CBSE Class 10 Science Electricity Notes

ELECTRICITY

Electricity is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena such as lightning and static electricity, but in addition, less familiar concepts such as the electromagnetic field and electromagnetic induction.

Key Learnings:

1. Electric current is the rate of flow of charge.

2. Battery provides the driving force required to move the charges along the wire from one terminal to another.

3. The constant voltage difference between the two terminals of the wire maintains the constant electric current through the wire.

4. Electric current is measured in terms of amperes where 1 ampere = 1 coulomb / second

5. Voltage is measured in terms of volt where 1 volt = 1 joule /coulomb

6. Resistance is a property that resists the flow of electrons in a conductor. It controls the magnitude of the current. The SI unit of resistance is ohm (Ω).

7. Resistivity is defined as the resistance offered by a cube of the material of side 1 m when the current flows perpendicular to the opposite faces of the cube.

8. Ohm’s law: The potential difference across the ends of a resistor is directly proportional to the current through it, provided its temperature remains the same.

9. The resistance of a conductor depends directly on its length, inversely on its area of cross – section, and also on the material of the conductor.

10. In Series combination of resistors:

- The current flowing through each resistor is the same

- The potential difference across the ends of the series combination is distributed across the resistors

- The equivalent resistance is greater than the greatest resistance in the combination.

11. In Parallel combination of resistors:

- The potential difference across each resistor is same and is equal to the potential difference across the combination.

- The main current divides itself and a different current flow through each resistor.

- The equivalent resistance is lesser than the least of all the resistances.

12. The effect of heating current due to which heat is produced in a wire when current is passed through it is called heating effect of current.

13. Electric power is the rate at which electrical energy is produced or consumed in an electric circuit.

14. The unit of power is watt (W). One watt of power is consumed when 1 A of current flows at a potential difference of 1 V.

15. The commercial unit of electric energy is kilowatt hour (kW h), commonly known a ‘unit’.

Top Formulae:

1. The current I through the cross – section of a conductor is 

I = Q/t

Where Q is net charge flowing across the cross – section of a conductor in time t.

2. Potential difference (V) between two points = work done (W)/ Charge (Q)

V = W/Q

3. Ohm’s law: V = I R

4. The equivalent resistance in series circuit is the sum of the individual resistances - R = R1 + R2 + R3

5. The equivalent resistance of a parallel circuit containing resistances R1, R2, R3 is given as

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

6. The electric power P is given by

P = VI 

Or

P = I²R = V²/ R

7. The electrical energy dissipated in a resistor is given by W = V * I * t 

8. Joule’s law of heating; H = I²Rt

9. 1 kW h = 3, 600, 000 J = 3.6 x 10⁶ J

Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces. Electric charge is conserved, additive and quantised.

The S.I. unit of electric charge is ‘C’ coulomb. Any other charged body will have a charge Q
                                                                                                                                             Q = ne
where n is the number of electrons and e is the charge on electron = 1.6 x 10^–19 coulombs.

Electric current

Electric current is a flow of electrons in a conductor such as a metal wire. Electric current is expressed by the amount of charge flowing through a particular area in unit time. In other words, it is the rate of flow of electric charges. In circuits using metallic wires, electrons constitute the flow of charges. However, electrons were not known at the time when the phenomenon of electricity was first observed. So, electric current was considered to be the flow of positive charges and the direction of flow of positive charges was taken to be the direction of electric current. Conventionally, in an electric circuit the direction of electric current is taken as opposite to the direction of the flow of electrons, which are negative charges. The magnitude of electric current in a conductor is the amount of electric charge passing through a given point of conductor in 1 second.

I = Q/t

S.I. unit of electric current is ‘A’ (Ampere).
The electric current is expressed by a unit called ampere (A), named after the French scientist,
Andre-Marie Ampere (1775–1836).

