Magnetic Effects of Electric Current, Ch-13, for class 10th, by Farrukh

 

NCERT
Solutions for Class 10 Science Chapter 13 “Magnetic Effects of Electric Current”

NCERT Solutions For Class 10 Science Chapter 13 Magnetic Effects Of Electric Current by https://cbsencert21.blogspot.com : In this article, you will find out all the necessary information regarding the magnetic effect of electric current class 10 NCERT solutions. So the students who are in search of NCERT Solutions For Class 10 Science Chapter 13 Magnetic Effects Of Electric Current can refer to this article.

Magnetic Effects Of Electric Current Class 10 NCERT questions and answers were solved by the best academic experts in order to help you a better understanding. So the candidates who want to secure a decent grade in class 10 board exams can refer to this article and solve magnetic effect of electric current science class 10 NCERT solutions. Read on to find out everything about NCERT Solutions For Class 10 Science Chapter 13 Magnetic Effects Of Electric Current.

Answer The Following Question.

1.   Magnetic Effects Of Electric Current

2.   Magnetic Field And Field Lines

3.   Magnetic Field Due To A Current-Carrying Conductor

4.   Force On A Current-Carrying Conductor In A Magnetic Field

5.   Electric Motor

6.   Electromagnetic Induction

7.   Electric Generator

8.   Domestic Electric Circuits

NCERT Solutions for Class 10 Science Chapter 13 Intext Questions

Page Number: 224

Question 1
Why does a compass needle get deflected when brought near a bar magnet ?
Answer:
The magnetic field of the magnet exerts force on both the poles of the compass needle. The forces experienced by the two poles are equal and opposite. These two forces form a couple which deflects the compass needle.

Page Number: 228

Question 1
Draw magnetic field lines around a bar magnet.
Answer:

Question 2
List the properties of magnetic lines of force.
Answer:
Properties of magnetic lines of force :

The magnetic field lines originate from the north pole of a magnet and end at its south pole.

The magnetic field lines become closer to each other near the poles of a magnet but they are widely separated at other places.

Two magnetic field lines do not intersect one another.

Question 3
Why don’t two magnetic lines of force intersect each other?
Answer:
This is due to the fact that the resultant force on a north pole at any point can be only in one direction. But if the two magnetic field lines intersect one another, then the resultant force on north pole placed at the point of intersection will be along two directions, which is not possible.

Page Number: 229 – 230

Question 1
Consider a circular loop of wire lying on the plane of the table. Let the current pass through the loop clockwise. Apply the right hand rule to determine the magnetic field's direction inside and outside the loop.
Answer:
The right-hand rule is a simple way to determine the direction of the magnetic field around a current-carrying conductor.

·        Point your thumb in the direction of the current.

·        Curl your fingers.

·        The direction your fingers curl indicates the direction of the magnetic field lines.

Applying the Right-Hand Rule to a Circular Loop

1.   Inside the Loop:

·        Point your thumb in the direction of the current (clockwise).

·        Curl your fingers.

·        Your fingers will point into the plane of the loop.

2.   Outside the Loop:

·        Point your thumb in the direction of the current (clockwise).

·        Curl your fingers.

·        Your fingers will point out of the plane of the loop.

Visualizing the Magnetic Field

 

circular loop with current flowing clockwise, showing the magnetic field lines inside and outside the loop

Here are the Key Points:

·        The magnetic field lines form concentric circles around the wire.

·        The direction of the magnetic field inside and outside the loop is determined by the right-hand rule.

·        The magnetic field is stronger closer to the wire and weaker farther away.

Question 2
The magnetic field in a given region is uniform. Draw a diagram to represent it. [CBSE 2013, 2014]
Answer:
A uniform magnetic field in a region is represented by drawing parallel straight lines, ail pointing in the same direction.
For example, the uniform magnetic field which exists inside a current-carrying solenoid can be represented by parallel straight lines pointing from its S-pole to N-pole (as shown in the figure).

Here are the Key Points:

·        Parallel Lines: The lines are parallel to each other, signifying that the field's direction is constant.

·        Equal Spacing: The spacing between the lines is uniform, indicating that the field's strength is the same everywhere.

·        Direction: The direction of the lines represents the direction of the magnetic field.

Question 3
Choose the correct option.
The magnetic field inside a long straight solenoid-carrying current
(i) is zero
(ii) decreases as we move towards its end
(iii) increases as we move towards its end
(iv) is the same at all points
Answer:
(iv) Is the same at all points.

Page Number: 231 – 232

Question 1
Which of the following properties of a proton can change while it moves freely in a magnetic field. (There may be more than one correct answer.)
(i) Mass
(ii) Speed
(iii) Velocity
(iv) Momentum
Answer:
The correct options are (iii) velocity, (iv) momentum.

Question 2
In Activity 13.7 how do we think the displacement of rod AB will be affected if (i) current in rod AB is increased (ii) a stronger horse-shoe magnet is used; and (iii) length of the rod AB is increased ?
Answer:
(i) When the current in the rod AB is increased, force exerted on the conductor increases, so the displacement of the rod increases.
(ii) When a stronger horse-shoe magnet is used, the magnitude of the magnetic field increases. This increases the force exerted on the rod and the displacement of the rod.
(iii) When the length of the rod AB is increased, force exerted on the conductor increases, so the displacement of the rod increases.

Question 3
A positively charged particle (alpha particle) projected towards the west is deflected towards the north by a magnetic field.
The direction of the magnetic field is :
(i) towards the south
(ii) towards east
(iii) downward
(iv) upward
Answer:
(iv) Upward.
Here, the positively charged alpha particles are moving toward the west, so the direction of the current is towards the east. The deflection is towards north, so the force is towards the north, so, we are given that
(i) The direction of the current is towards the west
(ii) direction of force is towards north.
Let us now hold the forefinger, middle finger and thumb of our left-hand at right angles to one another. Adjust the hand in such a way that our mid finger points towards west (in the direction of current) and thumb points towards north (in the direction of force). Now, if we look at our forefinger, it will be pointing upward. Because the direction of the forefinger gives the direction of the magnetic field, therefore, the magnetic field is in the upward direction.

