11.Electricity

Electric circuit : A continuous and closed path of an electric current is called an elecic circuit.

Electric current : The rate of flow of electric charge in a conductor is called electric current.
The unit of electric current is ampere.
Electric current flow: The conventionally, current flow is from positive to the negative terminal.
Electron flow: The electron flow is from negative to positive terminal.
If a charge Q, flows across any cross-section of a conductor in time t, then the current I, through the cross-section is
I= Q/t
The SI unit of electric charge is coulomb (C)
Number of electrons in one coulomb of charge = 6×10¹⁸ electrons.
Negative charge on one electron= =1.6 x 10⁻¹⁹ coulomb
The flow of one coulomb of charge per second is called One ampere
Small amount of electric current is measured in milliampere mA (1mA = 10⁻³ A) or microampere μA (1μA = 10 ⁻⁶A).
Ammeter : The instrument used to measure electric current in an electric circuit is called ammeter. It is always connected in series in a circuit.
Electric potential and Potential difference
The electric potential at a point is equal to the work done in bringing a unit positive charge from infinity to that point.
Electric potential difference between two points in an electric circuit is equal to the work done in bringing a unit positive charge from one point to the other
Potential difference (V) between two points = Work done(W)/Charge (Q)
V = W/Q
The SI unit of electric potential difference is volt (V)
If the amount of work done in bringing a unit positive charge from one point to another is 1 J in an electric field then potential difference b/w the two points is said to be 1 volt.
1 volt = 1 joule /1 coulomb
The potential difference is measured by an instrument called the voltmeter. Voltmeter is connected in parallel sequence in the electric circuit.
Components of electric circuit
1. Electric cell 2. Battery

3. Plug key or switch (open) 4. Plug key or switch (closed)

5. A wire joint 6. Wires crossing without joining

7. Electric bulb 8. A resistor of resistance R

9. Ammeter 10. Voltmeter

11. Variable resistance or rheostat

Ohm's Law : At constant temperature the potential difference generated between the two ends of a conductor is proportional to the electric current flowing in that conductor. In other words-
V ∝ I
V = IR............(1)
R=V/I............(2)
I = V/R............(3)
R = is a constant which is called the resistance of the wire.

Resistance : The property of a conductor that opposes the flow of charge through it is called resistance.
The unit of resistance is Ohm (Ω).
by Ohm's law
R=V/I
One ohm : When a current of 1 ampere flows through a conductor with a potential difference of 1 volt, then the resistance of that conductor is called one ohm.
That is, 1 ohm = 1 volt/1 ampere
We know that,
I = V/R
The electric current flowing through a resistor is inversely proportional to its resistance.
Variable resistance : A component used to regulate current without changing the voltage source is called variable resistance.
Factors on which the resistance of a conductor depends
1. Length of conductor – The resistance of a conductor wire is directly proportional to its length.
R∝l ................(i)
2. Area of cross section of a conductor – The resistance of a conducting wire is inversely proportional to the area of its cross section.
R∝ 1/A ................(ii)
From (i) and (ii)
R∝l/A
R=𝞺 l/A
Where 𝞺 (Rho) is a constant which is called the electrical resistivity of the conducting material. The unit of resistivity is Ωm.
The resistance of alloys is higher than that of its constituent metals. , That is why alloys do not undergo oxidation at high temperatures. Therefore, they are used to make components of heating elements of electric toasters, irons etc.
Tungsten is used for filaments of electric bulbs
3. Nature of the material - The resistance of a good conductor of electricity is low and the value of resistance increases as the conductivity decreases.
Combination of resistances
There are two methods of connecting resistors together.
1. Series combination: When two or more resistances are connected end to end respectively, then this type of combination is called series combination.
Equivalent resistance for series combination

