the earth potential. After the company
fuse, the cable is connected to a kWh meter. From the meter, connections are made to
the distribution board through a main fuse and a main switch.

The main switch is a double pole switch. It has iron covering. The covering is earthed.
This switch is used to cut the connections of the live as well as the neutral wires
simultaneously. The main switch and the meter are locally earthed (in the compound of
house). From the distribution board, the wires go to the different parts of the house.

There are two systems of wiring which are in common use:

1. the tree system

2. the ring system

Tree System:
In this system, different branch lines are taken from the distribution board for the different
parts of the house. These branch lines look like the different branches of a tree. Each
branch line is taken to a room through a fuse in the live wire. The different circuits are
connected in parallel so that if there is a short circuiting in one distribution circuit, its fuse
will blow off, without affecting the electric supply in the other circuits. The neutral N and
the earth E are common for all circuits. The connection to the neutral N is to complete the
circuit. All the appliances in a room are connected in parallel so that they work at the
same voltage. The line wires used for connections should be of proper current carrying
capacity depending on the rating of the appliance to avoid their overheating. The
overheating in line often results in fire. The switches and sockets should also have the
proper current carrying capacity.

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 Disadvantage:
• It requires plugs and sockets of different sizes for different current carrying
capacities.
• When the fuse in one distribution line blows, it disconnects all the appliances in
the distributing line.
• This wiring is expensive.
• If a new appliance is to be installed requiring higher current, say 15A, while the
original circuit in the room is for 5A rating, then it is necessary to put new leads up
to the distribution box. This could be quite expensive and inconvenient.

Ring System:
The ring-system of electric wiring is now rapidly replacing the older tree system described
above. It consists of a ring-circuit. Wires starting from the main fuse-box, run around all
the main rooms of the house and then come back to the fuse-box again. The fuse box
contains a fuse of rating about 30 A. A separate connection is taken from the live wire of
the ring for each appliance. The terminal of the appliance is connected to the live wire
through a separate fuse and a switch. If the fuse of one appliance burns, it does not affect
the other appliances. For each appliance, the wires used for connection should be of
proper current carrying capacity.

Advantages:
It can be noted that the current can travel to an individual appliance through two separate
paths. Thus, effectively the connection for each appliance is through double thickness of
wire. Therefore, the wire used for ring main is of a lower rating than that which would be
required for a direct connection to the mains. This reduces the cost of wiring considerably.
Plugs and sockets of the same size can be used, but each plug should have its own fuse
of rating suitable for the particular appliance.

Another advantage of this system is in installing a new appliance, since a new line up to
the distribution box is not required. The appliance can be directly connected to ring main
in the room. The only consideration is that the total load on the ring circuit should not
exceed the main fuse viz. 30 A.

Domestic Heating Applications:

Electric appliances like iron, heater, radiator etc. depend on the fact that when a current
is sent through a wire, the wire is heated up and it begins to radiate energy.
The most widely used material for making the heater wire is nichrome. It is an alloy of
nickel and chromium in the ratio of 4: 1. It is chosen because of the following reasons:
• It has high resistivity. A nichrome wire of ordinary length shows sufficient
resistance.
• It can withstand high temperature without oxidation.
• Its melting point is very high.

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 Hazards of Electricity:
We have seen earlier that touching a bare electricity wire with current flowing through it
can give a dangerous electric shock. This is because electricity then flows through the
body and damages the cells. The amount of damage caused depends on the magnitude
of current and the duration for which it flows in the body. The magnitude of current
increases if the body is wet. That is why we are always advised not to touch any electrical
appliances or a switch with wet hands.

A severe electric shock affects the muscles. Sometimes the shock may be so severe that
the person may not be able to use his muscle to pull his hand away from the wire. In
extreme cases, the heart muscles may get affected and may even lead to death.

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