Page Number: 233

Question 1
State Fleming’s left-hand rule. [CBSE 2018]
Answer:
Fleming’s left-hand rule: Stretch the first finger, the middle finger and the thumb of your left hand mutually perpendicular to each other in such a way that the first finger represents the direction of the magnetic field, the middle finger represents the direction of the current in the conductor, then the thumb will represent the direction of motion of the conductor.

Question 2
What is the principle of an electric motor? [CBSE 2018]
Answer:
A motor works on the principle of the magnetic effect of current. When a rectangular coil is placed in a magnetic field and current is passed through it, a force acts on the coil which rotates it continuously.
When the coil rotates, the shaft attached to it also rotates. In this way, the electrical energy supplied to the motor is converted into the mechanical energy of rotation.

Question 3
What is the role of the split ring in an electric motor?
Answer:
The split ring reverses the direction of current in the armature coil after every half rotation, i.e., it acts as a commutator. The reversed current reverses the direction of the forces acting on the two arms of the armature after every half rotation. This allows the armature coil to rotate continuously in the same direction.

Page Number: 236

Question 1
Explain different ways to induce a current in a coil.
Answer:
Different ways to induce current in a coil are :

moving a magnet towards or away from the coil or vice-versa, and

changing current in the neighboring coil.

Page Number: 237

Question 1
State the principle of an electric generator.
Answer:
The electric generator works on the principle that when a straight conductor is moved in a magnetic field, then current is induced in the conductor.
In an electric generator, a rectangular coil is made to rotate rapidly in the magnetic field between the poles of a horse-shoe type magnet. When the coil rotates, it cuts the magnetic field lines due to which a current is produced in the coil.

Question 2
Name some sources of direct current.
Answer:
Some of the sources of direct current are dry cells, button cells, and lead accumulators.

Question 3
Which sources produce alternating current?
Answer:
Alternating current is produced by AC generators of nuclear power plants, thermal power plants, hydroelectric power stations, etc.

Question 4
Choose the correct option: A rectangular coil of copper wires is rotated in a magnetic field. The direction of the induced current changes once in each:
(i) two revolution
(ii) one revolution
(iii) half revolution
(iv) One-fourth revolution
Answer:
(iii) Half revolution.

Page Number: 238

Question 1
Name two safety measures commonly used in electric circuits and appliances.
Answer:
(i) Earthing and
(ii) Electric fuse.

Question 2
An electric oven of 2 kW power rating is operated in a domestic electric circuit (220 V) that has a current rating of 5 A. What result do you expect ? Explain.
Answer:
The electric oven draws a current given by

Thus the electric oven draws current much more than the current rating 5 A. That is the circuit is overloaded. Due to excessive current, the fuse wire will blow and the circuit will break.
What precautions should be taken to avoid the overloading of domestic electric circuits ?
To avoid the overloading of domestic electric circuits, the following precautions should be taken :
(i) The wires used in the circuit must be coated with good insulating materials like PVC, etc.
(ii) The circuit must be divided into different sections and a safety fuse must be used in each section.
(iii) High-power appliances like air-conditioners, refrigerators, water heaters, etc. should not be used simultaneously.

NCERT Solutions for Class 10 Science Chapter 13 Textbook Chapter End Questions

Question 1
Which of the following correctly describes the magnetic field near a long straight wire ?
(i) the field consists of straight lines perpendicular to the wire
(ii) the field consists of straight lines parallel to the wire
(iii) the field consists of radial lines originating from the wire
(iv) The field consists of concentric circles centered on the wire
Answer:
(iv) The field consists of concentric circles centred on the wire

Question 2
The phenomenon of electromagnetic induction is
(i) the process of charging a body
(ii) the process of generating a magnetic field due to a current passing through a coil
(iii) producing induced current in a coil due to relative motion between a magnet and the coil
(iv) the process of rotating a coil of an electric motor
Answer:
(iii) Producing induced current in a coil due to relative motion between a magnet and the coil

Question 3
The device used for producing electric current is called a
(i) generator
(ii) galvanometer
(iii) ammeter
(iv) motor
Answer:
(i) Generator.

Question 4
The essential difference between an AC generator and a DC generator is that
(i) AC generator has an electromagnet while a DC generator has permanent magnet
(ii) DC generator will generate a higher voltage
(iii) AC generator will generate a higher voltage
(iv) AC generator has slip rings while the DC generator has a commutator
Answer:
(iv) AC generator has slip rings while the DC generator has a commutator

Question 5
At the time of short circuit, the current in the circuit
(i) reduces substantially
(ii) does not change
(iii) increases heavily
(iv) varies continuously
Answer:
(iii) Increases heavily.

Question 6
State whether the following statements are True or False.
(i) An electric motor converts mechanical energy into electrical energy.
(ii) An electric generator works on the principle of electromagnetic induction.
(iii) The field at the centre a long circular coil carrying current will be parallel straight lines.
(iv) A wire with a green insulation is usually the live wire of an electric supply.
Answer:
(i) False
(ii) True
(iii) True
(iv) False.

Question 7
List three sources of magnetic fields.
Answer:
(i) Current carrying conductor
(ii) Electromagnets
(iii) Permanent magnets

Question 8
How does a solenoid behave like a magnet ? Can you determine the north and south poles of a current-carrying solenoid with the help of a bar magnet? Explain.
Answer:
A solenoid behaves like a magnet in the following ways.