One Ampere

When 1 coulomb of charge flows through any cross-section of a conductor in 1 second, the
electric charge flowing through it is said to be 1 ampere.
Smaller unit current is milliampere(mA) and microampere(m A)
1 mA = 10^–3A
1 m A = 10^–6A
An instrument called ammeter measures electric current in a circuit. It is always connected in series in a circuit through which the current is to be measured. The direction of electric current is from positive terminal to negative terminal through the electric circuit.

INTEXT QUESTIONS 

1. What does an electric circuit mean?

Ans. An electric circuit consists of electric devices, switching devices, source of electricity, etc. that are connected by conducting wires.

2. Define the unit of current.

Ans. The unit of electric current is ampere (A). 1 A is defined as the flow of 1 C of charge through a wire in 1 s.

3. Calculate the number of electrons constituting one coulomb of charge.

Ans. One electron possesses a charge of 1.6 × 10⁻¹⁹ C, i.e., 1.6 × 10⁻¹⁹ C of charge is contained in 1 electron.
∴ 1 C of charge is contained in 1/1.6 × 10⁻¹⁹ =1 6.25×10¹⁸ electrons 

Therefore, 6.25´10¹⁸ electrons constitute one coulomb of charge.

Potential difference

Potential difference, VA – VB between two points A and B is the work done per unit charge in taking a charge from B to A.

Potential difference, VA – VB =work done/charge, where VA is potential at point A, VB is potential at point B and S.I. unit of potential is volts (V), named after Alessandro Volta (1745–1827), an Italian physicist.  

Electric Potential

Electric Potential at a point is defined as the work done per unit charge in bringing a charge from infinity to that point.

V = work done / Charge = W/Q

The potential difference is measured by means of an instrument called the voltmeter. The voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

One volt: The potential difference between two points is said to be 1 volt if 1 joule of work is done in moving 1 coulomb of electric charge from one point to the other.

Electrons always flow from lower potential to higher potential.

INTEXT QUESTIONS

1. Name a device that helps to maintain a potential difference across a conductor.

Ans. A source of electricity such as cell, battery, power supply, etc. helps to maintain a potential difference across a conductor.

2. What is meant by saying that the potential difference between two points is 1 V?

Ans. If 1 J of work is required to move a charge of amount 1 C from one point to another, then it is said that the potential difference between the two points is 1 V.

3. How much energy is given to each coulomb of charge passing through a 6 V battery?

Ans. The energy given to each coulomb of charge is equal to the amount of work required to move it. The amount of work is given by the expression,

Potential difference = Work done / Charge

Work done = Potential difference * Charge

Where, Charge = 1 C and Potential difference = 6 V

Work done = 6*1= 6 J

Therefore, 6 J of energy is given to each coulomb of charge passing through a battery of 6 V.

NUMERICAL PROBLEMS

1. Find the charge if the number of electrons is 4 x 10–18.

2. Find the number of electrons constituting one coulomb of charge.

3. How much work done in moving a charge of 3 coulombs from a point at 118 V to a point at 128 volt?

4. How much work done in moving a charge of 2C across two points having a potential difference of 12V?

5. Calculate the amount of work done to carry 4C from a point at 100 V to a point at 120 volt?

6. How much work will be done in bringing a charge of 2 x 10–3 coulombs from infinity to a point P at which the potential is 5 V?

7. How much work will be done in bringing a charge of 3 x 10–2 coulombs from infinity to a point P at which the potential is 20 V?

8. How much energy is given to each coulomb of charge passing through a 6V battery?

9. How much energy is transferred by a 12 V power supply to each coulomb of charge which it moves around a circuit?

10. 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?

11. What is the potential difference between the conductors A and B shown in below figure? If the conductors are connected by a length of wire, which way will electrons flow? When will this flow of electrons stop?

12. A particle of charge 2C is taken from a point at a potential of 100V to another point at a potential of 150V. Calculate the work done.

