Electricity

Electricity:
Electricity is a controllable and convenient form of energy for a verity of uses in homes, schools,
hospitals and industries etc.,
Electric circuit:
A continuous and closed path of an electric current is called electric circuit.
Conductor:
The materials which can conduct electricity are called conductors.
Ex: copper, silver, aluminium, iron
 Conductors have free electrons.
Insulators:
The materials which cannot conduct electricity are called insulators.
Ex: glass, wood, plastic, rubber etc.,
 Insulators do not have any free electrons.
Charge:
Def: It is fundamental property of subatomic particles which experience force in the presence of electric and
magnetic fields.
SI unit of charge: Coulomb (C)
Charge is scalar quantity.
Coulomb: If two equal and same charges separated by a distance 1 meter and they have repulsion force of
8.99 x 109 N then the magnitude of each charge is said to be 1 coulomb.
Properties of charge:
Charges are two types i) positive charge ii) negative charge
Like charges repels each other and unlike charges attracts each other.
Charge is quantized i.e., 𝑄 = 𝑛 𝑒
Charge obeys additive property. Q net = Q1 +Q2
Charge is conserved.
Charge of an electron: -1.6 x 10-19 C
Charge of proton: 1.6 x 10-19 C

Questions:
1. What does an electric circuit mean?
2. What is meant by conductors and insulators? Give two examples of conductors and two of insulators.
3. The atoms of copper contain electrons and the atoms of rubber also contain electrons. Then why does
copper conduct electricity but rubber does not conduct electricity?
4. Calculate the number of electrons constituting one coulomb of charge.
5. If a body have 13 X 1018 protons and 17.5x 1018 electrons on it. Then what is the positive charge,
negative charge and total charge on it.

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 Potential difference
Potential difference (p.d.):
It is defined as the amount of work done in moving a unit charge from one point to the other point.
Formula: 𝑉 =
SI unit of p.d. : volt (v) (or) joule/coulomb
It is a scalar quantity.
Volt: if 1 joule of work is done in moving 1 coulomb of electric charge from one point to the other.
P.d. is measure by using voltmeter.
A voltmeter is a device which is used to measure the potential difference between two points in an electric
circuit.
Symbol:

Voltmeter is always connected in parallel.

Voltmeter has a high resistance so that it takes a negligible current from the circuit.
Ideal voltmeter has infinite resistance.
Battery or cell produces the potential difference between its two terminals.

Questions:

1. What do you understand by the term “potential difference”?

2. What is meant by saying that the potential difference between two points is 1 volt?
3. What is the potential difference between the terminals of a battery if 250 joules of work is required to
transfer 20 coulombs of charge from one terminal of battery to the other?
4. What is a voltmeter? How is a voltmeter connected in the circuit to measure the potential difference
between two points? Explain with the help of a diagram.
5. State whether a voltmeter has a high resistance or a low resistance. Give reason for your answer.
6. How much energy is transferred by a 12 V power supply to each coulomb of charge which it moves
around a circuit?
7. Three 2 V cells are connected in series and used as a battery in a circuit. What is the p.d. at the terminals
of the battery? Draw a sketch for battery.
8. Name a device that helps to maintain a potential difference across a conductor.
9. How much energy is given to each coulomb of charge passing through a 6 V battery?

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 Electric current
Electric current:
The amount of charge crossing any cross-section of the conductor in one second is called electric
current.
(Or) Rate of flow charge is called current.
Formula:
𝑄
𝐼=
𝑡
SI Unit of current: Ampere (A) or coulomb/sec.
Ampere: If one coulomb charge flowing across the conductor in one second, then we said that the current
carried out by the conductor is 1 ampere.
Cause for current flow: Potential difference between the two points.
Current flows from high potential regions to the low potential regions.
Current flow in conductors due to the free electrons
Conventional direction of current in a circuit is from positive terminal of the battery to the negative terminal
of the battery. But electrons are flows form negative terminal of the battery to the positive terminal.
Current is measured by the instrument Ammeter.
Symbol of ammeter:

Ammeter always connects in a circuit in series.

Ammeter has a low resistance so that it not alters the current in the circuit.
Ideal ammeter has zero resistance.