·        The magnetic field produced by a current-carrying solenoid is very much similar to that of a bar magnet.

·        Like a bar magnet, one end of the solenoid has N-polarity while the other end has S-polarity.

To determine the north and south poles, we bring N-pole of the bar magnet near one end of the solenoid. If there is an attraction, then that end of the solenoid has south polarity and the other has north polarity. If there is a repulsion, then that end of the solenoid has north polarity and the other end has south polarity because similar poles repel each other.

Question 9
When is the force experienced by a current-carrying conductor placed in a magnetic field largest ?
Answer:
When the conductor carries current in a direction perpendicular to the direction of the magnetic field, the force experienced by the conductor is largest.

Question 10
Imagine that you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally from back wall towards the front wall, is deflected by a strong magnetic field to your right side. What is the direction of magnetic field ?
Answer:
Here the electron beam is moving from our back wall to the front wall, so the direction of current will be in the opposite direction, from front wall towards back wall or towards us. The direction of deflection (or force) is towards our right side.
We now know two things :

·        direction of current is from front towards us, and

·        direction of force is towards our right side.

Let us now hold the forefinger, middle finger and thumb of our left hand at right angles to one another. We now adjust the hand in such a way that our centre finger points towards us (in the direction of current) and thumb points towards right side (in the direction of force). Now, if we look at our forefinger, it will be pointing vertically downwards. Since the direction of forefinger gives the direction of magnetic field, therefore, the magnetic field is in the vertically downward direction.

Question 11
Draw a labeled diagram of an electric motor. Explain its principle and working. What is the function of a split ring in an electric motor?
Answer:
Electric Motor: The device used to convert electrical energy to mechanical energy is called Electric Motor. It is used in fans, machines, etc.
Principle: NCERT Solutions for Class 10 Science Chapter 13 Magnetic Effects of Electric CurrentElectric motor works on the principle of force experienced by a current carrying conductor in a magnetic field. The two forces in the opposite sides are equal and opposite. Since they act in different lines they bring rotational motion.

Working of an electric motor :
When the current starts to flow, the coil ABCD is in horizontal position. The direction of current through the armature coil has the direction from A to B in the arm AB and from C to D in the arm CD. The direction of force exerted on the coil can be found through Fleming’s left-hand law.
According to this law, it is found that the force exerted on the part AB, pushes the coil downwards. While the force exerted on the part CD pushes it upwards. In this way, these two forces being equal and opposite form a couple that rotates the coil in an anticlockwise direction.

When the coil is in vertical position, the brushes X and Y would touch the centre of the commutator and the current in the coil is stopped. Though current is stopped but the coil comes back in horizontal state due to momentum.

After half rotation, the polarity of the commutator also changes, because now Q makes contact with brush X and P with brush Y. Therefore, now the force exerts downwards on the arm AB and upwards on the arm CD and thus again a couple of forces is formed that rotates the coil in clockwise direction. This process is repeated again and again and the coil rotates til! the current flows across it.
Function of split ring : Split ring in a motor acts as a commutator, i.e., it reverses the flow of current in the circuit due to which the direction of the forces acting on the arms also reverses.

Question 12
Name some devices in which electric motors are used.
Answer:
Electric motor is used in the appliances like electric fans, washing machine, mixers, grinders, blenders, computers, MP3 players, etc.

Question 13
A coil of insulated copper wire is connected to a galvanometer. What will happen if a bar magnet is (t) pushed into the coil (ii) withdrawn from inside the coil (iii) held stationary inside the coil ? [CBSE (Delhi) 2017, AICBSE 2016]
Answer:
(i) As a bar magnet is pushed into the coil, a momentary deflection is observed in the galvanometer indicating the production of a momentary current in the coil.
(ii) When the bar magnet is withdrawn from the coil, the deflection of galvanometer is in opposite direction showing the production of an opposite current.
(iii) When the bar magnet is held stationary inside the coil, there is no deflection in galvanometer indicating that no current is produced in the coil.

Question 14
Two circular coils A and B are placed closed to each other. If the current in the coil A is changed, will some current be induced in the coil B ? Give reason.
Answer:
Yes, some current will be induced in the coil B. When the current in coil A is changed, some current is induced in the coil B. Due to change in current in coil A, the magnetic field lines linked with coil A and with coil B get changed. This sets up induced current in coil B.

Question 15
State the rule to determine the direction of a (i) magnetic field produced around a straight conductor-carrying current (it) force experienced by a current-carrying straight conductor placed in a magnetic field which is perpendicular to it, and (in) current induced in a coil due to its rotation in a magnetic field.
Answer:
(i) Right hand thumb rule : If the current carrying conductor is held in the right hand such that the thumb points in the direction of the current, then the direction of the curl of the fingers will give the direction of the magnetic field.
(ii) Fleming’s left hand rule : NCERT Solutions for Class 10 Science Chapter 13 Magnetic Effects of Electric Current Stretch the forefinger, the central finger and the thumb of the left hand mutually perpendicular to each other. If the forefinger points in the direction of the magnetic field, the middle finger in the direction of current, then the thumb points in the direction of force in the conductor.
(iii) Fleming’s right hand rule : Stretch the thumb, forefinger and the central finger of the right hand mutually perpendicular to each other. If the forefinger points in the direction of magnetic field, thumb in the direction of motion of the conductor, then the middle finger points in the direction of current induced in the conductor.

Question 16
Explain the underlying principle and working of an electric generator by drawing a labeled diagram. What is the function of brushes ?
Answer:
Principle : The electric generator is based on the principle of electromagnetic induction. When a coil is rotated with respect to a magnetic field, the number of magnetic field lines through the coil changes. Due to this a current is induced in the coil whose direction can be found by Fleming’s right hand rule.