In the series combination of resistances, the value of electric current flowing through each resistance of the circuit is sam. It means that the current I is flowing in the series connected resistances R₁, R₂ and R₃ and the potential difference generated between the ends of these resistances is V₁, V₂ and R₃ respectively. If the total potential difference of the circuit is V then it is equal to the sum of all three potential differences V₁, V₂ and V₃. Therefore
V = V₁ + V₂ + V₃ . , , , , , , , (i)
If the equivalent resistance of the circuit is R, then according to Ohm's law for the entire circuit-
V=IR
According to Ohm's law, the value of potential difference for each resistance will be as follows
V₁ = IR₁
V₂ = IR₂
V₃ = IR₃
On keeping the values of V, V₁, V₂, and V₃ in equation (i)
IR = IR₁ + IR₂ + IR₃
R = R₁ + R₂ + R₃ . , , , , , , , (ii)
Therefore, in series connection the total equivalent resistance of the circuit is equal to the sum of all the resistances.
2. Parallel series combination: When two or more resistances are connected between two ends, it is called parallel series combination.
Equivalent resistance for parallel combination

In parallel combination of resistances, the value of potential difference between the two ends of each resistance of the circuit is equal. Suppose three resistances R₁, R₂ and R₃ are connected in parallel, current I₁, I₂ and I₃ respectively flows in them. If the total current flowing in the circuit is If I is then it is equal to the sum of the current flowing in each resistance. Therefore
I= I₁+ I₂+ I₃. ........................ (i)
If the equivalent resistance of the circuit is R and the potential difference is V, then according to Ohm's law for the entire circuit-
I=V/R
If the potential difference generated at the ends of the resistors is V, then according to Ohm's law the value of current flowing in each resistance will be as follows:
I₁ = V/R₁
I₂ = V/R₂
I₃ = V/R₃
On keeping the values of I, I₁, I₂ and I₃ in equation (i)
V/R = V/R₁ + V/R₂ + V/R₃
V/R = V( 1/R₁ + 1/R₂ + 1/R₃)
1/R = 1/R₁ + 1/R₂ + 1/R₃ . , , , , , , , (ii)
Thus, the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
Disadvantage of a series circuit
In a series circuit the current is constant throughout the electric circuit. Thus it is obviously impracticable to connect an electric bulb and an electric heater in series, because they need currents of different values to operate properly
When one component fails the circuit is broken and none of the components works.
On the other hand, a parallel circuit divides the current through the electrical gadgets. The total resistance in a parallel circuit is decreased .This is helpful particularly when each gadget has different resistance and requires different current to operate properly.
Thermal effects of electric current
When electric current is passed through a conductor, it gets heated. This is called the thermal effect of electric current.
This effect is used in devices like electric heater, electric kettle, electric iron.
If electric current I is flowing in a conductor. The potential difference between its ends is V if a charge Q flows in this conductor in time t. so the work done
W = VQ { V = W/Q }
W = VIt { I = Q/t }
This input energy (VIt) will be converted into heat energy, hence
H = VIt
H = IRIt { V= IR by Ohm's law }
H=I²Rt
joule's heating law
When electric current is passed through a resistance, the value of heat produced in it -
1. Is proportional to square of current flowing through the conducter
H ∝ I²
2. Is proportional to resistance is
H ∝ R
3. Is proportional to the time for which the current flows through the resistance
H ∝ t
Therefore,
H=I²Rt
This is called Joule's law of heating.
Electric iron, electric laundry, electric toaster, electric tandoor, electric kettle and electric heater are devices based on Joule's heating.
Practical Applications of Heating Effect of Electric Current
1. The Heating Effect of electric current is used to produce light in an electric bulb
An electric bulb's filament is made of tungsten, which has a high melting point. When current flows through the tungsten wire, it becomes heated and emits light. The bulbs are usually filled with chemically inactive nitrogen and argon gases to increase the lifetime of filament. Most of the energy consumed by the filament appears in the form of heat, and the rest is emitted in the form of light energy.
2. The heating effect of electric current is used in fuses used in electrical circuits It protects circuits and appliances by stopping the flow of any high electric current.
A fuse is a piece of metal or alloy wire with appropriate melting point for example aluminium, copper, iron, lead etc. It is connected in series with the device. When electric current more than the specified value flows through the circuit, the temperature of the fuse wire increases. Due to this, melts the fuse wire and breaks the circuit.
The fuses used for domestic purposes are rated as 1 A, 2 A, 3 A, 5 A, 10 A, etc.
Electric power : The rate at which electric energy is consumed in an electric circuit is called electric power
The power P is given by
P = VI
P = I²R [ ∵V = IR]....(i)
P = V²/R [V =I/R]....(ii)
The SI unit of electric power is watt (W).
It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus,
1 W = 1 volt × 1 ampere = 1 V A
The unit ‘watt’ is very small. Therefore, in actual practice we use a much larger unit called ‘kilowatt’. It is equal to 1000 watts. Since electrical energy is the product of power and time, the unit of electrical energy is watt hour.
When one watt of power is used for one hour, the energy consumed is one watt hour.
The commercial unit of electrical energy is kilowatt hour, which is commonly called 'unit'.
1 kWh = 1000 watts × 3600 seconds
1 kWh = 3.6 X 10⁶ watt second
1 kWh = 3.6 X 10⁶ joules

