Mind Map Overal Idea Content Speed Notes Quick Coverage The circle, thesquare, the rectangle, the quadrilateral and the triangle are examples of plane figures; the cube, the cuboid, the sphere, the cylinder, the cone and the pyramid areexamples of solid shapes. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content… readmore
Mind Map
Overal Idea
Content
Speed Notes
Quick Coverage
The circle, thesquare, the rectangle, the quadrilateral and the triangle are examples of plane figures; the cube, the cuboid, the sphere, the cylinder, the cone and the pyramid areexamples of solid shapes.(Scroll down till end of the page)
Study Tools
Audio, Visual & Digital Content
Plane figures areof two-dimensions (2-D) and the solid shapes are of three- dimensions (3-D). The corners of a solid shape are called its vertices; theline segments ofits skeleton areits edges; and itsflat surfaces areits faces. A net is a skeleton-outline of a solid that can be folded to make it. The same solid can haveseveral types ofnets. Solid shapes can be drawn on a flat surface (like paper) realistically. We call this 2-D representation of a 3-Dsolid. Two types ofsketches of asolid are possible: (a) An oblique sketch does nothave proportional lengths. Still it conveys all important aspects of the appearance of the solid. (b) An isometric sketch is drawn on an isometric dot paper, a sample of which isgiven at theend of thisbook. In an isometric sketch of the solidthe measurements kept proportional. Visualising solidshapesis a veryuseful skill. Youshould be ableto see ‘hidden’ parts of thesolid shape. Different sections of a solid can be viewed in many ways: (a) One way is to viewby cutting or slicing the shape, whichwould result in the cross- section of thesolid. (b) Another way isby observing a 2-D shadow of a 3-Dshape. (c) A third wayis to lookat the shapefrom different angles; the front-view, theside- view and thetop view canprovide a lotof information aboutthe shape observed.
19. When a grouping symbol preceded by ‘ sign is removed or inserted, thenthe sign of eachterm of thecorresponding expression ischanged (from ‘ + ‘ to ‘−’ and from‘− ‘ to + ‘).
Mind Map Overal Idea Content Speed Notes Quick Coverage Electricity Electricity is a branch of physics that deals with the study of phenomena associated with stationary or moving electric charges. Therefore, the various manifestations of electricity are the result of the accumulation or motion of electrons. Electricity is classified into two types. They are Static… readmore
Mind Map
Overal Idea
Content
Speed Notes
Quick Coverage
Electricity
Electricity is a branch of physics that deals with the study of phenomena associated with stationary or moving electric charges.
Therefore, the various manifestations of electricity are the result of the accumulation or motion of electrons.
Electricity is classified into two types. They are Static Electricity and Current Electricity. (Scroll down to continue …)
Study Tools
Audio, Visual & Digital Content
ELECTRICITY
V-Lab
Book
Slides
V-Class
Quiz
Solutions
Resources of Electricity
Static Electricity
Static Electricity is a branch of physics that deals with the study of phenomena associated with stationary electric charges.
Current Electricity.
Current Electricity is a branch of physics that deals with the study of phenomena associated with moving electric charges.
Electric Charge
Electric charge is a fundamental property of matter.
Though we can’t say what is charge with certainty, we can study the properties and behaviour of charge.
Charge is defined as the property associated with matter due to which it produces and experiences electrical and magnetic effects.
The electric charge is caused by the elementary particles, electrons and protons.
Protons possess positive charge, electrons possess negative charge and Neutrons do not possess any charge.
Laws of Electric Charges:
Similar electric charges repel each other
Dissimilar (opposite) electric charges attract each other.
Conductors And Insulators
Conductors are the materials in which electrons move freely.
Example: All metals.
Insulators are the materials which do not have any free electrons to move.
Example: Wood and plastic.
Electric Circuit:
The path of flow of current is known as electric circuit.
Electric Potential Energy
Electric potential energy of a group of charges is defined as the amount of work done in bringing the charges to their respective positions in the system.
Electric Potential At A Point
The electric potential at a point, in an electric field, is defined as the amount of work done in moving a unit + ve charge from infinity to that point, without acceleration or without a change in K.E., against the electric force due to the electric field.
The potential at a point is given by the expression V = W/q
The S.I Unit of potential is mathematically written as 1 volt = 1 joule/1 coulomb.
Potential is a scalar quantity, therefore it is added algebraically.
For a positively charged body, potential is positive and for a negatively charged body potential is negative.
Electric current flows through a conductor only if there is a potential difference across its ends.
Work done in moving a charge in the electric field of another charge is given by:
W = Vq
More is the charge on a body, the more is its potential due to it.
Electric current flows through a conductor only if there is a potential difference across its ends.
Positive charge flows from a body at higher potential to a body at lower potential and negative charge flows from a body at a lower potential to a body at higher potential.
Potential difference
The work done in moving a unit positive charge from one point to another is known as Potential Difference between those points.
Example
The work done in moving a unit positive charge from point A to another point B is known as Potential Difference between the points A and B.
SI Unit: volt
The unit of potential difference is volt (V).
Volt
In other words, Volt is defined as the potential difference between two points, if 1 Joule of work is done in moving 1 coulomb charge from one point to another.
Potential difference between two points across a conductor is measured by using a voltmeter.
Voltmeter is always connected in parallel to the points across which potential difference is to be measured.
Battery:
Battery is an arrangement that creates a constant potential difference between its terminals.
Battery is defined as a combination of a number of cells in series.
Electric Current
The literary meaning of Electric Current isflow of electric charge.
Definition
Electric current is defined as the amount of charge passing a cross section of conductor per a unit time (second in SI Units).