   

Working : When the armature coil ABCD rotates in a magnetic field produced by the permanent magnets, it cuts through the magnetic lines of force.
Due to the rotation of armature coil, the associated magnetic field changes and an induced electromagnetic force is produced in it. The direction of this induced electromotive force or current can be determined by using Fleming’s right hand rule.
In first half cycle the current flows in one direction by brush B1 and in second it flows in opposite direction by brush B2. This process continues. So the current produced is alternating in nature.
Functions of Brushes : Brushes in contact with rings provide the current for external use.

Question 17
When does an electric short circuit occur ?
Answer:
In a domestic circuit, short-circuit occurs when live and neutral wire come in direct contact with each other without any resistance. The resistance of the circuit becomes zero and excessive current starts to flow through it.

Question 18
What is the function of an earth wire ? Why is it necessary to earth metallic appliances ?
Answer:
Earth wire is a safety measure that provides a low resistance conducting path to the current. Sometimes due to excess heat or wear and tear, the live wire comes in direct contact with the metallic cover of the appliances, which can give an electric shock on touching them. To prevent from the shock the metallic part is connected to the earth through a three-pin plug due to which the current flows to the earth at the instant there is a short circuit.

It is necessary to earth metallic appliances because it ensures that if there is any current leakage in the metallic cover, the potential of the appliance becomes equal to that of the earth. The potential of the earth is zero. As a result, the person handling the appliance will not get an electric shock.

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Chapter 12 “Electricity” of Class 10, NCERT Solutions

 

NCERT Solutions for Class 10 Science Chapter 12 “Electricity”

The details of NCERT Solutions For Class 10 Science Chapter 12 “Electricity”,
let us have a glimpse of the topics and subtopics under Electricity class 10 

NCERT Solutions:

1.     Electricity

2.     Electric Current And Circuit

3.     Electric Potential And Potential Difference

4.     Circuit Diagram

5.     Ohms’ Law

6.     Factors On Which The Resistance Of A Conductor Depends

7.     Resistance Of A System Of Resistors

8.     Heating Effect Of Electric Current

9.     Electric Power

10. What We Have Learnt?

Free download NCERT Solutions for Class 10 Science Chapter 12 Electricity PDF in either language using Translate option from the Blog. Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2024-25.

• किसी भी भाषा मे अनुवाद कर पढ़ें ब्लॉग मे दिए गए option की सहायता से।

NCERT Solutions for Class 10 Science Chapter 12 Intext Questions

Page Number: 200

Question 1. What does an electric circuit mean ?

Answer:
A continuous and closed path along which an electric current flows is called an electric circuit.

Question 2. Define the unit of current.
Answer:
Unit of current is ampere. If one coulomb of charge flows through any section of a conductor in one second then the current through it is said to be one ampere.
I = Qt or 1 A = I C s^-1

Question 3. Calculate the number of electrons constituting one coulomb of charge.
Answer:
Charge on one electron, e = 1.6 x 10^-19 C
Total charge, Q = 1 C
Number of electrons, n = Qe = 1C1.6x10−19 = 6.25 x 10¹⁸

Page Number: 202

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

A battery.

Question 2. What is meant by saying that the potential difference between two points is IV?
Answer:
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.

Question 3. How much energy is given to each coulomb of charge passing through a 6 V battery ?
Answer:
Energy given by battery = charge x potential difference
or W = QV = 1C X 6V = 6J.

Page Number: 209

Question 1: On what factors does the resistance of a conductor depend?
OR
List the factors on which the resistance of a conductor in the shape of a wire depends.

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

Question 2: Will current flow more easily through a thick wire or a thin wire of the same material, when connected to the same source ? Why ?
Answer:
The current will flow more easily through a thick wire than a thin wire of the same material. Larger the area of cross-section of a conductor, more is the ease with which the electrons can move through the conductor. Therefore, smaller is the resistance of the conductor.

Question 3: Let the resistance of an electrical component remains 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:
When potential difference is halved, the current through the component also decreases to half of its initial value. This is according to ohm’s law i.e., V ∝ I.

Question 4: Why are coils of electric toasters and electric irons are made of an-alloy rather than a pure metal ?
OR
Why are alloys commonly used in electric heating devices? Given reason. 

 Answer:
The coils of electric toasters, electric irons and other heating devices are made of an alloy rather than a pure metal because (i) the resistivity of an alloy is much higher than that of a pure metal, and (ii) an alloy does not undergo oxidation (or burn) easily even at high temperature when it is red hot.

Question 5: Use the data in Table 12.2 (in NCERT Book on Page No. 207) to answer the following :
(i) Which among iron and mercury is a better conductor ?
(ii) Which material is the best conductor ?
Answer:
(i) Resistivity of iron = 10.0 x 10^-8 Ω m
Resistivity of mercury = 94.0 x 10^-8 Ω m.
Thus iron is a better conductor because it has lower resistivity than mercury.
(ii) Because silver has the lowest resistivity (= 1.60 x 10^-8 Ω m), therefore silver is the best conductor.

Page Number: 213

Question 1: Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5Ω resistor, an 8 Ω resistor, and a 12 Ω resistor, and a plug key, all connected in series.
Answer:
The required circuit diagram is shown below:

Question 2: Redraw the circuit of Questions 1, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the potential difference across the 12 Ω resistor. What would be the readings in the ammeter and the voltmeter ?
Answer:
The required circuit diagram is shown on the right.
Total voltage, V = 3 x 2 = 6V
Total resistance, R = 5Ω + 8Ω + 12Ω = 25Ω

Page Number: 216

Question 1: Judge the equivalent resistance when the following are connected in parallel :

(i) 1 Ω and 106 Ω,
(if) 1 Ω and 103 Ω and 106 Ω.
Answer:
When the resistances are connected in parallel, the equivalent resistance is smaller than the smallest individual resistance.
(i) Equivalent resistance < 1 Ω.
(ii) Equivalent resistance < 1 Ω.