Questions:
1. What do mean of current?
2. Define the unit of current.
3. What actually travels through the wires when you switch on a light?
4. Which particles constitute the electric current in a metallic conductor?
5. In which direction does conventional current flow around a circuit? In which direction do electrons
flow?
6. If 20 C of charge pass a point in a circuit in 1 s, what current is flowing?
7. A current of 4 A flows around a circuit for 10 s. How much charge flows past a point in the circuit in
this time?
8. What is an ammeter? How is it connected in a circuit? Draw a diagram to illustrate your answer.
9. A flash of lightning carries 10 C of charge which flows for 0.01 s. What is the current? If the voltage is
10 MV, what is the energy?

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 OHM’S Law
Ohm’s law:
At constant temperature, the current flowing through a given conductor is directly proportional to the
potential difference across the conductor.
According ohm’s law
𝐼 𝛼 𝑉 ( 𝑎𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑟𝑢𝑟𝑒)
𝑉𝛼𝐼
𝑉 =𝑅𝑋𝐼
Where, R is a constant called Resistance of the conductor.
Resistance of a conductor: The property of a conductor due to which it opposes the flow of current
through it is called resistance.
According to Ohm’s law:
𝑉 = 𝑅 .𝐼
𝑉
𝑅=
𝐼
Hence, the ratio of p.d. applied between the ends of a conductor and current flowing through it is
constant quantity called resistance.
The S.I. Unit of resistance is Ohm (Ω) (or) volt/ampere
Definition of ohm: One ohm is the resistance of a conductor such that when a potential difference of 1 volt
is applied across the ends of the conductor, a current of 1 ampere flows through it.
The strength of the electric current in a given conductor depends on two factors:
The current is directly proportional to p.d. and
The current is inversely proportional to resistance.
Graph between V and I:If we plot a graph by taking potential difference across the ends of a conductor
on y-axis and current flows through it on x-axis, it is a straight line passing through the origin as shown in
the figure.

Slope of the V-I curve gives the resistance of the conductor.

∆𝑉
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟𝑒 = 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑉 − 𝐼 𝑔𝑟𝑎𝑝ℎ =
∆𝐼

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Types of conductors:
Depends on the shape of the V-I curve (obeying ohm’s law), conductors are two types
1. Ohmic conductor and 2. Non ohmic conductors
Difference between Ohmic and Non-Ohmic Conductors:
Ohmic Conductors Non-ohmic Conductors
Definition The types of conductors that obey The types of conductors which do
Ohm's law are called Ohmic not obey Ohm's law are called as
Conductors. Non-Ohmic Conductors.
Effect on Resistance Ohmic conductors have a constant The resistance of the non-ohmic
electrical resistance over a wide conductor changes with changes
range of voltages and currents. in voltage and current.
Linearity The relationship between current and The relationship between current
voltage is linear. and voltage is not linear.
V-I Slope The voltage-current graph of ohmic The voltage-current graph of non-
conductors will be a straight line. ohmic conductors will be a curved
line.

Ohmic Conductors Non-ohmic Conductors

Examples Examples of Ohmic conductors are Examples of non-ohmic
metals, resistors, etc. conductors are diodes, transistors,
semiconductors, filament bulbs,
etc.

Factors affecting the resistance of a conductor: The resistance of a conductor (wire) depends on
1. Length of the conductor.
The resistance of a conductor is directly proportional to its length.
2. Area of cross-section of the conductor is inversely proportional to its area of cross section
The resistance of a conductor is
3. Nature of the material.
The resistance of different materials are different.