13. What is the potential difference between the conductors A and B shown in below figure? If the conductors are connected by a length of wire, which way will electrons flow? When will this flow of electrons stop?

14. A particle of charge 5 x 10–2 C is taken from a point at a potential of 50V to another point at a potential of 250V. Calculate the work done.

15. Three 2V cells are connected in series and used as a battery in a circuit.

(a) What is the potential difference at the terminals of the battery?

(b) How many joules of electrical energy does 1 C gain on passing through (i)one cell (ii)all three cells.

CIRCUIT DIAGRAM

The Schematic diagram, in which different components of the circuit are represented by the symbols conveniently used, is called a circuit diagram. Conventional symbols used to represent some of the most commonly used electrical components are given below:

Ohm’s law

According to Ohm’s law, “At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.”

I ∝ V or V ∝ I at constant temperature

V = IR where R is constant of proportionally which is know as resistance.

Resistance

It is the ratio of potential difference applied between the ends of a conductor and the current flowing through it. The unit of resistance is ohm(Ω).

One Ohm

One Ohm is the resistance of a conductor such that when a potential difference of 1 volt is applied to its ends, a current of 1 ampere flows through it.

If the resistance is doubled the current gets halved. In many practical cases it is necessary to increase or decrease the current in an electric circuit. A component used to regulate current without changing the voltage source is called variable resistance. In an electric circuit, a device called rheostat is often used to change the resistance in the circuit.

Factors on which the Resistance of a conductor depends

The resistance of the conductor depends (i) on its length, (ii) on its area of cross-section, and (iii) on the nature of its material.

Resistance depends on area of cross section: It is inversely proportional to the area of cross section (A)

R ∝ 1/A

Resistance depends on length of wire: It is directly proportional to the length of the wire (l)

R ∝ l

Combining the above we get R ∝ 1/A

⇒ R = þ.1/A

where þ (rho) is a constant of proportionality which is called the resistivity or specific resistance of the material.

If l = 1m, A = 1m2 then R = þ

Resistivity of a material is the resistance of a unit length of the material having unit area of cross section.

Question. Define Electric current.
Answer: The amount of charge flowing through a particular area in unit time
Or
it is the rate of flow of electric charges

Question. What is the direction of flow of current in a circuit?
Answer: Conventionally, in an electric circuit the direction of electric current is taken as opposite to the direction of the flow of electrons, which are negative charges i.e. from + to –

Question. How many electrons make one coulomb of charge?
Answer: coulomb (C), is equivalent to the charge contained in nearly 6 × 1018 electrons. (We know that an electron possesses a negative charge of 1.6 × 10^–19 C.)

Question. Define 1 Ampere.
Answer: One ampere is constituted by the flow of one coulomb of charge per second.

Question. Define the electric potential difference between two points in an electric circuit carrying some current.
Answer: The work done to move a unit 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)

Question. Define I volt.
Answer: One volt is the potential difference between two points in a current carrying conductor when 1 joule of work is done to move a charge of 1 coulomb from one point to the other.
Therefore, 1 volt =1 joule / 1 coulomb

Question. State Ohm’s Law.
Answer: The electric current flowing through a metallic wire is directly proportional to the potential difference V, across its ends provided its temperature remains the same. This is called Ohm’s law. In
other words –
or V/I = constant= R or V = IR
R is a constant for the given metallic wire at a given temperature and is called its resistance.

Question. What is meant by resistance of a conductor?
Answer: It is the property of a conductor to resist the flow of charges through it. Its SI unit is ohm, represented bythe Greek letter Ω^∼

Question. Define one ohm.
Answer: If the potential difference across the two ends of a conductor is 1 V and the current through it is 1 A, then the resistance R, of the conductor is 1 Ω. That is, 1 ohm = 1 volt /1 ampere.

Question. What is variable resistance?
Answer: A component used to regulate current without changing the voltage source is called variable resistance. In an electric circuit, a device called rheostat is often used to change the resistance in the circuit.

