Electricity
Chapter 12
Electricity
Electricity is a basic
part of our nature and it is one of our most widely used forms of energy. We
use electricity virtually every minute of every day for example in lighting,
heating, refrigeration, air conditioning, power electromagnets, power computers,
power televisions, power pumps, power our vehicles etc.
Electric
Current
The flow of
electric charge is known as Electric Current, Electric current is carried by
moving electrons through a conductor.
By convention, electric current flows in the opposite direction to the movement
of electrons.
Electric
Circuit
Electric circuit is a continuous and closed path of electric
current.
Circuit Diagram
We know that electric circuit is a continuous path consisting of cell,
switch (plug key), electric components and connecting wires. Electric circuits
can be represented conveniently through a circuit diagram.
A diagram which indicates how different components in a circuit have to
be connected by using symbols for different electric components is called a
circuit diagram.
Expression
of Electric Current
Electric current is denoted by the letter ‘I’. Electric current is expressed by the rate of flow of electric charges. Rate of flow means, the amount of charge flowing through a particular area in unit time.
If a net electric charge (Q) flows through a cross-section of a conductor in time t, then,
Where I is electric current, Q is a net charge and t is a time in second.
S.I.
Unit of Electric Charge and Current
S.I. unit of
electric charge is coulomb (C).
One coulomb is nearly equal to 6 × 1018 electrons.
S.I. unit of
electric current is ampere (A). Ampere is the flow of electric charge through a
surface at the rate of one coulomb per second. This means, if 1 coulomb of
electric charge flows through a cross section for 1 second, it would be equal
to 1 ampere.
Therefore, 1 A = 1 C/1 s
Small
Quantity of Electric Current
Small quantity of
electric current is expressed in milliampere and microampere. Milliampere is
written as mA and microampere as pA.
1 mA (milliampere) = 10-3 A
1 PA (microampere) = 10-6 A
Ammeter
Charge
Like mass, the
charge is the fundamental property of matter. There are two types of charge
(i) Positive charge.
(ii) Negative charge.
Positive
and Negative Charge
The charge acquired
by a glass rod when rubbed with silk is called a positive charge and the charge
acquired by an ebonite rod when rubbed with wool is called negative charge.
Properties of Electric Charge
1) Unlike charges attract each other 2)
like charges repel each other.
S.I. unit of charge is coulomb (C).
1 coulomb = 1 ampere × 1 second.
1C = 1A × 1s
Thus, the quantity of charge which flows through a circuit when one ampere of
current flows through it in one second is known as a 1-coulomb charge.
Electric Potential
The
amount of electric potential energy at a point is called electric potential.
Potential Difference
The
difference in the amount of electric potential energy between two points in an
electric circuit is called electric potential difference.
Electric potential difference is known as voltage, which is equal to the amount
of work done to move the unit charge between two points against static electric
field.
Therefore, Voltage = Work done/Charge
Voltage or electric potential difference is denoted by V’. Therefore, V = W/Q
Where, W = Work done and Q = Charge
S.I. Unit of Electric Potential Difference
(Voltage)
S.I. unit of electric potential difference is volt and denoted by ‘V’ This is
named in honour of Italian Physicist Alessandro Volta.
Since joule is the unit of work and Coulomb is the
unit of charge.
1 volt of electric potential difference is equal to
the 1 joule of work to be done to move a charge of 1 coulomb from one point to
another in an electric circuit. Therefore
1V = 1Joule/1Coulomb = 1J/1C
1V = 1JC-1
Voltmeter
An apparatus to
measure the potential difference or electric potential difference between two
points in an electric circuit. It is always connected in parallel across the
points between which the potential difference is to be measured
.
Cell: The Difference of potential may be produced by a battery, consisting of
one or more electric cells.
Potential difference
across the terminals of the cell generated due to chemical reaction within the
cell. When cell is connected to a conducting wire, current flows from high
potential to low potential.
Ohm’s Law: Ohm’s
Law states that the potential difference between two points is directly
proportional to the electric current, at a constant temperature.
This means potential difference V varies as electric current.
V ∝
I
V = RI
I = VR
R = VI
Where, R is constant for the given conductor at a given temperature and is
called resistance.
1 Ohm: 1
ohm (Q) of resistance (R) is equal to the flow 1A of current through a
conductor between two points having a potential difference equal to 1V.
This means; 1Ω = 1V1A
From the expression of Ohm’s Law, it is obvious that electric current through a
resistor is inversely proportional to resistance. This means electric current
will decrease with an increase in resistance and vice versa. The graph of V
(potential difference) versus I (electric current) is always a straight line.