Question 2: An electric lamp of 100 Ω, a toaster of resistance 50 Ω, and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it ?
Answer:
Resistance of electric lamp, R₁ = 100 Ω
Resistance of toaster, R₂ = 50 Ω
Resistance of water filter, R₃ = 500 Ω
Equivalent resistance R_p of the three appliances connected in parallel, is

Resistance of electric iron = Equivalent resistance of the three appliances connected in parallel = 31.25 Ω
Applied voltage, V = 220 V
Current, I = VR = 220V31.25Ω

Question 3: What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?
Answer:
The advantages of connecting electrical devices in parallel with the battery are :

1.     In parallel circuits, if an 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 turned off independently, without affecting other appliances.

3.     In parallel circuits, each electrical appliance gets the same voltage (220 V) as that of the power supply line.

4.     In the parallel connection of electrical appliances, the overall resistance of the household circuit is reduced due to which the current from the power supply is high.

Question 4: How can three resistors of resistances 2Ω, 3 Ω, and 6Ω be connected to give a total resistance of (i) 4 Ω, (ii) 1 Ω ?
Answer:
(i) We can get a total resistance of 4Ω by connecting the 2Ω resistance in series with the parallel combination of 3Ω and 6Ω.

(ii) We can obtain a total resistance of 1Ω by connecting resistors of 2 Ω, 3 Ω, and 6 Ω in parallel.

Question 5: What is (i) the highest, (ii) the lowest total resistance that can be secured by combinations of four coils of resistance 4 Ω, 8 Ω, 12 Ω, 24 Ω?
Answer:
(i) Highest resistance can be obtained by connecting the four coils in series.
Then, R = 4Ω + 8Ω + 12Ω + 24Ω = 48Ω
(ii) Lowest resistance can be obtained by connecting the four coils in parallel.

Page Number: 218

Question 1: Why does the cord of an electric heater not glow while the heating element does?
Answer:
Heat generated in a circuit is given by I²R t. The heating element of an electric heater made of nichrome glows because it becomes red-hot due to the large amount of heat produced on passing current because of its high resistance, but the cord of the electric heater made of copper does not glow because negligible heat is produced in it by passing current because of its extremely low resistance.

Question 2: Compute the heat generated while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V.
Answer:
Here, Q = 96,000 C, t =1 hour = 1 x 60 x 60 sec = 3,600 s, V = 50 V
Heat generated, H = VQ = 50Vx 96,000 C = 48,00,000 J = 4.8 x 10⁶ J

Question 3: An electric iron of resistance 20Ω takes a current of 5 A. Calculate the heat developed in 30 s.
Answer:
Here, R = 20 Ω, i = 5 A, t = 3s
Heat developed, H = I² R t = 25 x 20 x 30 = 15,000 J = 1.5 x 10⁴ J

Page Number: 220

Question 1: What determines the rate at which energy is delivered by a current ?
Answer:
Resistance of the circuit determines the rate at which energy is delivered by a current.

Question 2: An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.
Answer:
Here, I = 5 A, V = 220 V, t = 2h = 7,200 s
Power, P = V I = 220 x 5 = 1100 W
Energy consumed = P x t = 100 W x 7200 s = 7,20,000 J = 7.2 x 10⁵ J

NCERT Solutions for Class 10 Science Chapter 12 Textbook Chapter End Questions.

Question 1:A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then the ratio R/R’ is :
(a) 125
(b) 15
(c) 5
(d) 25
Answer:
(d) 25

Question 2: Which of the following terms does not represent electrical power in a circuit?
(a) I²R
(b) IR²
(c) VI
(d) v22
Answer:
(fa) IR2

Question 3: An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be :
(a) 100 W
(b) 75 W
(c) 50 W
(d) 25 W
Answer:  

(d) 25 W

Question 4: Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be :
(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1
Answer:
(c) 1 : 4

Question 5: How is a voltmeter connected in the circuit to measure the potential difference between two points ?
Answer:
A voltmeter is connected in parallel to measure the potential difference between two points.

Question 6: A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10^-8 Ω m. What will be the length of this wire to make its resistance 10 Ω ? How much does the resistance change if the diameter is doubled ?
Answer:


If a wire of diameter doubled to it is taken, then the area of the cross-section becomes four times.
New resistance = 102 = 2.5 Ω, Thus the new resistance will be 14 times.
Decrease in resistance = (10 – 2.5) Ω = 7.5 Ω

Question 7
The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below :

Plot a graph between V and I and calculate the resistance of the resistor.
Solution:
The graph between V and I for the above data is given below.
The slope of the graph will give the value of resistance.
Let us consider two points P and Q on the graph.
and from P along the Y-axis, which meet at point R.
Now, QR = 10.2V – 34V = 6.8V
And PR = 3 – 1 = 2 ampere


Thus, resistance, R = 3.4 Ω

Question 8
When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistor's resistance.
Solution:
Here, V = 12 V and I = 2.5 mA = 2.5 x 10^-3 A
∴ Resistance, R = VI = 12V2.5×103A = 4,800 Ω = 4.8 x 10^-3 Ω

Question 9
A battery of 9V is connected in series with resistors of 0.2 O, 0.3 O, 0.4 Q, 0.5 Q and 12 £1, respectively. How much current would flow through the 12 Q resistor?
Solution:
Total resistance, R = 0.2 Ω + 0.3 Ω + 0.4 Ω + 0.5 Ω + 12 Ω – 13.4 Ω
Potential difference, V = 9 V
Current through the series circuit, I = VR = 12V13.4Ω = 0.67 A
∵ There is no division of current in series. Therefore current through 12 Ω resistor = 0.67 A.