Electric current is expressed mathematically in terms of rate of flow of charges as:
Electric Current =(Net Charge, Q)/(Time,t)
i =n.et , Where n = number of electrons, e = charge of one electron, t= time taken to flow,
Q = charge through the crosssection of the conductor.
The SI unit of electric current is Ampere (A).
Direction of electric current is the same as the direction of positive charges But it is opposite to the direction of flow of negative charges.
Potential difference, V between two points at a constant temperature is directly proportional to the current, I.
V ∝ I
⇒ V = lR
Where, R is a constant termed as ElectricResistance.
The SI unit of resistance is ohm (Ω)
Q.1. State Ohm’s law. How can it be verified?
Answer: It states “Physical conditions’ remaining same, the current flowing through a conductor is directly proportional to the potential difference across its two ends”.
i.e., V∞ I
or
V = IR, where, R is the constant of proportionality.
R is called the electrical resistance or resistance of the conductor.
Verification:
V∞ I or V = IR, where the constant of proportionality R is called the electrical resistance or resistance of the conductor.
The following circuit diagram is used to verify Ohm’s law.
Take a few cells; connect one cell across a nichrome wire AB, along with an ammeter and a voltmeter as shown in figure. Note the voltage and the current from the voltmeter and the
ammeter.
Now, connect two cells and again note the voltage and the current. Repeat the procedure for three cells and four cells. Calculate the ratio for each set.
You will find the ratio is nearly the same in all cases. If a graph of current against voltage is plotted, it will turn to be a straight line as shown in figure. This shows that the current is directly proportional to the potential difference.
Laws of Electric Resistance
Or
Factors Affecting Resistance
Resistance is directly proportional to length of conductor.
Resistance is inversely proportional to the area of cross-section.
Resistance is directly proportional to the temperature.
Depends on the nature of the material. This is determined by the resistivity of material.
Laws of Electric Resistance
The resistance of any substance depends on the following factors,
Length of the substance.
Cross sectional area of the substance.
The nature of material of the substance.
Temperature of the substance.
There are mainly four (4) laws of resistance from which the resistivity or specific resistance of any substance can easily be determined.
The resistance of a substance is directly proportional to the length of the substance. Electric resistance, R of a substance is written as
Where L is the length of the substance.
The resistance of a substance is inversely proportional to the cross-sectional area of the substance. Electrical resistance R of a substance is
Where A is the cross-sectional area of the substance.
Resistivity
Combining these two laws we get,
Where, ρ (rho) is the proportionality constant and known as resistivity or specific resistance of the material of the conductor or substance.
Now if we put L = 1 and A = 1 in the equation, we get, R = ρ.
That means resistance of a material of unit length having unit cross – sectional area is equal to its resistivity or specific resistance.
Resistivity of a material can alternatively be defined as the electrical resistance between opposite faces of a cube of unit volume of that material.
Unit of Resistivity
The unit of resistivity can be easily determined form its equation
The unit of resistivity is Ω – m in the MKS system and Ω – cm in the CGS system and 1 Ω – m = 100 Ω – cm.
Resistivity
Resistivity is the property of the material. It does depend on the length and area of the conductor.
Resistance = (Resistivity) x (Length of Conductor) / (Cross Sectional Area)
The SI unit of resistivity is ohm-metre.
Resistivity of metals varies from 10-8 to 10-6.
Resistivity of insulators varies from 1012 to 1017
Copper and aluminium are used in electrical transmission due to their low resistivity.
Net Resistance in Resistors In Series
When several resistors are joined in series, the resistance of the combination Rs equals the sum of their individual resistances, R1, R2, R3
It is mathematically expressed as: RS = R1 + R2 + R3
Thus greater than any individual resistance.
Derivation of Net Resistance of Resistors In Series
When two or more resistors are joined in series, then their total resistance is given by the formula:
⇒ RS = R1 + R2 + R3
The current will remain the same through all resistors.
Total voltage is given by: V = V1 + V2 + V3
Voltage across each resistor is given as: V1 = IR1, V2 = IR2, V3 = IR3
⇒ V = V1 + V2 + V3
But Total Voltage V = I × R, Here I = Current in electric circuit and R = Net Resistance in the circuit.
⇒ IR = IR1 + IR2 + IR3 ⇒ IR = I(R1 + R2 + R3) ⇒ R = R1 + R2 + R3
Resistors In Parallel
The reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
(V/Rp) = (V/R1) + (V/R2) + (V/R3)
Derivation of Net Resistance of Resistors In Parallel
In this case, voltage is the same across each resistor and is equal to applied voltage.
Total current is given as:
I = I1 + I2 + I3
It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.
I = I1 + I2 + I3 ————– (i)
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: I = V/Rp ————– (ii)
On applying Ohm’s law to each resistor, we have
I1= V /R1; I2= V /R2; and I3= V /R3 —————– (iii)
From Eqs. (ii) to (iii), we have
(V/Rp) = (V/R1) + (V/R2) + (V/R3)
⇒ V(1/Rp) = V[(1/R1) + (1/R2) + (1/R3)]
⇒ (1/Rp) = [(1/R1) + (1/R2) + (1/R3)] ————– ()
Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
Advantages of Parallel Combination over Series Combination:
If one component fails in series, then the complete circuit is broken and no component can work properly. Different appliances need different current, this can be met through parallel.
Heating effects of Electric Current
When charge Q moves against the potential difference V in time t, the amount of work is given by-
Joule’s Law of Heating
Heat produced in a resistor is directly proportional to square root of current.
It is also directly proportional to resistance for a given current.