Graph of Potential Difference (V) Vs Electric Current (I)Voltage, i.e. Potential diffrence (V) = ?We know, from Ohm’s Law that,R = VI15 Ω = V15AV = 225V
Resistance: Resistance is a property of conductor due to
which it resists the flow of electric current through it.
Resistor: A component that is used to resist the flow of
electric current in a circuit is called a resistor.
In practical application, resistors are used to increase or decrease the
electric current.
Variable
Resistance: The component of an electric
circuit which is used to regulate the current, without changing the voltage
from the source, is called variable resistance.
Cause of Resistance in a Conductor: Flow of electrons in a conductor is electric current. The positive particles of conductor create hindrance to flow of electrons, because of attraction between them, this hindrance is the cause of resistance in the flow of electricity.
Factors
on Which Resistance of a Conductor Depends:
Resistance in a conductor depends on nature, length and area of cross section
of the conductor.
(i)
Nature of Material: Some materials create least
hindrance are called good conductors. Silver is the best conductor of
electricity.
While some other
materials create more hindrance in the flow of electric current, i.e., flow of
electrons through them. Such materials are called bad conductors. Bad conductor
is also known as insulators. Hard plastic is the one of the best insulators of
electricity.
(ii)
Length of Conductor: Resistance (R) is directly
proportional to the length of the conductor. This means, resistance increases
with increase in length of the conductor. This is the cause that long electric
wires create more resistance to the electric current.
Thus, Resistance
(R) ∝
length of conductor (l)
or, R ∝
l …(i)
(iii) Area of Cross Section: Resistance R is inversely proportional to the
area of cross section (A) of the conductor. This means R will decrease with an
increase in the area of conductor and vice versa. More area of conductor
facilitates the flow of electric current through more area and thus, decreases
the resistance. This is the cause that thick copper wire creates less
resistance to the electric current.
Thus, resistance (R) ∝
L /Area of cross section of conductor (A)
or, R ∝ L /A ….
(ii)
From equations (i) and (ii)
R ∝ L/A
R = ρ L/A …(iii)
Where, ρ
(rho) is the proportionality constant. It is called the electrical resistivity
of the material of conductor.
From equation (iii) RA = ρ l
⇒
ρ = R A/L ...(iv)
S.I. of Resistivity: Since, the S.I. unit of R is Ω, S.I. unit of area
is m2 and S.I. unit of length is m.
Hence,
unit of resistivity (ρ)
= Ω
x m2 / m = Ωm
Resistivity: It
is defined as the resistance offered by a cube of a material of side 1m when current
flows perpendicular to its opposite faces. It’s S.I. unit is ohm-meter (Ωm).
Resistivity, ρ
= RA/L
Resistivity is also known as specific resistance.
Resistivity depends on the nature of the material of the conductor.
Materials having a resistivity in the range 10 –
8 Ω m to 10 – 6 Ω
are considered as very good conductors. Silver has resistivity equal to 1.60 × 10-8 Ωm
and copper has resistivity equal to 1.62 × 10-8 Ωm.
Rubber and glass are very good insulators. They have a resistivity in the order
of 10-12 Ωm to 10-8 Ωm.
The resistivity of materials varies with temperature.
Conductor: The material which can allow the flow of
electrons through itself is called the conductor. It has a large number of free
electrons. It offers low opposition in the flow of current.
Insulator: The material which does not allow the flow of
electrons through itself is called insulator. It has less or no free electrons.
It offers high opposition in the flow of current.
Combination
of resistors (Series and Parallel combination):
(i) Series combination
(ii) Parallel combination.
1.
Resistors in Series: When resistors are joined from
end to end, it is called in series. In this case, the total resistance of the
system is equal to the sum of the resistance of all the resistors in the
system.
Let, three resistors R1, R2, and R3 get connected in series.
Potential difference across A and B = V
Potential difference across R1, R2 and R3 = V1, V2 and V3
Current flowing through the combination = I
We, know that
V= V1 + V2 + V3 …. (i)
According to Ohm’s Law:
V1 = IR1, V2 = IR2 and V3 = IR3 ….. (ii)
Let, total resistance = R
Then, V = IR …(iii)
From equations (i) and (ii) and (iii)
IR = IR1 + IR2 + IR3
R = R1 + R2 + R3
When the resistors are connected in series, the current flowing through each resistor is the same and is equal to the total current.
2.
Resistors in Parallel: When
resistors are joined in parallel, the reciprocal of the total resistance of the
system is equal to the sum of reciprocal of the resistance of resistors.
Let three resistors R1, R2 and R3 connected in parallel.
Potential difference across point A and B = V
Total current flowing between point A and B = I
Currents flowing through resistors R1, R2 and R3 = I1, I2 and I3 respectively.