Question 10
How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line? [CBSE (Delhi) 2013]
Solution:
Suppose n resistors of 176 Ω are connected in parallel.

Thus 4 resistors are needed to be connect.

Question 11
Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of (i) 9 Ω, (ii) 4Ω
Solution:
Here, R₁ = R₂ = R₃ = 6 Ω.

(i) When we connect R₁ in series with the parallel combination of R₂ and R₃ as shown in Fig. (a).
The equivalent resistance is

(ii) When we connect a series combination of R₁ and R₂ in parallel with R₃, as shown in Fig. (b), the equivalent resistance is

Question 12
Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A ?
Solution:
Here, current, I = 5 A, voltage, V = 220 V
∴ Maxium power, P = I x V = 5 x 220 = 1100W
Required no. of lamps =Max.PowerPowerof1lamp=110010=110
∴ 110 lamps can be connected in parallel.

Question 13
A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of 24 Ω resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases ?
Solution:
(i) When the two coils A and B are used separately. R = 24 Ω, V = 220 V

(ii) When the two coils are connected in series,

(iii) When the two coils are connected in parallel.

Question 14
Compare the power used in the 2 Ω resistor in each of the following circuits
(i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and
(ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.
Solution:
(i) The circuit diagram is shown in figure.
Total resistance, R = 1Ω + 2Ω = 3Ω
Potential difference, V = 6 V

Power used in 2Ω resistor = I²R = (2)² x 2 = 8 W

(ii) The circuit diagram for this case is shown :
Power used in 2 resistor = v2R =422 = 8 W.

[ ∵ Current is different for different resistors in parallel combination.]

Question 15
Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V ? [CBSE 2018]
Solution:
Power of first lamp (P₁) = 100 W
Potential difference (V) = 220 V

Question 16
Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes ?
Solution:
Energy used by 250 W TV set in 1 hour = 250 W x 1 h = 250 Wh
Energy used by 1200 W toaster in 10 minutes = 1200 W x 10 min
= 1200 x 1060 = 200 Wh 60
Thus, the TV set uses more energy than the toaster.

Question 17
An electric heater of resistance 8 Ω draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater.
Solution:
Here, R = 8 Ω, 1 = 15 A, t = 2 h
The rate at which heat is developed in the heater is equal to the power.
Therefore, P = I² R = (15)² x 8 = 1800 Js^-1

Question 18: Explain the following:
(i) Why is tungsten used almost exclusively for filament of electric lamps ?
(ii) Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal ?
(in) Why is the series arrangement not used for domestic circuits ?
(iv) How does the resistance of a wire vary with its area of cross-section ?
(v) Why are copper and aluminium wires usually employed for electricity transmission?
Answer:
(i) The tungsten is used almost exclusively for filament of electric lamps because it has a very high melting point (3300°C). On passing electricity through tungsten filament, its temperature reaches to 2700°C and it gives heat and light energy without being melted.
(ii) The conductors of electric heating devices such as bread-toasters and electric irons, are made of an alloy rather than a pure metal because the resistivity of an alloy is much higher than that of pure metal and an alloy does not undergo oxidation (or burn) easily even at high temperature.
(iii) The series arrangement is not used for domestic circuits because in series circuit, if one electrical appliance stops working due to some defect, than all other appliances also stop working because the whole circuit is broken.
(iv) The resistance of a wire is inversely proportional to its area of cross-section, i.e., Resistance R ∝ (1/πr²). If the area of cross section of a conductor of fixed length is increased, then resistance decreases because there are more free electrons for movement in conductor.
(v) Copper and aluminum wires usually employed for electricity transmission because they have very low resistances. So, they do not become too hot on passing electric current.

Electric current, potential difference and electric current, Ohms law, Resistance, Resistivity factors on which the resistance of a conductor depends; Series combination of resistors, parallel combination of resistors; and its application on daily life; Heating effect of Electric current, electric Power, Interrelation between P, V, and R.

Page 200
What does an electric circuit mean?
Electric circuit is a continuous and closed path made of conducting wires, through which the electric current flows. It uses a cell, ammeter, voltmeter, plug key, etc.
Define the unit of current.
SI unit of electric current is ampere (A).
Ampere is the flow of electric charges through an area at the rate of one coulomb per second, i.e. if 1 coulomb of electric charge flows through a cross-section of wire for 1 second, then it would be equal to 1 ampere.

Page 202

Question 1: Name a device that helps to maintain a potential difference across a conductor.
Answer:
Cell or battery eliminator.

Question 2: What is meant by saying that the potential difference between two points is 1 V?
Answer:
As we know that V = W / q
Thus, the potential difference between two points is one volt when one joule of work is done to carry a charge of one coulomb between the two points in the electric field.

Question 3: How much energy is given to one coulomb of charge passing through a 6 V battery
Answer:

Page 209

Question 1: On what factors does the resistance of a conductor depend
Answer:
Resistance of a conductor depends upon:
(i) Resistivity of the material.
(ii) Length of the conductor.
(iii) Cross-sectional area of the conductor.

Question 2: Will current flow more easily through a thick wire or thin wire of the same material when connected to the same source? Why?
Answer:
The current flows more easily through a thick wire than through a thin wire because the resistance of thick wire is less than that of a thin wire as R ∝ 1/A.

Question 3: Let the resistance of an electrical component remains 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:

Hence, the current through an electrical component also becomes half of its previous value.

Question 4: Why are the coils of electric toasters and electric irons made of an alloy rather than a pure metal
Answer:
The coils of electric toaster and electric iron are made of an alloy rather than a pure metal because of the following reasons;
(i) The resistivity of an alloy is higher than that of a pure metal.
(ii) It has a high melting point and does not oxidize.

Question 5: Use the data in Table 12.2 of NCERT book to answer the following:
(a) Which among iron and mercury is a better conductor?
(b) Which material is the best conductor? ‘
Answer:
(a) Iron because its resistivity is less than mercury.
(b) Silver is the best conductor as it has least resistivity.