Also, directly proportional to time
⇒ H = l2 Rt
Filament of an electric bulb is made up of tungsten because it has a very high melting point and also does not oxidise readily at a high temperature.
Electric fuse is a safety device to protect the electrical appliance from short circuits.
Electric Power
The rate at which electric energy is dissipated or consumed in an electric current. The SI unit of power is Watt.
⇒ P = Vl
⇒ P = l2 R = V2/R
The commercial unit of electric energy is kilowatt hour (KWh).
Mind Map Overal Idea Content Speed Notes Quick Coverage Content Study Tools MAGNETIC EFFECTS OF ELECTRIC CURRENT | ELECTROMAGNETISM | FULL NOTES Chapter At A Glance Interactive Notes E-Book L-Plan Solutions Assessment (Quiz Time) Assignment (Worksheet/QB) Summary Interactive Notes Summary L-Plan Q-Bank E-Book Assessment V-Lab Video Key Assignment Magnetic Effects of… readmore
Mind Map
Overal Idea
Content
Speed Notes
Quick Coverage
Content
Study Tools
MAGNETIC EFFECTS OF ELECTRIC CURRENT | ELECTROMAGNETISM | FULL NOTES
Take a battery (12 V), a variable resistance (or a rheostat), an ammeter (0–5 A), a plug key, connecting wires and a long straight thick copper wire.
Insert the thick wire through the centre, normal to the plane of a rectangular cardboard.
Take care that the cardboard is fixed and does not slide up or down.
Connect the copper wire vertically between thepoints X and Y, as shown in Fig. 13.6 (a), in series with the battery, a plug and key.
Sprinkle some iron filings uniformly on the cardboard. (You may use a salt sprinkler for this purpose.)
Keep the variable of the rheostat at a fixed position and note the current through the ammeter.
Close the key so that a current flows through the wire. Ensure that the copper wire placed between the points X and Y remains vertically
straight.
Gently tap the cardboard a few times. Observe The pattern of the iron filings. You would find that the iron filings align themselves showing a pattern of concentric circles around the copper wire.
What do these concentric circles represent?
They represent the magnetic field lines.
How can the direction of the magnetic field be found? Place a compass at a point (say P) over a circle.
Observe the direction of the needle.
The direction of the north pole of the compass needle would give the direction of the field lines produced by the electric current through the straight wire at point P. Show the direction by an arrow.
Does the direction of magnetic field lines get reversed if the direction of current through the straight copper wire is reversed? Check it out.
Finding Direction of Magnetic Field
Right Hand Thumb Rule Or Right Hand Grip Rule
Imagine that you are holding a current-carrying straight conductor in your right hand such that the thumb points towards the direction of current.
Then your fingers will wrap around the conductor in the direction of the field lines of the magnetic field, as shown in Figure known as the right-hand thumb rule*.
The field lines about the wire consist of a series of concentric circles whose direction is given by the right-hand rule.
Right hand thumb rule states that if we hold the conductor in the right hand such that the thumb points in the direction of electric current, then the direction in which the fingers curl gives the direction of the magnetic field
If we point the thumb downwards in the direction of the current, the magnetic field would be represented by the curled fingers as the circles around the conductor.
So, if it is viewed from the above plane these field lines will be clockwise circles, but the direction of the magnetic field at any point on these circular magnetic lines is in the direction of the tangent drawn to the circular magnetic lines at the desired points.
Example:
A current through a horizontal power line flows in an east to west direction. What is the direction of the magnetic field at a point directly below it and at a point directly above it?
Solution
The current is in the east-west direction. Applying the right-hand thumb rule, we get that the magnetic field (at any point below or above the wire) turns clockwise in a plane perpendicular to the wire, when viewed from the east end, and anti-clockwise, when viewed from the west end.
Maxwell’ cork screwrule is also known as maxwell’s right hand thumb rule Maxwell’s right hand thumb rule states that, if the head of a cork-Screw is rotated such that the tip of the screw advances in the direction of electric current, then the direction of rotation of the head of the screw represents the direction of the magnetic field around the conductor.
A magnetic field caused by a current-carrying conductor consists of sets of concentric lines of force. The direction of the magnetic field lines depends on the direction of the current passed through the conductor.
Example 13.1
A current through a horizontal power line flows in east to west
direction. What is the direction of magnetic field at a point directly
below it and at a point directly above it?
Solution
The current is in the east-west direction. Applying the right-hand
thumb rule, we get that the magnetic field (at any point below or
above the wire) turns clockwise in a plane perpendicular to the wire,
when viewed from the east end, and anti-clockwise, when viewed
from the west end.
Clock-S Rule
Clock-S rule is a rule which helps us to find the formation of magnetic South Pole due to electromagnetic induction in a current carrying conducting coil.
According to clocks rule if one face of a current carrying conducting coil is placed such that one face of the coil is faced to us and current is moving in the clockwise direction with respect to us then the face of the coil which is faced to us becomes as a magnetic south pole and the other face behaves as the north magnetic pole.
A current carrying conductor in the form of a rectangular loop behaves like a magnet and when suspended in an external magnetic field experiences force.
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of west.
Case 2
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of east.
Case 3
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of east.
Case 4
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Above the conducting wire, the needle of the compass deflects in the direction of west.
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of east.
Current Direction
Compass Position
N – of Compass Deflection
S – of Compass Deflection
South to North
Above
SNOWWest
East
North to South
Above
East
West
South to North
Below
East
West
North to South
Below
West
East
Magnetic Field due to a Current through a
Circular Loop
We have so far observed the pattern of the magnetic field lines produced around a current-carrying straight wire.
Suppose this straight wire is bent in the form of a circular loop and a current is passed through it.
What would the magnetic field lines look like?