We, know that,
I = I1 + I2 + I3 …….(i)
Since, the potential difference across R1, R2, and R3 is the same = V
According to Ohm’s Law,
In parallel combination, the potential difference across each resistor is the
same and is equal to the total potential difference.
Heating
Effect of Electric Current: When electric
current is supplied to a purely resistive conductor, the energy of electric
current is dissipated entirely in the form of heat and as a result, resistor
gets heated. The heating of resistor because of dissipation of electrical
energy is commonly known as Heating Effect of Electric Current.
Examples: When electric energy is supplied to an electric
bulb, the filament gets heated because of which, it gives light. The heating of
electric bulb happens because of heating effect of electric current.
Cause
of Heating Effect of Electric Current: Electric
current generates heat to overcome the resistance offered by the conductor
through which it passes. Higher the resistance, the electric current will
generate higher amount of heat. Thus, generation of heat by electric current
while passing through a conductor is an inevitable consequence. This heating
effect is used in many appliances, such as electric iron, electric heater,
electric geyser, etc.
Joule’s Law Of Heating: Let, an electric current, I is flowing
through a resistor having resistance = R.
The potential difference through the resistor is = V.
The charge, Q flows through the circuit for the time, t
Thus, work done in moving of charge (Q) of potential difference (V),
W = V × Q
Since this charge, Q flows through the circuit for time t
Therefore, power input (P) to the circuit can be given by the following
equation :
P = W/t
P = V × Q/t …..(i)
We know, electric current, I = Q/t
Substituting Q/t = I in equation (i), we get,
P = VI …(ii)
i.e., P = VI
Since, the electric energy is supplied for time ?, thus, after multiplying both
sides of equation (ii) by time t, we get,
P × t = VI × t = VIt ……(iii)
i.e., Pt= Vit
the energy supplied to
the circuit by the source in time t
H= P × t
from equation (iii)
H
= VIt
This energy gets
dissipated in the resistor as heat
Thus, for steady current I, the heat produced (H)
in time t is equal to VIt
We know, according to Ohm’s Law,
V = IR
By substituting this value of V in equation (iii), we get,
H = IR × It
H = I2Rt ……(iv)
The expression (iv) is known as Joule’s Law of Heating, which states that heat
produced in a resistor is directly proportional to the square of current given
to the resistor, directly proportional to the resistance for a given current
and directly proportional to the time for which the current is flowing through
the resistor.
Electric
Bulb: In an electric bulb, the
filament of bulb gives light because of the heating effect of electricity. The
filament of bulb is generally, made of tungsten metal, having melting point
equal to 3380°C.
Electric
Iron: The element of electric iron is
made of alloys having high melting point Electric heater and geyser work on the
same mechanism.
Electric Fuse: Electric
fuse is used to protect the electric appliances from high voltage if any.
Electric fuse is made of metal or alloy of metals, such as aluminium, copper,
iron, lead, etc. In the case of flow of higher voltage than specified, fuse
wire melts and protect the electric appliances.
Fuse of 1A, 2A, 3A, 5A, 10A, etc., used for domestic purpose.
Suppose, if an electric heater consumes 1000W at 220 V.
Then electric current in circuit
I = PV
I = 1000W220V = 4.5 A
Thus, in this case of 5A should be used to protect the electric heater in the
flow of higher voltage.
Electric
Power: The work done per unit time is called
power. P=W/T
S.I. unit of power is watt (W).
Electric power is also defined as the electric energy consumed per unit time.
P = E/t
S.I. unit of
electric power is Watt. When one joule of energy is used for one second,
electric power is equal to one watt.
Derivation of formula for electric power
We know that electric work done, W = V × I × t
P = Vit/t
P = VI
Electric power in watts = Volts × ampere
Also V = IR … [According to Ohm’s Law]
So P = IR × I
P = I2R
We know that I = V/R
P = (V/R)2 × R
P = V2/ R
SI unit of electric power is watt (W)
1w = 1 volt x 1 ampere =
1v x 1a
1 kilo watt or 1kw = 1000
w
Unit of energy is kilo
watt hour (kwh)
1 kwh = 1000-watt x 1
hour = 1000 w x 3600 s ⇒
1kwh = 3.6 x 106 watt second = 3.6 x 106 j
current rating of electric appliance
The maximum value of electric current
that can pass through an electric appliance without damaging electric appliance
is called current rating of electric appliance.
Electric
Energy
is amount of work
done to maintain the continuous flow of electric current in the circuit.
Its S.I. unit is joule (J).
BY-APURV SHUKLA
(M.SC(AU) B. ED)
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