Page 213

Question 1: Draw a schematic diagram of a circuit consisting of a battery of three cells of 2 V each, a 5 Ω resistor, a 8 Ω resistor and a 12 Ω resistor and a plug key, all connected in series.
Answer:

Question 2: Redraw the circuit of the above question, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the voltage across the 12 resistors. What would be the reading in the ammeter and the voltmeter?
Answer:

The total resistance of the circuit = R
Since all three resistors are connected in series, so, the equivalent resistance R is equal to the sum of all resistances.
R = 5 Ω + 8 Ω + 12 Ω = 25 Ω

Page 216

Question 1: Judge the equivalent resistance when the following are connected in parallel.
(a) 1 Ω and 10⁶ Ω
(b) 1 Ω , 10³ Ω and 10⁶ Ω
Answer:
Equivalent resistance in a parallel combination of resistors is always less than the least resistance of any resistor in the circuit.
Hence, in both the given cases, the equivalent resistance is less than 1 Ω.

Question 2: An electric lamp of 100 Ω, a toaster of resistance 50 Ω and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances and what is the current flows through it?
Answer:

Resistance of electric lamp, R₁ = 100 Ω
Resistance of toaster, R₂ = 50 Ω
Resistance of water filter, R₃ = 500 Ω
The equivalent resistance R_p of the three appliances connected in parallel, is

Question 3: What are the advantages of connecting electrical devices in parallel with the battery instead of in series?
Answer:
Advantages of connecting electrical devices in parallel:

1.     When the appliances are connected in parallel with the battery, each appliance gets the same potential difference as that of battery which is not possible in series connection.

2.     Each appliance has different resistances and requires different currents to operate properly. This is possible only in parallel connection, as in series connection, same current flows through all devices, irrespective of their resistances.

3.     If one appliance fails to work, the other will continue to work properly.

Question 4: How can three resistors of resistances 2 Ω, 3 Ω, and 6 Ω be connected to give a total resistance of (a) 4 Ω (b) 1 Ω?
Answer:
(i) We can get a total resistance of 4Ω by connecting the 2Ω resistance in series with the parallel combination of 3Ω and 6Ω.

(ii) We can obtain a total resistance of 1Ω by connecting resistors of 2 Ω, 3 Ω and 6 Ω in parallel.

Question 5: What is (a) the highest (b) the lowest total resistance that can be secured by a combination of four coils of resistances 4 Ω, 8 Ω, 12 Ω, 24 Ω?
Answer:
(a) The highest resistance is secured by combining all four coils of resistance in series.
R_s = 4 Ω+ 8 Ω + 12 Ω + 24 Ω = 48 Ω
(b) The lowest resistance is secured by combining all four coils of resistance in parallel.

Page 218

Question 1: Why does the cord of an electric heater not glow while the heating element does?
Answer:
The cord of an electric heater is made up of metallic wire such as copper or aluminum which has low resistance while the heating element is made up of an alloy which has more resistance than its constituent metals. Also heat produced ‘H’ is
H = I²Rt
Thus, for the same current H oc R, so for more resistance, more heat is produced by heating element and it glows.

Question 2: Compute the heat generated while transferring 96000 C of charge in one hour through a potential difference of 50 V.
Answer:

Question 3: An electric iron of resistance 20 Q takes a current of 5 A. Calculate the heat developed in 30 s.
Answer:
Given R = 20 Ω, I = 5 A, t = 30 s
H = I²Rt = (5)² x 20 x 30 = 15000 J = 1.5 x 10⁴ J

Page 220

Question 1: What determines the rate at which energy is delivered by a current?
Answer:
Electric power determines the rate at which energy is delivered by a current.

Question 2: An electric motor takes 5 A from a 220 V line. Determine the power of the motor and the energy consumed in 2 h.
Answer:
Given I = 5 A, V = 220 V, t = 2 h Power,
p = VI = 220 x 5 = 1100 W
Energy consumed = Vlt = Pt
= 1100 x 2 = 2200 Wh

Textbook Questions

Question 1: A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then the ratio R/R’ is

Answer:

Question 2: Which of the following terms does not represent electrical power in a circuit?
(a) I²R
(b) IR²
(c) VI
(d) V^2/R
Answer:
(b) P = V^2/R = I²R = VI Option (b) does not represent electrical power.

Question 3: An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be
(a) 100 W
(b) 75 W
(c) 50 W
(d) 25 W
Answer:

Question 4: Two conducting wires of same material and of equal lengths and diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be
(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1
Answer:

Question 5: How is a voltmeter connected in the circuit to measure the potential difference between two points?
Answer:
A voltmeter is connected in parallel across any two points in a circuit to measure the potential difference between them with its +ve terminal to the point at higher potential and -ve terminal to the point at lower potential of the source.

Question 6: A copper wire has a diameter 0.5 mm and resistivity of 1.6 X 10^-8 Ωm. What will be the length of this wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?
Answer:

Question 7: The values of the current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below:

Plot a graph between V and I and calculate the resistance of that resistor.
Answer:

The graph between V and I for the above data is given below.
The slope of the graph will give the value of resistance.
Let us consider two points P and Q on the graph.
and from P along Y-axis, which meet at point R.
Now, QR = 10.2V – 34V = 6.8V
And PR = 3 – 1 = 2 ampere

Question 8: When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistor's resistance.

Answer:

Question 9: A battery of 9 V is connected in series with resistors of 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5 Ω and 12 Ω, respectively. How much current would flow through the 12 Ω resistor?
Answer:
Since all the resistors are in series, the same current, 0.67 A flows through the 12 Ω resistor.

Question 10: How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?
Answer:

Suppose n resistors of 176 Ω are connected in parallel.