Question. What are the factors on which the resistance of a conductor depend?
Answer: Resistance of the conductor depends (i) on its length, (ii) on its area of cross-section (iii) on the nature of its material (iv) temperature.

Question. What is meant byresistivity of a material?
Answer: Resistivity of a material is the resistance ofthe conductor of that material having length 1m
and area of cross section 1m²
R=ρL/A
If L=1m and A=1m²
Then R=ρ
The SI unit of resistivity is Ωm. It is a characteristic property of the material.

Question. Why are alloys preferably used in electrical heating devices?
Answer: (1) the resistivity of an alloy is generally higher than that of its constituent metals.
(2) Alloys do not oxidise (burn) readily at high temperatures. For this reason, they are commonly used in electrical heating devices, like electric iron, toasters etc.

Question. Derive that equivalent resistance Rs = R₁ +R₂ + R₃ if R₁ ,R₂, R₃ are connected in series.

Answer: You will observe that the potential difference V is equal to the sum of potential differences V₁, V₂, and V₃. That isthe total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors. That is,
V = V₁ + V₂ + V₃
let I be the current through the circuit. The current through each resistor is also I. It is possible to replace the three resistors joined in series by an equivalent single resistor of resistance R,such that the potential difference V across it, and the current I through the circuit remains the same.
Applying the Ohm’s law to the entire circuit, we have
V=IR
On applying Ohm’s law to the three resistors separately, we further have
V₁ = I R₁
V₂ = I R₂
and V3 = I R₃
So I R = I R₁ + I R₂ + I R₃
Or Rs = R₁ +R₂ + R₃
We can conclude that when several resistors are joined in series, the resistance ofthe combination Rs equals the sum of their individual resistances, R₁ ,R₂, R₃ and is thus greater than
any individual resistance.

Question. Derive that equivalent resistance if R₁ ,R₂, R₃ are connected in parallel. 

Answer: The total current I, is equal to the sum ofthe separate currents through each branch of the combination.
l = l₁ + l₂ + l₃
Let Rp be the equivalent resistance of the parallel combination of resistors. By applying Ohm’s law to the parallel combination of resistors, we have
l = V/Rp
On applying Ohm’s law to each resistor, we have
l1 = V/R₁; l₂ = V/R₂; and l₃ = V/R₃
V/Rp = V/R₁ + V/R₂ + V/R₃
or
1/Rp = 1/R₁ + 1/R₂ + 1/R₃

Question. What do you mean by heating effect of current ?
Answer: To maintain the current, the source has to keep expending its energy. A part of the source energy in maintaining the current may be consumed into useful work (like in rotating the blades of an electric fan). Rest of the source energy may be expended in heat to raise the temperature of gadget.For example, an electric fan becomes warm if used continuously for longer time etc. On the other hand, ifthe electric circuit is purely resistive, that is, a configuration of resistors only connected to a battery; the source energy continually gets dissipated entirely in the form of heat. This is known as the heating effect of electric current.
This effect is utilised in devices such as electric heater, electric iron etc.

ELECTRICITY

Think life without “electricity” in this modern society. Is it possible to survive without electrical energy in world of technology. Since we are science student, so it is necessary to understand the basic concept behind the word “electricity”

Charge-> (q) It is a very small particles present in an atom it can be either negative (electron) or positive (proton)

“Coulomb” is the SI unit of charge, represented by C.

Net charge (Q)– Total charge

In an electric circuit the electric current flow in the opposite direction of the flow of electron (–ve charge) conventionally. It flows from the +ve terminal of battery or cell to –ve terminal.
Small quantity of current are expressed in
                            mA (milli Ampere) = 10^–3 A
                            uA (micro Ampere) = 10^–6 A
Ammeter– It is an instrument used to measure the electric current in a circuit.
It is always connected in series m a circuit
It is represented by the symbol ––––––––⁺ A ^– ––––––– in an electric circuit. It has low resistance.
Electric Circuit– It is a closed path along which an electric current flow.