We know that the magnetic field produced by a current-carrying straight wire depends inversely on the distance from it.
Similarly at every point of a current-carrying circular loop, the concentric circles representing the magnetic field around it would become larger and larger as we move away from the wire (Fig. 13.8). By the time we reach the centre of the circular loop, the arcs of these big circles would appear as straight lines.
Every point on the wire carrying current would give rise to the magnetic field appearing as straight lines at the centre of the loop.
By applying the right hand rule, it is easy to check that every section of the wire contributes to the magnetic field lines in the same direction
within the loop.
We know that the magnetic field produced by a current-carrying
wire at a given point depends directly on the current passing through it.
Therefore, if there is a circular coil having n turns, the field produced is
n times as large as that produced by a single turn.
This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up.
Factors affecting magnetic field of a circular current carrying conductor-
Magnetic field is directly proportional to the current passing through the conductor.
Magnetic field is inversely proportional to the distance from the conductor.
Magnetic field is directly proportional to number of turns in coil.
Solenoid
The solenoid is an electromagnet which is a long cylindrical coil of wire consisting of a large number of turns bound together very tightly.
Note: The length of the coil should be longer than its diameter. (Or)
Solenoid is a coil of a number of turns of insulated copper wire closely wrapped in the shape of a cylinder.
When a soft iron rod is placed inside the solenoid, it behaves like an electromagnet.
The use of soft iron as core in the solenoid produces the strongest magnetism.
A solenoid consists of an insulated conducting wire wound on a cylindrical tube made of plastic or cardboard.
Magnetic Field due to a Current in a Solenoid
The magnetic field of a solenoid carrying a current is similar to that of a bar magnet.
Compare the pattern of the field with the magnetic field around a bar magnet.
Do they look similar?
Yes, they are similar.
In fact, one end of the solenoid behaves as a magnetic north pole, while the other behaves as the south pole.
The field lines inside the solenoid are in the form of parallel straight lines.
This indicates that the magnetic field is the same at all points inside the solenoid.
That is, the field is uniform inside the solenoid.
These appear to be similar to that of a bar magnet.
One end of the solenoid behaves like the North Pole and the other end behaves like the South Pole.
Magnetic field lines inside the solenoid are in the form of parallel straight lines.
This means that the field is the same at all the points inside the solenoid.
Electromagnet
An electromagnet consists of a core of soft iron wrapped around with a coil of insulated copper wire.
An electromagnet is a magnet made up of a coil of insulated wire wrapped around a soft iron core that is magnetised only when current flows through the wire.
A strong magnetic field produced inside a solenoid can be used to magnetise a piece of magnetic material, like soft iron, when placed inside the coil.
It is a temporary magnet that can be easily demagnetized.
In this type of magnet, polarity can be reversed and strength can be varied. They are very strong magnets.
Magnetic Field of An electromagnet
Force on A current-carrying conductor placed in a magnetic field
Placing acurrent-carrying conductor in a magnetic field experiences a force.
Finding direction of force on a current-carrying conductor placed in a magnetic field Using Fleming’s left-hand rule
If the direction of the magnetic field and that of the current are mutually perpendicular to each other, then the force acting on the conductor will be perpendicular to both and will be given by Fleming’s left-hand rule.
Flemings Left Hand Rule
Stretch the thumb, forefinger and middle finger of the left hand such that they are mutually perpendicular. If the forefinger is in the direction of the magnetic field, Central finger in the direction of current, then the thumb will point in the direction of motion or force.
Rules & Laws of Electromagnetism
Clock-S Rule
Clock-S rule is a rule which helps us to find the formation of magnetic South Pole due to electromagnetic induction in a current carrying conducting coil.
According to clocks rule if one face of a current carrying conducting coil is placed such that one face of the coil is faced to us and current is moving in the clockwise direction with respect to us then the face of the coil which is faced to us becomes as a magnetic south pole and the other face behaves as the north magnetic pole.
A current carrying conductor in the form of a rectangular loop behaves like a magnet and when suspended in an external magnetic field experiences force.
SNOW Rule
Case 1
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of west.
Case 2
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of east.
Case 3
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of east.
Case 2
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of west.
Maxwell’ cork screwrule is also known as maxwell’s right hand thumb ruleIf the head of a cork-Screw is rotated such that the tip of the screw advances in the direction of electric current, then the direction of rotation of the head of the screw represents the direction of the magnetic field around the conductor.
A magnetic field caused by a current-carrying conductor consists of sets of concentric lines of force. The direction of the magnetic field lines depends on the direction of the current passed through the conductor.
Ampere Right Hand Thumb Rule
Right hand thumb rule states that if we hold the conductor in the right hand such that the thumb points in the direction of electric current, then the direction in which the fingers curl gives the direction of the magnetic field
If we point the thumb downwards in the direction of the current, the magnetic field would be represented by the curled fingers as the circles around the conductor.
So, if it is viewed from the above plane this field lines will be clockwise circles, but the direction of the magnetic field at any point on this circular magnetic lines is in the direction of the tangent drawn to the circular magnetic lines at the desired points.
Example 13.1
A current through a horizontal power line flows in east to west
direction. What is the direction of magnetic field at a point directly
below it and at a point directly above it?
Solution
The current is in the east-west direction. Applying the right-hand
thumb rule, we get that the magnetic field (at any point below or
above the wire) turns clockwise in a plane perpendicular to the wire,
when viewed from the east end, and anti-clockwise, when viewed
from the west end.
Fleming’s Right Hand rule (Working Principle of Transformer and generator )
Fleming’s right hand rule gives the direction of the induced current in a conductor when it is moved in a magnetic field.