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 Ex: copper and nichorme alloy has different resistance.
4. Temperature of the conductor.
The resistance of all pure metals increases on raising the temperature, due to increase in the random
motion of free electrons.
Resistivity:
It is the resistance of the rod of that substance which is 1 meter long and 1 square meter in cross section.
It is also called specific resistance.
It is the characteristic property of the material.
It is independent of length and cross sectional area.
It depends on the nature and temperature of the material.
S.I. unit of resistivity is ohm-meter (Ω-m).
Expression for the resistivity:
The resistance of a given conductor is directly proportional to its length.
𝑅 𝛼 𝑙 --- (1)
The resistance of a given conductor is indirectly proportional to its cross-sectional area.
𝑅𝛼 --- (2)
By combining (1) & (2)
𝑙
𝑅𝛼
𝐴
𝑙
𝑅=𝜌
𝐴
𝐴
𝜌= 𝑅
𝑙
Where, ρ is called Resistivity of the material.
Good conductors, Resistors and insulators:
On the basis of their electrical resistance substances are divided into three groups:
1. Good conductors
2. Resistors
3. Insulators
Good conductors: The substances which have very low electrical resistivity are called good conductor.
Ex: silver, aluminium, copper etc.,
Resistors: The substances which have comparatively high resistivity are called resistors.
Ex: alloys like nichorme (alloy of Ni, Cr, and Mn ), Manganin (alloy of Cu, Mn and Ni), constantans (alloy
of Cu and Ni) etc.
Insulators: The substances which have high electrical resistivity are called insulators.
Ex: Rubber, plastic, glass etc.
The heating element of electrical heating appliance such as electric iron, toaster, etc., are made of an alloy
rather than a pure metal, because, (i) the resistivity of an alloy is higher than the pure metal (ii) an alloy doex
not easily undergoes oxidation even at high temperature.

Questions:
1. What is Ohm’s law?.
2. What is meant by the “resistance of a conductor”? Write the relation between resistance, potential
difference and current.
3. Define the unit of resistance.

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4. A potential difference of 20 volts is applied across the ends of a resistance of 5 ohms. What current
will flow in the resistance?
5. A resistance of 20 ohms has a current of 2 amperes flowing in it. What potential difference is there
between its ends?
6. A current of 5 amperes flows through a wire whose ends are at a potential difference of 3 volts.
Calculate the resistance of the wire.
7. Why do electricians wear rubber hand gloves while working with electricity?
8. An electric circuit consisting of a 0.5 m long nichorme wire XY, an ammeter, a voltmeter, four cells
of 1.5 V each and a plug key was set up.
(i) Draw a diagram of this electric circuit to study the relation between the potential difference
maintained between the points ‘X’ and ‘Y’ and the electric current flowing through XY.
(ii) Following graph was plotted between V and I values :

What would be the values of 1V ratios when the potential difference is 0.8 V, 1.2 V and 1.6 V
respectively? What conclusion do you draw from these values?
(iii) What is the resistance of the wire?
9. An electric room heater draws a current of 2.4 A from the 120 V supply line. What current will this
room heater draw when connected to 240 V supply line?
10. A current of 200 mA flows through a 4 kΩ resistor. What is the p.d. across the resistor?
11. Distinguish between good conductors, resistors and insulators. Name two good conductors, two
resistors and two insulators.
12. Classify the following into good conductors, resistors and insulators :
Rubber, Mercury, Nichrome, Polythene, Aluminium, Wood, Manganin, Bakelite, Iron, Paper,
Thermocol, Metal coin
13. Write any four differences between ohmic and non-ohmic conductors.
14. On what factors does the resistance of a conductor depend?
15. Write down an expression for the resistance of a metallic wire in terms of the resistivity.
16. Calculate the area of cross-section of a wire if its length is 1.0 m, its resistance is 23 Ω and the
resistivity of the material of the wire is 1.84 x 10-6 Ωm
17. Define resistivity. Write an expression for the resistivity of a substance. Give the meaning of each
symbol which occurs in it.
18. State the SI unit of resistivity.
19. Distinguish between resistance and resistivity.
20. Name two factors on which the resistivity of a substance depends and two factors on which it does
not depend.
21. The resistance of a metal wire of length 1 m is 26 Ω at 20°C. If the diameter of the wire is 0.3 mm,
what will be the resistivity of the metal at that temperature?

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Combination of Resistances:
The resistances can be combined in two ways
(i) Series
(ii) Parallel
Series connection:
When two or more resistances are connected end to end consecutively, they are said to be connected in
series.
When two or more resistors connected in series are joined to the terminals of a battery
(i) Each resistance have different p.d.
(ii) Same current flows through each resistance.
(iii) Sum of the p.d. across all the resistors is equal to the voltage of the battery.
Parallel connection:
When two or more resistances are connected between the same two points, they are said to be connected
in parallel.
When two or more resistors connected in parallel
(i) The p.d. across each resistance is the same, which is equal to the voltage of the battery applied.
(ii) Different amount of current flow through each resistance.
(iii) The sum of the currents flowing through all the resistances is equal to the total current flowing in
the circuit.
Resistances in series:
Law of series combination:
The combined resistance of any number of resistances connected in series is equal to the sum of the
individual resistances.
𝑅 = 𝑅 +𝑅 +𝑅

Expression for resultant resistance of three resistances connected in series:

Consider three resistances R1, R2 and R3 connected in series with the battery of ‘V’ volts as shown in the
figure.