What is the SI unit of electric potential?
Volt is the SI unit of electric potential.
What happens to the resistance of a conductor when temperature is increased?
The resistance of a conductor increases with rise in temperature.
Why do we use copper and aluminium wires for transmission of electric current?
The copper and aluminium have low resistivity and high conductivity.
What is the resistance of an ideal voltmeter?
The resistance of an ideal voltmeter is infinite.
What material is used in making the filament of an electric bulb?
Tungsten is used in making filament.
Name and state the law that gives relationship between the current through a conductor and the potential difference across its two terminals
The law is Ohm’s law.
A thick wire and a thin wire of the same material are successively connected to the same circuit to find their respective resistance. Which one will have lower resistance? Give reason.
Thick wire has lower resistance because the resistance of a conducting wire is inversely proportional to the area of its cross section.
Mention two special features of the material to be used as element of an electric iron.
1.High resistance
2.Free from oxidation in open atmosphere.
What are the values of mA and μA ?
1mA (1 milli ampere) = 10⁻³ A
1μA (1 micro ampere)= 10 ⁻⁶A)
Define electric current and state its SI unit
The rate of flow of electric charge in a conductor is called electric current.
The unit of electric current is ampere.
Define power. Write SI and unit of power
The rate at which electric energy is consumed in an electric circuit is called electric power. The SI unit of electric power is watt (W).
Elements of electric toasters and electric iron are made of an alloy rather than a pure metal. Give two reasons to justify the statement.
(i) The resistance of alloys is higher than that of its constituent metals.
(ii) At high temperature alloys do not oxidise.
How does the resistivity of alloys compare with those of pure metals from which they may have been formed?
The resistivity of pure metals is lesser than resistivity of alloys with which these alloys are made.
Name the device/instrument used to measure potential difference. How is it connected in an electric circuit?
The potential difference is measured by an instrument called the voltmeter.
Voltmeter is connected in parallel sequence in the electric circuit.
Mention one reason why tungsten is used for making filament of electric lamp.
Tungsten is used for making filament because of its high melting point and low resistivity.
Nichrome is used to make the element of electric heater. Why?
Nichrome is used to make element of electric heater because nichrome is an alloy which has high melting point and resistances.
What happens to the resistance of a conductor when the length of the conductor is reduced to half?
Resistance is directly proportional to the length of the conductor. So if length of the conductor becomes half the resistance also become half.
Define 1 kilowatt hour.
When 1000 watt of power is used for one hour, the energy consumed is one kilowatt hour.
(i) Name the instrument/device used to measure electric current in a circuit.
Ammeter is used to measure electric current.
(ii) How is an ammeter connected in a circuit to measure current flowing through it?
Ammeter is connected in series in an electric circuit.
Draw the symbols of battery and rheostat.
If the charge on an electron be 1.6 x 10⁻¹⁹ C, find the approximate number of electrons in 1 C.
Number of electrons in 1.6 x 10⁻¹⁹ coulomb of charge = 1
Number of electrons in one coulomb of charge =
=6×10¹⁸ electrons.
In an electric circuit, state the relationship between the direction of conventional current and the direction of flow of electrons.
Electrons flows from negative terminal to positive terminal where as current flows from +ve terminal to ve- terminal in external circuit i.e. Conventional current and electrons flow are opposite to each other.
State a difference between the wire used in the element of an electric heater and in a fuse wire.
The wire used in element of electric heater has high resistance and high melting point where as a fuse wire has a low resistance and low melting point.
What do you mean by heating effect of electric current? Name two devices based on heating effect of current.
When electric current is passed through a conductor, heat is produced and it gets heated. This is called the heating effect of electric current.
This effect is used in devices like electric heater, electric kettle, electric iron.
Define potential difference between two points in a conductor.
Electric potential difference between two points in an electric circuit is equal to the work done in bringing a unit positive charge from one point to the other.
Why is much less, heat generated in long electric cables than in filaments of electric bulbs?
Electric cables are made of thick good conductor whose resistance is very less where as filaments are made of thin tungsten wire whose resistances is high. . So heat produced in cable is much lesser than filaments
Why the elements of heating electrical appliances are made-up of an alloy rather than pure metal.