Transformers are based on this principle, which consist of a primary coil and a secondary coil.
The number of turns in the coils is selected based on the type of the transformer to be made, namely, step-up or step-down.
Magnetic Field Due to An Electric Conducting Coil (Motor Working Basics)
Working Principle of electric motors is Fleming’s left hand rule.
The direction of the force is given by Fleming’s left hand rule. This gives the basis for an electric motor.
An electric motor essentially consists of a coil as an armature, a split ring commutator for changing the direction of the current in the coil.
There are two brushes linked with the split rings that maintain the contact with the armature for the current flow.
Electric motor converts electrical energy to mechanical energy.
A number of such loops form a coil and the coil is termed solenoid.
If there is a soft iron core in the solenoid, it behaves like a magnet as long as there is current through the coil. Thus it is an electromagnet.
When an electric current passes through a conductor, a magnetic field is created around the conductor. This phenomenon is known as the magnetic effect of electricity.
A magnetic field is the extent of space surrounding a magnet where the magnet’s effect can be felt.
Magnetic field lines represent the lines of action of the force acting on a unit North Pole placed in a magnetic field.
Electromagnetic Induction
Electromagnetic Induction – Electric Effects of Changing Magnetic Field
The phenomenon of electromagnetic induction is the production of induced current in a coil placed in a region where the magnetic field changes with time.
The magnetic field may change due to a relative motion between the coil and a magnet placed near to the coil.
If the coil is placed near to a current-carrying conductor, the
the magnetic field may change either due to a change in the current through the conductor or due to the relative motion between the coil and conductor.
The direction of the induced current is given by the Fleming’s right-hand rule.
Fleming’s Right Hand Rule
A generator converts mechanical energy into electrical energy. It works on the basis of electromagnetic induction.
Electromagnetic Induction is the electric effects of relative motion between magnetic field and electric conductor.
When we place a conductor in a changing magnetic field, some current is induced in it. This current is known as Induced Current and the phenomenon is known as Electromagnetic Induction.
Faraday’s Experiment
The working principle of electric generators and Transformers is Fleming’s right hand rule.
Faraday’s experiment proved that the strength of the induced current depends on several factors like the strength of the magnet, the speed of motion of the magnet, its orientation, the number of turns in the coil and the diameter of the coil. The induced current can be detected by a galvanometer.
Electric Generator
An electric device that converts mechanical energy into electrical energy is called an electric generator.
Working Principle: Fleming Right Hand Rule
Fleming Right Hand Rule
Hold the forefinger, middle finger and thumb of your right hand at right angles to each other. Forefinger points towards the direction of the magnetic field, thumb points in the direction of motion of conductor and middle finger shows direction of induced current.
Electric Energy is a device used to convert mechanical energy into an alternating form of electrical energy. It consists of insulated copper wire, magnetic poles, split rings, axle, brushes and galvanometer.
The axle is rotated so that it moves clockwise, that is AB moves up and CD moves down. After half rotation, CD starts to move up and AB moves down. After every half rotation current changes its direction, this is called AC current.
Electric generators work on the same principle.
They have an armature which is free to rotate in a magnetic field.
Its terminals are connected to two slip rings, which are further connected to two brushes and they are connected across a load resistance through which the generated electricity can be trapped.
The rotation of the armature in the magnetic field changes the magnetic flux in the coil of the armature and an electric current is induced.
As the direction of the induced current changes for every half rotation, it is called alternating current.
The current at the power plants is distributed through transmission lines at a high voltage and hence the lines are referred to as high tension power lines.
At the substations these are stepped down to a lower voltage and supplied to houses at a low voltage.
A domestic electric circuit essentially contains mains, a fuse, live or line, neutral and earth wires.
From the poles supply cables bring the current to the mains.
Within the house, all the equipment is connected in parallel.
Electromagnetic induction (EMI) is the process of generating an electromotive force by moving a conductor through a magnetic field.
The electromotive force generated due to electromagnetic induction is called induced emf. The current due to induced emf is called induced current.
Alternating current (AC) is the current induced by an AC generator. AC current changes direction periodically. Direct current (DC) always flows in one direction, but its voltage may increase or decrease.
An electric motor is different from an electric generator. A generator converts mechanical energy (Kinetic energy) into electrical energy while an electric motor converts electrical energy into mechanical energy (Kinetic energy).
AC Generator:
Principle: It works on the principle that when a coil rotates in a uniform magnetic field, a current is induced in the coil. The direction of induced current is determined by Fleming’s right hand rule.
Construction: An ac generator consists of the following components as shown in figure.
(i) Armature coil: It consists of a large number of turns of a rectangular coil ABCD made of copper wire wound over a soft iron laminated core.
(ii) Strong field magnets: Two concave poles (NS) of permanent magnets between which the armature coil is rotated.
(iii) Slip-rings: The two ends of the coil are welded to two different circular metallic rings R, and R,. These rings are called the slip-rings. The function of the slip-rings is to ensure that the ion of current flowing through the coil after each half rotation.
A schematic diagram of common domestic circuit is as shown below
(iv) Brushes : Two carbon brushes B, and B2 make a contact with the slip-rings R, and R2
An electric generator is as shown in fig. 7.7.
Domestic Electric Circuit
HouseHold Electric Circuits
In our houses we receive AC electric power of 220 V with a frequency of 50 Hz. One of the wires in this supply is with red insulation, called live wire.
The other one is of black insulation, which is a neutral wire. The potential difference between the two is 220 V.
The third is the earth wire that has green insulation and this is connected
to a metallic body deep inside earth. It is used as a safety measure to ensure that any leakage of current to a metallic body does not give any severe shock to a user.