The electron can only flow when there is difference of electric pressure. For example “water flowing through a tube” It is only possible when there high pressure at one side and low at another side, then it will move from high pressure to low pressure.
In case of electric current, the flow of charge is made possible due to chemical action with in a cell that generates the potential difference across the terminals of the cell.
8. Electric potential Difference– It is defined as the work done in carrying a unit charge from one point to another between the two points of an electric circuits.

One Volt → When 1 Joule of work is done to carry one coulomb (1C) of charge from one point to another of a current carrying conductor then the potential difference is send to be IV.

Voltmeter → It is an instrument, used to measure the potential difference and represented by the symbol in an electric circuit. It is always connected in parallel across the points between which the potential difference is to be measured. It has high resistance.

Symbols for some commonly used instrument in circuit diagrams

Georg Simon Ohm (physicist) 1787 – 1854

Found the relationship between the current (I) flowing through a conductor and potential difference (V) across the terminals of a conductor using the circuit diagram.

Where “R” is the proportionality constant for the given metal at given temperature

and is said to be resistance, the graph between V and I is always straight line.

Resistance– It is the property of a conductor that opposes the flow of current. It is represented by ‘R’ and symbol is SI unit of resistance “Ohm” OR Ω

1 Ohm – The resistance of a conductor is said to be one Ohm, when the potential difference across the conductor is 1V and the current flowing through it is 1A.

Rheostate– 

So to increase or decrease the current accordingly in the circuit a component is used is called “Rheostat”, that regulates the current without changing potential difference. Represented by “Rh” 

it a conductor has less Resistance, then more current will flow through it.

FACTORS ON WHICH RESISTANCE OF A CONDUCTOR DEPENDS–
(1) On its length (l)
(2) On its cross sectional area (A)
(3) On the nature of material  

Resistantly of a material vary with temperature

Resistivity of an alloy (homogeneous mixture of metals) is generally higher than of its constituent metals. Example Constantan (alloy of Cu & Ni) Alloys have high resistivity and do not oxidise (burn) readly at high temperature, for this reason they are commonly used in electrical heating devices, like electric iron, heater, toasters etc. For example “Tungsten” as filament of electric bulb.
Resistance in Series– (Maximum Effective Resistance)
Let us take three resistance R₁₉, R₂ and R₃ that are connected in series in a circuit. 

The current (I) flowing through the resistance in series will remain same, where as the potential difference (V) across each resistor will be different. 

is equal to the sum of their individual resistance.
Resistance in Parallel (Minimum Effective Resistance)
Let us take three R19 , R2 and R3 , that are connected in parallel in the electric circuit.

Thus, we conclude that the reciprocal of total effective resistance of the several resistors connected in parallel is equal to the sum of the reciprocals of the individual resistance.

Disadvantage of series connection in on electric circuit :–

1. In series connection if any of the component fail to work, the circuit will break and then none of the component (ex. TV, bulb, fan..) will work.
2. It is not possible to connect a bulb and a heater in series, because they need different value of current to operate properly.

Hence, to overcome this problem we generally use parallel circuit.

Heating effect of Electric Current :
Explanation® Battery or a cell is a source of electrical energy. 

Mathematical Expression :–

Let us suppose that current (I) is flowing through a resistor of resistance (R) for the time (t). The potential difference across the resistance is (V).

The law stated that the heat produced in a resistor is
(i) directly proportional to square of the current(I)
(ii) directly proportional to resistance (R) for given current
(iii) directly proportional to time (t) for which current flow through resistor.