The resistance of alloys is higher than that of its constituent metals. That is why alloys do not undergo oxidation at high temperatures. Therefore, they are used to make components of heating elements of electric toasters, irons etc.
When is potential difference between two points said to be 1 volt?
If the amount of work done in bringing a unit positive charge from one point to another is 1 J in an electric field then potential difference b/w the two points is said to be 1 volt.
State the difference between 1 watt and 1 watt hour.
One watt is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 Volt, while One watt - hour is the amount of electrical energy consumed which an electrical device of 1 watt power is used for 1 hour.
Write the relation between electric power (P) of a device with potential difference (Volt) across it and current (amp) flowing through it.
The power (P) in watts is found by multiplying the potential difference (V) in volts by the current (I) in amperes.
Electric power = Potential difference × Current
∴ P = V × I
Mention the condition under which charges can move in a conductor. Name the device which is used to maintain this condition in an electric circuit.
When a potential difference is applied across the two ends of the conductor, charges (electrons) will move in the conductor.
Electric cell or a battery is used to maintain this condition in an electric circuit.
An electric iron draws a current of 0.5 A when the voltage is 200 volt. Calculate the amount of electric charge flowing through it in one hour.
Gven I = 0.5 A, V =200, volt t = 1hour = 3600 s
Q = It
= 0.5 x 3600 C
= 1800C
A charge of 150 coulomb flows through a wire in one minute. Find the electric current flowing through it.
Givin : Charge, Q = 150 C, Time, t = 1 min = 60 s
I = Q/t
I = 150/60
= 2.5 Amp
Power of a lamp is 60 W. Find the energy in joules consumed by it in 1 s.
P = 60 W, t = 1
Energy = (VI)t
E = Pt
= 60 x 1
= 60 J
The amount of charge passing through a cell in four second is 12 C. Find the current supplied by cell.
Given: t = 4 s, Q = 12 C
I = Q/t
= 4/2
= 2A
The current through a resistor is made three times its initial value. Calculate how it will affect the heat produced in the resistor.
Initial heat generated in the resistor
H=I²Rt
when current is made three times.
It means I = 3I
H=(3I)²Rt
H = 9I²Rt
Therefore heat generated is 9 times the initial heat generated.
Find the increase in the amount of heat generated in a conductor if another conductor of double resistance is connected in the circuit keeping all other factors unchanged.
Initial heat generated in the conductor
H=I²Rt
Another conductor of 2R is connected in series then total resistance = R + 2R = 3R.
It means R = 3R
H=I²3Rt
H = 3I²Rt
Therefore heat generated is three times
Explain two disadvantages of series arrangement for household circuit.
In series circuit, if one electrical appliance stops working due to some defect then all other appliances also stop working because the whole circuit is broken.
In series circuit, all the electrical appliances have only one switch due to which they cannot be turned off or turned on separately.
Define the term electrical resistivity of a material. Write SI unit of resistivity.
The resistance of the conductor of unit length & unit area of cross section is called its resistivity.
R=𝞺 l/A
Where 𝞺 (Rho) is a constant which is called the electrical resistivity of the conducting material. The unit of resistivity is Ωm.
Establish the relationship between commercial unit of electric energy and SI unit of energy.
The commercial unit of electrical energy is kilowatt hour, which is commonly called 'unit'.
1 kWh = 1000 watts × 3600 seconds
1 kWh = 3.6 X 10⁶ watt second
1 kWh = 3.6 X 10⁶ joules
Define electric circuit. Distinguish between open and closed circuit.
A continuous and closed path of an electric current is called an electric circuit.
1. In open circuit, current does not flow whereasin closed circuit, current flows.
2. Closed circuit is represented by ( . ) sign whereasin open circuit is represented by ( ) sign.
What is meant by resistance of a conductor? Name and define its SI unit.
The property of a conductor that opposes the flow of charge through it is called resistance.
The unit of resistance is Ohm (Ω).
1 Ohm - When one ampere current flows through a conductor with a potential difference of one volt, then the resistance of that conductor is called one ohm.
That is, 1 ohm = 1 volt/1 ampere
Explain two disadvantages of series arrangement for household circuit.
In series circuit, if one electrical appliance stops working due to some defect then all other appliances also stop working because the whole circuit is broken.
In series circuit, all the electrical appliances have only one switch due to which they cannot be turned off or turned on separately.
Draw a schematic diagram of a circuit consisting of a cell of 1.5 V, 10 ohm resistor and 15 ohm resistor and a plug key all connected in series.
What is the lowest resistance that can be obtained by combining four coils of resistances 4 W , 8 W , 12 W and 24 W ?
If the resistances are combined in parallel then we shall get the lowest resistance. In parallel combination:
What do the following symbols represent in a circuit? Write the name and one function of each.