Question 11: Show how you would connect three resistors, each of resistance 6 Ω , so that the combination has a resistance of (i) 9 Ω , (it) 4 Ω .
Answer:

Here, R₁ = R₂ = R₃ = 6 Ω.

(i) When we connect R₁ in series with the parallel combination of R₂ and R₃ as shown in Fig. (a).
The equivalent resistance is

(ii) When we connect a series combination of R₁ and R₂ in parallel with R₃, as shown in Fig. (b), the equivalent resistance is

Question 12: Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of the 220 V line if the maximum allowable current is 5 A?

Answer:
Since N bulbs of power P are each connected in parallel will make the total power of NP,

Question 13: A hot plate of an electric oven connected to 220 V line has two resistance coils A and B, each of 24 Q resistance, which may be used separately, in series, or in parallel. What are the currents in the three cases?
Answer:

(i) When the two coils A and B are used separately. R = 24 Ω, V = 220 V

(ii) When the two coils are connected in series,

(iii) When the two coils are connected in parallel.

Question 14: Compare the power used in the 2 Ω resistor in each of the following circuits.
(i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and
(ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.
Answer:

(i) The circuit diagram is shown in figure.
Total resistance, R = 1Ω + 2Ω = 3Ω
Potential difference, V = 6 V

Power used in 2Ω resistor = I²R = (2)² x 2 = 8 W

(ii) The circuit diagram for this case is shown :
Power used in 2 resistor = v2R =422 = 8 W.

Question 15: Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?
Answer:

Power of first lamp (P₁) = 100 W
Potential difference (V) = 220 V

Question 16: Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?
Answer:
Energy consumed by 250 W TV set in 1 h = 250 x 1 = 250 Wh.
Energy consumed by 1200 W toaster in 10 min = 1200 X 1/6 = 200 Wh.
∴ Energy consumed by TV set is more than the energy consumed by toaster in the given timings.

Question 17: An electric heater of resistance 8 f2 draws 15 A from the service mains 2 hours. Calculate the rate at which heat is developed in the heater.
Answer:

Question 18: Explain the following.
(a) Why is the tungsten used almost exclusively for filament of electric lamps?
(b) Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?
(c) Why is the series arrangement not used for domestic circuits?
(d) How does the resistance of a wire vary with its area of cross-section?
(e) Why are copper and aluminum wires usually employed for electricity transmission?
Answer:
(a) It has high melting point and emits light at a high temperature.
(b) It has more resistivity and less temperature coefficient of resistance.
(c) (i) All appliances do not get same potential in series arrangement.
(ii) All appliances cannot be individually operated.
(d) R ∝ =1 / Area of cross-section.
(e) They are very good conductors of electricity.

Short Answer Type Questions

Question 1: Three 2 Ω resistors, A, B and C are connected as shown in figure. Each of them dissipates energy and can withstand a maximum power of 18 W without melting. Find the maximum current that can flow through the three resistors.
Answer:

Question 2: Should the resistance of an ammeter be low or high? Give reason.
Answer:
The resistance of an ammeter should be low so that it will not disturb the magnitude of current flowing through the circuit when connected in series in a circuit.

Question 3: How does use of a fuse wire protect electrical appliances?
Answer:
The fuse wire is always connected in series with the live wire or electrical devices. If the flow of current exceeds the specified preset value due to some reason, the heat produced melts it and disconnects the circuit or the device from the mains. In this way, fuse wire protects the electrical appliances.

Question 4: What is electrical resistivity? In a series electrical circuit comprising a resistor made up of a metallic wire, the ammeter reads 5 A. The reading of the ammeter decreases to half when the length of the wire is doubled. Why?
Answer:
The resistance offered by a metallic wire of unit length and unit cross-sectional area is called electrical resistivity.

Hence, when the length of wire is doubled, the resistance becomes double and current decreases to half.

Question 5: A current of 1 ampere flows in a series circuit containing an electric lamp and a conductor of 5 Ω when connected to a 10 V battery. Calculate the resistance of the electric lamp.
Now if a resistance of 10 Ω is connected in parallel with this series combination, what change (if any) in current flowing through 5 Ω conductor and potential difference across the lamp will take place? Give reason.
Answer:

Question 6: Why is parallel arrangement used in domestic wiring?
Answer:
Parallel arrangement is used in domestic wiring because
(i) Each appliance gets the same voltage as that of the mains supply.
(ii) If one component is switched off, others can work properly.
(iii) Fault in any branch of the circuit can be easily identified.

Question 7: B_1, B₂ and B₃ are three identical bulbs connected as shown in figure. When all three bulbs glow, a current of 3A is recorded by the ammeter A.

(i) What happens to the glow of the other two bulbs when the bulb B j gets fused?
(ii) What happens to the reading of A₁ ,A₂ , A₃ and A when the bulb B₂ gets fused?
(iii) How much power is dissipated in the circuit when all the three bulbs glow together?
Answer:
(i) Since B₁,B₂ and B₃ are in parallel, the potential difference across each of them will remain the same. So when the bulb B₁ gets fused, B₂ and B₃ have the same potential and continue with the same energy dissipated per second, i.e. they will glow continuously as they were glowing before.

 

What You Learnt.

·        A stream of electrons moving through a conductor constitutes an electric current. Conventionally, the direction of current is taken opposite to the direction of flow of electrons.

·        The SI unit of electric current is ampere. n To set the electrons in motion in an electric circuit, we use a cell or a battery. A cell generates a potential difference across its terminals. It is measured in volts (V).

·        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).

·        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.

·        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.

·        The equivalent resistance of several resistors in series is equal to the sum of their individual resistances.

·        The commercial unit of electrical energy is kilowatt hour (kWh). 1 kW h = 3,600,000 J = 3.6 × 106 J.

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