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Let the p.d. across the resistances R1, R2 and R3 is V1, V2 and V3 respectively.
The total p.d. across the three resistances is equals to the voltage of the battery.
𝑉 = 𝑉 + 𝑉 + 𝑉 ---(1)
The total p.d. due to battery is V. Let the total resistance of the combination be R. The current flowing
through the whole circuit is I. So applying ohm’s law to the whole circuit,
𝑉 = 𝐼𝑅 ---(2)
Due to series combination, same current I flows through all the resistances R1, R2 and R3 in series, by
applying ohm’s law to each resistor separately, we have
𝑉 = 𝐼𝑅 ---(3)
𝑉 = 𝐼𝑅 ---(4)
𝑉 = 𝐼𝑅 ---(5)
Using 2,3,4 & 5 in 1
𝑉 = 𝑉 +𝑉 +𝑉
𝐼𝑅 = 𝐼𝑅 + 𝐼𝑅 + 𝐼𝑅
𝐼𝑅 = 𝐼(𝑅 + 𝑅 + 𝑅 )
𝑅 = 𝑅 +𝑅 +𝑅
When a number of resistances are connected in series, then their combined resistance is greater than the
individual resistance.
Resistances in parallel:
Law of parallel combination:
The reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the
sum of the reciprocals of all the individual resistances.
1 1 1 1
= + +
𝑅 𝑅 𝑅 𝑅
Expression for resultant resistance of three resistances connected in parallel:
Consider three resistances R1, R2 and R3 connected in parallel with the battery of ‘V’ volts as shown in the
figure.
Due to the parallel connection, the p.d. across the ends of the all three resistors will be the same say ‘V,.
Let the current passing through the resistors R1, R2 and R3 will be I1, I2 and I3 respectively.

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Total current, 𝐼 = 𝐼 + 𝐼 + 𝐼 --- (1)
Suppose the resultant resistance of this combination is R,
By ohm’s law, current in whole circuit, 𝐼 = --- (2)
By ohm’s law,
Current in R1 resistor, 𝐼 = --- (3)

Current in R2 resistor, 𝐼 = --- (4)

Current in R3 resistor, 𝐼 = --- (5)
Putting equations (2), (3), (4) & (5) in (1), we have
𝑉 𝑉 𝑉 𝑉
= + +
𝑅 𝑅 𝑅 𝑅
Cancelling V from both sides, we get, = + +
When a number of resistances are connected in parallel, then their combined resistance is smaller than the
individual resistance.
The arrangement of lights and other various appliances in Domestic electric circuits are made in parallel.
Disadvantages of Series circuits in domestic circuits:
1. In series circuit, if one electrical appliance stops working due to some defect then all other
appliances also stopping.
2. In series circuit, all the electrical appliances have only one switch due to which they cannot be turned
on or off separately.
3. In series circuit, the appliances do not get same voltage (220V)
4. The overall resistance of the household electrical circuit increases to much due to which the current
from the power supply is low.
Advantages of Parallel circuits in domestic circuits:
1. In parallel circuits, if one electrical appliance stops working due to some defect then all other
appliances keep working normally.
2. In parallel circuits, each electrical appliance has its own switch due to which it can be turned on or
turned off independently, without affecting other appliances.
3. In parallel circuits, each electrical appliance gets the same voltage (220V).
4. The overall resistance of the household electrical circuit decreases due to which the current from the
power supply is high.