(i)

(ii)

(i) Variable resistance
Variable resistor used to change the current in circuit.
(ii) Wires crossing without joining.
It is used when large number of connections are to be made with the help of wires out joining them.

Given below is a circuit showing current flowing in it. Identify each component A, B, C, D of this circuit.

A — Bulb (load)
B — Rheostat
C — Cell
D — Ammeter (being in series)
(i) Draw a circuit diagram to show how two resistors are connected in series.
(ii) In a circuit, if the two resistors of 5 ohm and 10 ohm are connected in series, how does the current passing through the two resistors compare?
In series combination of resistances, the current remains same.
An electric heater rated 800 W operates 6h/day. Find the cost of energy to operate it for 30 days at ₹3.00 per unit.
Power of the heater, P = 800 W, Time, t = 6 hour/day;
No. of days, n = 30, Cost per unit = ₹3.00, Total cost of its usage = ?;
Energy consumed E = P × t
Energy consumed in 1 day = 800 × 6
                                    = 4800 Wh
Total energy consumed in 30 days = 4800 × 30
                                                   = 144000 Wh
                                                   = 144 kWh (units)
Cost of 1 unit = ₹3
Cost of 144 units = 3 × 144 = ₹432
List in a tabular form two differences between a voltmeter and an ammeter.
Voltmeter
1. It is used to measure potential difference.
2. It is connected in parallel sequence in circuit.
3. Its resistance is very high
Ammeter
1. It is used to measure electric current in an electric circuit.
2. It is connected in series in a circuit.
3. Its resistance is very low
What is the shape of the graph between V and I, where V is the potential difference applied between the ends of a wire and I is the current flowing through it?
The graph between the potential difference (V) and the corresponding current (I) is a straight line passing through the origin.
List any two factors on which resistance of a conductor depends.
1. Length of conductor – The resistance of a conductor wire is directly proportional to its length.
R∝l
2. Area of cross section of a conductor – The resistance of a conducting wire is inversely proportional to the area of its cross section.
R∝ 1/A
A wire of resistance 5 W is bent in the form of a closed circle. What is the resistance between two points at the ends of any diameter of the circle?
Two semi circles are connected across diameter AB. Total resistances of circle is 5 W. So resistance of every semi circle will be 2/5W.
Calculate the number of electrons that would flow per second through the cross- section of a wire when 1 A current flows in it.
Given: I = 1A, t = 1s
I = Q/t
Q = It
   = 1 x 1
   = 1 C
But Q = ne