Fuse is the most important safety device, used for protecting the circuits due to short-circuiting or overloading of the circuits.
Electrical components and wires fitted in a household to supply electricity to various appliances form a domestic electric circuit.
The old colour convention of the three wires used in household electrical circuits was Red, called live wire, Black, called neutral wire and Green, called earth wire. Now, this colour convention has changed.
The new colour convention is Brown, called live wire, Light blue, called neutral wire and Green or Yellow, called earth wire.
In our houses, we receive AC electric power of 220 V with a frequency of 50 Hz. One of the wires in this supply is with red insulation, called live wire.
The other one is of black insulation, which is a neutral wire. The potential difference between the two is 220 V.
The third is the earth wire that has green insulation and this is connected to a metallic body deep inside earth.
It is used as a safety measure to ensure that any leakage of current to a metallic body does not give any severe shock to a user.
Earthing
Earthing of an electrical appliance is very important.
Suppose, a conductor is exposed to the appliance due to bad insulation.
If a person touches such an appliance, he will receive a severe shock.
If the metal casing of the appliance is connected to the earth with the help of a conductor, the metal casing will be then at the same potential as the earth i.e., zero volt.
If there is a leakage of current, the current will safely flow to the earth.
The earth connection can also save the appliance from the damage.
Fuse
Fuse is the most important safety device, used for protecting the circuits due to short-circuiting or overloading of the circuits.
It is a safety device to limit the current in an electric circuit.
It prevents the electric appliances from damage.
It is made up of material which has high resistivity and low melting point.
Exam Revision
Magnetic Compass
A compass needle is a small magnet. Its one end, which points towards north, is called a north pole, and the other end, which points towards south, is called a south pole.
Magnetic Field
A magnetic field exists in the region surrounding a magnet, in which the force of the magnet can be detected.
Field lines
Field lines are used to represent a magnetic field. A field line is the path along which a hypothetical free north pole would tend to move. The direction of the magnetic field at a point is given by the direction that a north pole placed at that point would take. Field lines are shown closer together where the magnetic field is greater.
Magnetic Effects of Electric Current
A metallic wire carrying an electric current has a magnetic field associated with it.
The field lines about the wire consist of a series of concentric circles whose direction is given by the right-hand rule.
Right Hand Rule
Magnetic Field Around a Conductor Due to An Electric Current
The pattern of the magnetic field around a conductor due to an electric current flowing through it depends on the shape of the conductor.
Magnetic Field of a solenoid
The magnetic field of a solenoid carrying a current is similar to that of a bar magnet.
Magnetic Field of An electromagnet
An electromagnet consists of a core of soft iron wrapped around with a coil of insulated copper wire.
Force on A current-carrying conductor placed in a magnetic field
O placing acurrent-carrying conductor in a magnetic field experiences a force.
Direction of Force on A current-carrying conductor placed in a magnetic field Using Fleming’s left-hand rule
If the direction of the magnetic field and that of the current are mutually perpendicular to each other, then the force acting on the conductor will be perpendicular to both and will be given by Fleming’s left-hand rule.
Electric Motor
An electric motor is a device that converts electric energy into mechanical energy.
Fleming’s left-hand rule is the basis of an electric motor.
Electromagnetic Induction – Electric Effects of Changing Magnetic Field
The phenomenon of electromagnetic induction is the production of induced current in a coil placed in a region where the magnetic field changes with time.
The magnetic field may change due to a relative motion between the coil and a magnet placed near to the coil.
If the coil is placed near to a current-carrying conductor, the
magnetic field may change either due to a change in the current through the conductor or due to the relative motion between the coil and conductor.
The direction of the induced current is given by the Fleming’s right-hand rule.
Fleming’s Right Hand Rule
A generator converts mechanical energy into electrical energy. It works on the basis of electromagnetic induction.
HouseHold Electric Circuits
In our houses we receive AC electric power of 220 V with a frequency of 50 Hz. One of the wires in this supply is with red insulation, called live wire.
The other one is of black insulation, which is a neutral wire. The potential difference between the two is 220 V.
The third is the earth wire that has green insulation and this is connected
to a metallic body deep inside earth. It is used as a safety measure to ensure that any leakage of current to a metallic body does not give any severe shock to a user.
Fuse is the most important safety device, used for protecting the circuits due to short-circuiting or overloading of the circuits.
Mind Map Overal Idea Content Speed Notes Quick Coverage Content Study Tools Content … Key Terms Topic Terminology Term: Important Tables Topic Terminology Term: Assessments Test Your Learning readmore
Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Cuboid What is a cuboid? Parts And Their Alignment Of A Cuboid Faces The flat surfaces of a cuboid are known as its faces. A cuboid has six faces, and… readmore
Mind Map
Overal Idea
Content
Speed Notes
Quick Coverage
Content : (Scroll down till end of the page)
Study Tools
Audio, Visual & Digital Content
Cuboid
What is a cuboid?
A cuboid is a three-dimensional geometric shape that resembles a rectangular box or a rectangular prism. A cuboid has 3 Pairs of opposite, congruent and parallel rectangular faces, 12 edges, and 8 vertices.
Note 1: All squares are rectangles.
Note 2: Cuboid may have one, or Three equal pairs of squares. (Square is a special type of Rectangle.
Note 3: If All three pairs of faces of a cuboid are squares then it it becomes a Cube.
Note 4: A cube is a special case of cuboid.
Parts And Their Alignment Of A Cuboid
Faces
The flat surfaces of a cuboid are known as its faces.
A cuboid has six faces, and each face is a rectangle.
These faces are arranged such that three pairs of opposite faces are parallel to each other.