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ELECTRIC POWER
Def:
The electrical work done per unit time is called electrical power.
Formula: 𝑃 =
The SI unit of power is watt (or) joule/second.
Definition of watt:
When an electrical appliance consumes electrical energy at 1 joule per one second, its power is said
to be 1 watt.
Other formula for electrical power:
𝑃𝑜𝑤𝑒𝑟 = 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑋 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
Derivation:
𝑊𝑜𝑟𝑘
𝑃𝑜𝑤𝑒𝑟 =
𝑡𝑖𝑚𝑒
𝑃= --- (1)
We know that 𝑉 =
𝑊=𝑉𝑋𝑄
𝐼=
𝑡=
Using W and t in equation (1)
𝑊 𝑉𝑋𝑄
𝑃= = =𝑉𝑋𝐼
𝑡 𝑄
𝐼
𝑉
𝑃= 𝑉 𝐼= I 𝑅=
𝑅

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 Electrical Energy:
Electrical energy consumed by electrical appliances is equals to the work done by electric current.
We know that 𝑃 =
𝑃=
E= PXt
So, the electrical energy is also defined as the product of power and time.
The other unit of electrical energy is watt-hour (W-h)
One watt-hour is the amount of electrical energy consumed when an electrical appliances of 1 watt power is
used for l hour.
Commercial unit of Electrical Energy: Kilo watt- Hour (KWh)
Def:
Kilo watt-hour: It the amount of electrical energy consumed when an electrical appliance having a power
rating of one kilo watt is used for 1 hour.
Relation between kilowatt-hour and joule: 1 𝐾𝑊 − ℎ = 3.6 𝑋 10 𝐽
1 𝐾𝑊 − ℎ = 1000 𝑤𝑎𝑡𝑡 𝑋 1 ℎ𝑜𝑢𝑟
𝑗𝑜𝑢𝑙𝑒𝑠
= 1000 𝑋 𝑋 60 𝑋 60 𝑠𝑒𝑐
𝑠𝑒𝑐
= 1000 𝑋 60 𝑋 60 𝑗𝑜𝑢𝑙𝑒𝑠
= 1000 𝑋 60 𝑋 60 𝑗𝑜𝑢𝑙𝑒𝑠
= 3600000 𝑗𝑜𝑢𝑙𝑒𝑠 = 3.6 𝑋10 𝐽

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Effects produced by electric current:
1. Heating effect
2. Magnetic effect
3. Chemical effect
Heat effect of current:
When an electric current is passed through a high resistance wire, like nichorme wire, the wire becomes very
hot and produces heat. This is called the heating effect of current.
Formula of heat produced:
𝐻= 𝐼 𝑅𝑡
Expression for the Heat produced:
We know that, 𝑊 = 𝑉𝑋𝑄
By ohm’s law, V = I R
𝐼= => 𝑄 = 𝐼 𝑋 𝑡
Therefore, 𝑊 = 𝐼𝑅 𝑋 𝐼𝑡
𝑊= 𝐼 𝑅𝑡
Assuming that, all the electrical work is converted into heat energy.
𝐻=𝑊 = 𝐼 𝑅𝑡
Joule’s law of heating:
The heat produced in a wire is directly proportional to
(i) Square of current (I2)
(ii) Resistance of wire (R)
(iii) Time (t)
Applications of the heating effect of current:
The heating effect of current is
1. utilised in the working of electrical heating appliances such as electric iron, electric kettle, electric
toaster, electric oven, room heaters, water heaters etc.,
2. Utilised in electric bulb for producing light.
3. Utilised in electric fuse for protecting household wiring and electrical appliances.
Electric bulb:

Tungsten metal is used for making the filaments of electric bulbs.

Properties of tungsten which make it suitable for making filament of electric bulbs:
1. Very high melting point ( 3380oC)
2. High flexibility
3. Low rate of evaporation at high temperature.
The electric bulb is filled with a chemically unreactive gas like argon or nitrogen (or a mixture of both)
Reason:
The gases like argon and nitrogen do not react with a hot tungsten filament and hence prolong the life of the
filament of the electric bulb

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If air is present in an electric bulb, then the extremely hot tungsten filament would burn up quickly in the
oxygen of air.
Electric fuse:
A fuse is a short length of a thin tin plated copper wire having high resistance and low melting point placed
between the metal caps and enclosed in quartz glass.

When the current in a household electric circuit rises too much due to some reason, then the fuse wire gets
heated too much, melts and breaks the circuit. This prevents the fire in house due to overheating of wiring
and also prevents damage to various electrical appliances.

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