   = 6×10¹⁸ electrons.
Out of the two, a toaster of 1 kW and an electric heater of 2 kW, which has a greater resistance?
P₁ = 1 KW, P₂ = 2 KW
∵P = V²/R ∴ R = V²/P
R₁ = V²/P₁ R₂ = V²/P₂
R₁ = V²/1 R₂ = V²/2
R₁ = V²/1 R₂ = V²/2
R₁/ R₂ = V²/1/V²/2
R₁/ R₂ = 2/1
R₁ = 2, R₂ = 1
As P = V²/R If V is constant. Then P ∝ 1/R i.e. Power is inversely proportional to resistance. Toaster has lesser power than electric heater therefore resistance of toaster is more than resistances of heater.
What is the total resistance of n resistors each of resistance ‘R’ connected in: (i) series? (ii) parallel?
In series combination
RS = R₁ + R₂ +R₃ + ....Rₙ
In parallel combination
1/R = 1/R₁ + 1/R₂ + 1/R₃.....1/Rₙ
Why is much less, heat generated in long electric cables than in filaments of electric bulbs?
As heat produced= I²Rt
Electric cables are made of thick good conductor where as filaments are made of thin tungsten wire whose resistances is high. The resistance of electric cables is very less. So heat produced in cable is much lesser than filaments
A cylinder of a material is 10 cm long and has a cross-section of 2 cm². If its resistance along the length be 20 ohm, what will be its resistivity
R=𝞺 l/A
𝞺 = R A/l
l = 10 cm, A = 2 cm², R = 20 ohm
𝞺 = 20 x 2/10
𝞺 = 4 Ωcm.
An electric bulb is rated at 200 V–100 W. What is its resistance? Five such bulbs bum for 4 hours. What is the electrical energy consumed? Calculate the cost, if the rate is 50 paise unit.
Givin V V200 = P = 200W, V = 200V

R = 400Ω
Electric current flows through three lamps when arranged in (i) a series (ii) a parallel. If the filament of one lamp breaks. Explain what happens to the other two lamps in both the cases.
(i) In series combination if the filament of one lamp breaks then the circuit will be broken and hence other lamps stops glowing.
work is done.
(ii) In parallel combination of lamps if the element of one lamp breaks then other two will continue to glow.
Write Joule’s law of heating.
When electric current is passed through a resistance, the value of heat produced in it -
1. Is proportional to square of current flowing through the conducter
H ∝ I²
2. Is proportional to resistance is
H ∝ R
3. Is proportional to the time for which the current flows through the resistance
H ∝ t
Therefore,
H=I²Rt
This is called Joule's law of heating.
An electric bulb is rated at 200 V–100 W. What is its resistance? Five such bulbs bum for 4 hours. What is the electrical energy consumed? Calculate the cost, if the rate is 50 paise unit.
Givin V V200 = P = 200W, V = 200V

R = 400Ω
Energy consumed in 4 hrs. by one bulb.
E = P x t
= 100 x 4
= 400Wh
Total energy consumed by 5 similar bulb
= 5 x .4
= 2kWh(Unit)
Cost of 2 units of electric energy = 2 x .50
= ₹1
Study the following circuit and answer the following questions:

(i) State the type of combination of the two resistors in the circuit.
10 W and 15 W are in parallel combination.
(ii) How much current would flow through: (1) 10 Ω resistor and (2) 15 Ω resistor?
Potential difference across each is 3V.
Givin R₁ = 10 Ω,  R₂ = 15Ω, V = 3 Volt
I in 10 Ω resistor , I₁ = R₁/V
                               = 10/3
                               = 0.3 A
I in 15Ω resistor, I₂ = R₂/V
                          = 15/3
                          = 0.2 A
(iii) What would be the ammeter reading?
Ammeter reading = I₁ + I₂
                          = 0.3 + 0.2
                          = 0.5 A
An electric heater rated 1000 W/220 V operates 2 hours daily. Calculate the cost of energy to operate for 30 days at the rate of Rs 5.00 per kWh.
Energy consumed by heater in one month
= 1000 x 2 x 30
= 60 kWh(units)
Total cost [@ 5/-kWh] = 5 x 60 = 300/-
Calculate the resistance of an electric bulb which allows a 10 A current when connected to a 220 V power source.
V = 220 Volt., I = 10 A
Resistance of bulb[R] = V/I
= 220/10
= 22 W

11.Electricity

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