The adjacent faces are perpendicular to each other (i.e., the angle between any two touching faces of a cube is right angle, 90°.
Note 1: All squares are rectangles.
Note 2: Rectangle may have one or two pairs of squares.
Note 3: If All three pairs of faces of a rectangle are squares then it it becomes a Cube.
Note 4: A cube is a special case of cuboid.
Edges
An edge is a line segment where the two surfaces of a cuboid meet.
There are 12 edges in a cuboid, where three edges meet at each vertex.
All edges form right angles with the adjacent edges and faces.
Vertices
A vertex is a point where the three edges meet. Vertices is the plural of vertex.
Cuboid has eight vertices.
Diagonals
Diagonal of a cuboid is a line segment that joins two opposite vertices.
The cuboid has four space diagonals.
Length of the diagonal of cuboid = √(length2 + breadth2 + height2) units.
Symmetry
Cuboids exhibit high symmetry.
They have rotational symmetry of order 4, meaning that you can rotate them by 90 degrees about their centre and they will look the same.
Features of a Cuboid
It is a three-dimensional, Rectangular figure.
It has 6 faces, 12 edges, and 8 vertices.
All 6 faces are rectangles.
Each vertex meets three faces and three edges.
The edges run parallel to those parallel to it.
All angles of a cuboid are right angles.
Mensuration of Cuboid
Surface Area of a Cuboid
The total surface area of a cuboid is defined as the area of its surface (Appearing face).
The Lateral Surface Area of a Cube.
Imagine yourself sitting in a cuboid shaped room. You can then see the four walls around you. This denotes the lateral surface area of that room.
That is, the lateral surface area of a cuboid shaped room is the area of its four walls, excluding the ceiling and the floor.
The lateral surface area of the cuboid is the sum of areas of its square faces, excluding the area of the top and the bottom face.
So the lateral surface area of a cube = sum of areas of 4 faces = (Length ✕ Height) + (Length ✕ Height) + (Length ✕ Height) + (Breadth ✕ Height) + (Breadth✕ Height)
Derivation of Total Surface Area of a Cuboid
Since the total surface area of a cuboid (TSA) is the area of its surface.
Total surface area of a cuboid = Lateral Surface Area + Area Of Bottom Surface + Area Of Top Surface
Total surface area of a cuboid = Area Of Front Surface + Area Of Back Surface + Area Of Left Srface + Area Of Right Surface + Area Of Bottom Surface + Area Of Top Surface
Total surface area of a cuboid = Lateral Surface Area 2[Area Of Bottom Surface]
Since Area Of Top Surface = + Area Of Bottom Surface We get, Total surface area of a cuboid = Lateral Surface Area + 2[Area Of Top Surface]
The volume of a three-dimensional object can be defined as the space required for it.
Similarly, Volume of a cuboid is defined as the space required for the cuboid or the Space occupied by the cuboid.
The volume of a cuboid can be calculated using the formula, V = lbh, where,
l = length, b = breadth or width, h = height
This formula shows that the volume of a cuboid is directly proportional to its length, breadth and height.
The volume is calculated by multiplying the object’s length, breadth, and height.
Hence the volume of the cube = lbh = lenth ✕ breadth ✕ height
Cuboids in Our Daily Life
Cuboids are commonly used in everyday objects, such as boxes, books, and building blocks.
They are used in architectural and engineering designs for modeling rooms, buildings, and structures.
In mathematics and geometry, cuboids serve as fundamental examples for teaching and understanding concepts related to three-dimensional shapes.
Similar Shapes:
A cube is a special type of cuboid where all sides are equal in length, making it a regular hexahedron.
Real-world Examples:
A shoebox is an example of a cuboid.
Most refrigerators, ovens, and TV screens have cuboidal shapes.
Buildings and houses often have cuboidal rooms.
Fun Fact:
Cuboids are among the simplest and most familiar three-dimensional shapes, making them a fundamental concept in geometry.
Remember that these notes provide an overview of cuboids, and there are more advanced topics and applications related to this shape in various fields of study.
What is a cube?
A cube is a three-dimensional regular polyhedron characterised by its 6 Identical (Congruent) Squares in which 3 Pairs of them parallel.
Parts And Their Alignment Of In A Cube
Faces
The flat surfaces of a cube are known as its faces.
A cube has six faces, and each face is a perfect square. These faces are arranged such that three pairs of faces are parallel to each other.
The adjacent faces are perpendicular to each other (the angle between any two touching faces of a cube is right angle, 90°.
All the edges have the same length.
A cube also has 8 vertices and 12 edges.
Edges
An edge is a line segment where the two surfaces of a cube meet.
There are twelve edges in a cube, where three edges meet at each vertex.
All edges have equal length and form right angles with the adjacent edges and faces.
Vertices
A vertex is a point where the three edges meet. Vertices is the plural of vertex.
Cube has eight vertices.
Diagonals
The cube has four space diagonals that connect opposite vertices, each of which has a length of √3 times the length of an edge.
Symmetry
Cubes exhibit high symmetry.
They have rotational symmetry of order 4, meaning that you can rotate them by 90 degrees about their centre and they will look the same.
Features of a Cube
It is a three-dimensional, square-shaped figure.
It has 6 faces, 12 edges, and 8 vertices.
All 6 faces are squares with equal area.
All sides have the same length.
Each vertex meets three faces and three edges.
The edges run parallel to those parallel to it.
All angles of a cube are right angles.
Mensuration of Cube
Surface Area of a Cube
The total surface area of a cube is defined as the area of its outer surface.
Derivation of Total Surface Area of a Cube
Since the total surface area of a cube is the area of its outer surface.
total surface area of a cube = 6 ✕ area of one face.