Application of Heating Effect of Electric Current :–
(1) Used in electric iron, toaster, oven, heater etc.
(2) It is also used in bulb to produce light.
(Filament of bulb is made of strong metal with high melting point such as tungsten (m.pt = 3380°C). This filament can retain as much of the heat generated as possible, to become very hot and emit light)
(3) It is also used in the “fuse connected in an electric circuit {Fuse a safety device, protect the circuits and appliance by stopping the flow of high current.
lead etc. The alloy should be of low m.pt and high resistivity, fuse is always connected in series circuit. When large current flow through the circuit, the temperature of fuse wire will increase. This melts the fuse wire and break the circuit.
“ Fuses” used for domestic purposes are rated as 1A, 2A, 3A, 5A, 10A etc. for various operation depending upon the power of appliance using.
Example- let us consider an appliance “electric Iron” which consume 1KW electric power, at 220V 

In this case a 5A fuse is required.
Electric Power :– In case of electricity, it is defined as the rate of change electrical energy dissipated or consumed in an electric electrical energy dissipated orconsumed in an electric  circuit. 

1 Watt→Defined as the power consumed by a device, when 1A of current passes through it at the potential difference of 1V. 

GIST OF THE LESSON

1. Positive and negative charges: The charge acquired by a glass rod when rubbed with silk is called positive charge and the charge acquired by an ebonite rod when rubbed with wool is called negative charge.

2. Coulomb: It is the S.I. unit of charge. One coulomb is defined as that amount of charge which repels an equal and similar charge with a force of 9 x 10⁹ N when placed in vacuum at a distance of 1 meter from it. Charge on an electron = -1.6 x 10^-19 coulomb.

3. Static and current electricities: Static electricity deals with the electric charges at rest while the current electricity deals with the electric charges in motion.

4. Conductor: A substance which allows passage of electric charges through it easily is called a ‗conductor‘. A conductor offers very low resistance to the flow of current. For example copper, silver, aluminium etc.

5. Insulator: A substance that has infinitely high resistance does not allow electric current to flow through it. It is called an ‗insulator‘. For example rubber, glass, plastic, ebonite etc.

6. Electric current: The flow of electric charges across a cross-section of a conductor constitutes an electric current. It is defined as the rate of flow of the electric charge through any section of a conductor. Electric current = Charge/Time or I = Q/t Electric current is a scalar quantity.

7. Ampere: It is the S.I. unit of current. If one coulomb of charge flows through any section of a conductor in one second, then current through it is said to be one ampere.

1 ampere = 1 coulomb/1 second or 1 A = 1C/1s = 1Cs^-1

1 milliampere = 1 mA = 10^-3 A

1 microampere = 1μA = 10^-6 A

8. Electric circuit: The closed path along which electric current flows is called an ‗electric circuit‘.

9. Conventional current: Conventionally, the direction of motion of positive charges is taken as the direction of current. The direction of conventional current is opposite to that of the negatively charged electrons.

10. Electric field: It is the region around a charged body within which its influence can be experienced.

11. Electrostatic potential: Electrostatic potential at any point in an electric field is defined as the amount of work done in bringing a unit positive charge from infinity to that point. Its unit is volt. Positive charges move from higher to lower potential regions. Electrons, being negatively charged, move from lower to higher potential regions.

12. Potential difference between two points: The Potential difference between two points in an electric field is the amount of work done in bringing a unit positive charge from one to another. Potential difference = Work done/Charge or V = W/Q

13. One volt potential difference: The Potential difference between two points in an electric field is said to one volt if one joule of work has to be done in bringing a positive charge of one coulomb from one point to another. 1 volt = 1 joule/1 coulomb or 1 V = 1J/1C

14. Galvanometer: It is device to detect current in an electric circuit.

15. Ammeter: It is device to measure current in a circuit. It is always connected in series in a circuit.

16. Voltmeter: It is a device to measure potential difference. It is always connected in parallel to the component across which the potential difference is to be measured.

17. Ohm’s law: This law states that the current passing through a conductor is directly proportional to the potential difference cross its ends, provided the physical conditions like temperature, density etc. remains unchanged.
V α I or V = RI
The proportionality constant R is called resistance of conductor.

18. Resistance: It is a property of a conductor by virtue of which it opposes the flow of current through it. It is equal to the ratio of the potential difference applied across its ends and the current flowing through it. Resistance = Potential difference/Current or R = V/I

19. Ohm: It is the S.I. unit of resistance. A conductor has a resistance of one ohm if a current of one ampere flows through it on applying a potential difference of one volt across its ends.

1 ohm = 1 volt/1 ampere or 1Ω = 1V/1A

20. Factors on which resistance of a conductor depends: The resistance R of a conductor depends

i) Directly on its length L i.e. R α L.

ii) inversely on its area of cross-section A i.e. R α 1/A

iii) on the nature of material of the conductor on.

On combining the above factors, we get R α L/A

R = ρ * L/A The proportionality constant ρ is called resistivity of conductor.

21. Resistivity: It is defined as the resistance offered by a cube of a material of side 1 m when current flows perpendicular to its opposite faces. Its S.I. unit is ohm-meter (Ωm). Resistivity, ρ = RA/L 

22. Equivalent resistance: If a single resistance can replace the combination of resistances in such a manner that the current in the circuit remains unchanged, then that single resistance is called the equivalent resistance.

23. Laws of resistances in series:
i) Current through each resistance is same.
ii) Total voltage across the combination = Sum of the voltage drops.
V= V₁ + V₂ + V₃
iii) Voltage drops across any resistor is proportional to its resistance.
V₁ = IR₁, V₂ = IR₂, V₃ = IR₃
iv) Equivalent resistance = Sum of the individual resistances.
R_s = R₁ + R₂ + R₃
v) Equivalent resistance is larger than the largest individual resistance.

24. Laws of resistances in parallel:
i) Voltage across each resistance is same and is equal to the applied voltage.
ii) Total current = Sum of the currents through the individual resistances.
I = I₁ + I₂ + I₃
iii) Currents through various resistances are inversely proportional to the individual resistances.
I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃
iv) Reciprocal of equivalent resistance = Sum of reciprocals of individual resistances.
1/Rp = 1/R₁ + 1/R2 + 1/R3
v) Equivalent resistance is less than the smallest individual resistance.

25. Joule’s law of heating: It states that the heat produced in a conductor is directly proportional to (i) the square of the current I through it (ii) proportional to its resistances R and (iii) the time t for which current is passed. Mathematically, it can be expressed as
H = I²Rt joule = I²Rt/4.18 cal
or
H = VIt joule = VIt/4.18cal

26. Electric energy: It is the total work done in maintaining an electric current in an electric
circuit for given time.
Electric energy, W = VIt = I²Rt joule

27. Electrical power: Electrical power is the rate at which electric energy is consumed by an
appliance.
P = W/t = VI = I²R = V²/R

28. Watt: It is the S.I. unit of power. The power of an appliance is 1 watt if one ampere of current flows through it on applying a potential differences of 1 volt across its ends.
1 watt = 1 joule/1 second =1 volt x 1 ampere
or 1 W = 1 Js^-1 = 1 VA
1 kilowatt = 1000 W

29. Kilowatt hour: It is the commercial unit of electrical energy. One kilowatt hour is the electric energy consumed by an appliance of 1000 watts when used for one hour.
1 kilowatt hour (kWh) = 3.6 x 10⁶ J

Assertion-Reason Type Questions

For question numbers 1 and 2 two statements are given-one labeled as Assertion (a) and the other labeled
Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below:
(a) Both ‘A’ and ‘R’ are true and ‘R’ is correct explanation of the Assertion.
(b) Both ‘A’ and ‘R’ are true but ‘R’ is not correct explanation of the Assertion.
(c) ‘A’ is true but ‘R’ is false.
(d) ‘A’ is false but ‘R’ is true.

Question. Assertion: Resistance depends on length and area of cross-section of material and temperature.
Reason: Resistivity is a characteristic property of material.
Answer : B

Question. Assertion: Fuse wire is thin and has high resistance.
Reason: Alloys do not oxidise readily at high temperature.
Answer : B

Very Short Answer Type Questions 

Question. Let the resistance of an electrical component remain constant, while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?
Answer : The current flowing through the electrical component will get halved.

Question. Suppose the ammeter or voltmeter you are using in Ohm’s law experiment do not have +ve and –ve
terminal markings, how will you use such an ammeter or voltmeter in the circuit?
Answer : (i) Connect the device in the circuit with battery.
(ii) Close the circuit and notice the deflection of the pointer.
(iii) If the deflection is in the opposite direction i.e. below zero, then interchange the terminals.

Question. Which among iron and mercury is a better conductor?
(Given: Ρ_Fe
= 10.0 × 10^–8 W – m, Ρ_Hg = 95 × 10^–8 W – m
Answer : Iron

Question. Nichrome is used to make the element of an electric heater, why?
Answer : It is an alloy with high resistivity and high melting point.

Question. How does resistivity of alloys compared with those of pure metals from which they have been formed?
Answer : Alloys have higher resistivity as compared to pure metals.

Question. List two factors on which resistance depends.
Answer : (i) Length, (ii) Area of cross section
It is directly proportional to the length and inversely proportional to the area of cross section of a resistor.

Question. Name a device which helps to maintain the potential difference across a conductor.
Answer : Cell or battery eliminator

Question. Mention two reasons why tungsten is used for making filaments of electric lamps.
Answer : (i) High resistivity, (ii) High melting point

Question. Name the factors on which the resistance of a conductor depend?
                                              OR
List the factors on which the resistance of a conductor in terms of shape of a wire depends.
Answer : (i) Nature of material, (ii) Length of conductor [or R ∝ l]
(iii) Area of cross section of the conductor [or R ∝ 1/A], (iv) Temperature

Question. What happens to the resistance of a conductor when its temperature is increased?
Answer : Its resistance increases

Question. A given length of wire is doubled on itself and the process is repeated once again. By what factor does the resistance of wire will change?
Answer : Length becomes 4 times whereas area becomes 1/4 times of the original value. Since,

Question. Mention two special features of the material to be used as an element of an electric iron.
Answer : The material should have (i) high resistivity, (ii) high melting point.

Question. Write the S.I. unit of resistivity.
Answer : Ω m (ohm metre)

Question. What does electric circuit mean?
Answer : It is a continuous and closed path in which current flows with the help of conducting wires. It consists
of a cell, an ammeter, voltmeter, plug key, bulb, etc

Question. In an electric circuit, state the relationship between the direction of conventional current and the direction of flow of electrons.
Answer : The direction of conventional current is opposite to the direction of flow of electrons

Question. State the difference between a wire used in the element of electric heater and in fuse wire.
Answer : The wire used in the elements of an electric heater has high melting point whereas a fuse wire has low melting point.

Question. What happens to resistance of a conductor when its area of cross section is increased?
Answer : Resistance decreases, ∴ R ∞ l/A Resistance is directly proportional to length but inversely proportional to area of cross-section.

Question. The electrical resistivity of three materials A, B, C are given below:
‘A’ = 2.3 × 10³ ohm metre ‘B’ = 2.63 × 10–8 ohm metre ‘C’ = 1.0 × 10¹⁵ ohm metre Which material will you use for making (i) electric wires, (ii) handles for soldering iron and (iii) solar cells? Give reason to support your answer.
Answer : (i) ‘B’ will be used for electric wires because it has lowest resistivity, therefore current can flow easily.
(ii) ‘C’ will be an insulator, so it can be used for handles of soldering iron. Since its resistivity is very high, therefore current cannot pass through it.
(iii) ‘A’ will be used in solar cells because it is a semiconductor which can convert solar energy into electric energy.