We know that the cube has six square faces and each of the square faces is of the same size, the total surface area of a cube = 6 ✕ area of one face.
Let the length of each edge is “s”.
Area of one square face = length of edge ✕ length of edge
Area of one square face == s ✕ s = s²
Therefore, the total surface area of the cube = 6s²
The total surface area of the cube will be equal to the sum of all six faces of the cube.
The Lateral Surface Area of a Cube.
Imagine yourself sitting in a cube shaped room. You can then see the four walls around you. This denotes the lateral surface area of that room.
That is, the lateral surface area of a cube shaped room is the area of its four walls, excluding the ceiling and the floor.
The lateral surface area of the cube is the sum of areas of its square faces, excluding the area of the top and the bottom face.
So the lateral surface area of a cube = sum of areas of 4 faces = 4a²
The Volume of a Cube
Volume
The volume of a three-dimensional object can be defined as the space required for it.
Similarly, Volume of a cube is defined as the space required for the cube or the Space occupied by the cube.
The volume of a cube can be calculated using the formula V = s3, where “s” represents the length of one side of the cube.
This formula shows that the volume of a cube is directly proportional to the cube of its side length.
The volume is calculated by multiplying the object’s length, breadth, and height. In the case of a cube shape, the length, width, and height are all of the same length. Let us refer to it as “s”.
Hence the volume of the cube is s ✕ s ✕ s = s³
Cubes in Our Daily Life
We encounter many cubes in our daily life such as Ice cubes, sugar cubes, dice and the building blocks used in games.
Cubes play a fundamental role in the study of geometry and serve as a basis for understanding three-dimensional space and concepts such as volume and surface area.
Also, Cubes have many applications in mathematics, engineering, architecture and art etc.
Study Tools
Audio, Visual & Digital Content
Cylinder is an important topic in Mathematics. It is a three-dimensional solid shape that has two parallel circular bases connected by a curved surface.
In this post, we will explore the properties of a cylinder and how to calculate its volume and surface area.
Let’s start with the basic definition of a right circular cylinder.
A cylinder is a solid shape that has two parallel circular bases of equal size and shape.
The curved surface that connects the two bases is called the lateral surface.
The axis of the cylinder is a line passing through the center of both bases.
Types Of Cylinders
(i). Solid Cylinder
(ii). Hollow Cylinder
Area Of A Solid Cylinder
Total Surface Area of Right Circular Cylinder = Curved Surface Area + Cicular Base Area + Circular Top Surface Area.
Since the Cicular Base Area And The Circular Top Surface Area of a cylinder are equal
Total Surface Area of Right Circular Cylinder = Curved Surface Area + 2(Cicular Top Surface Area)
Or
Total Surface Area of Right Circular Cylinder = Curved Surface Area + 2(Cicular Base Surface Area)
Therefore the formula to calculate the surface area of a cylinder is expressed as the following:
$$SA = 2\pi r h + 2\pi r^2$$
where SA is the surface area, r is the radius of the base, and h is the height of the cylinder.
Here, Curved Surface Area, $$CSA = 2\pi r h$$ and
Cicular Base Area = Top Surface Area = $$\pi r^2$$
Volume Of A Solid Cylinder
The formula to calculate the volume of a cylinder is given by:
$$V = \pi r^2 h$$
where V is the volume, r is the radius of the base, and h is the height of the cylinder.
Now let’s take an example to understand how to use these formulas. Suppose we have a cylinder with a radius of 4 cm and a height of 10 cm. To calculate its volume, we can use the formula:
$$V = \pi (4)^2 (10) = 160\pi$$
Therefore, the volume of the cylinder is 160π cubic cm.
To calculate its surface area, we can use the formula:
$$SA = 2\pi (4) (10) + 2\pi (4)^2 = 120\pi$$
Therefore, the surface area of the cylinder is 120π square cm.
In conclusion, understanding the properties of a cylinder and how to calculate its volume and surface area is important in CBSE Class 10 Mathematics. By using the formulas mentioned above, you can easily solve problems related to cylinders.
Hollow Cylinder
A hollow cylinder is a three-dimensional object with a circular base and a cylindrical shape. It is also known as a cylindrical shell. The cylinder has two circular faces and a curved surface. The thickness of the cylinder is uniform and it is hollow from inside.
Volume Of A Hollow Cylinder
The volume of a hollow cylinder can be calculated using the formula V = πh(R2-r2), where h is the height of the cylinder, R is the radius of the outer circle, and r is the radius of the inner circle.
Surface Area Of A Hollow Cylinder
The surface area of a hollow cylinder can be calculated using the formula A = 2πh(R+r), where h is the height of the cylinder, R is the radius of the outer circle, and r is the radius of the inner circle.
Hollow cylinders are used in various applications such as pipes, drums, and containers. They are also used in engineering structures such as bridges and towers.
In conclusion, a hollow cylinder is a useful shape in various fields and can be easily calculated using mathematical equations.
Cone
A cone is a three-dimensional geometric shape that has a circular base and a single vertex. It can be visualized as a pyramid with a circular base. In this note, we will cover the basic concepts and formulas related to cones.
Surface Area of a Cone
The surface area of a cone is the sum of the areas of its base and lateral surface. The formula to calculate the surface area of a cone is:
$$A = \pi r (r + l)$$
Where:
( A ) is the surface area of the cone
$$\pi = 3.14159$$
( r ) is the radius of the base of the cone
( l ) is the slant height of the cone
Volume of a Cone
The volume of a cone is the amount of space enclosed by it. The formula to calculate the volume of a cone is:
$$V = \frac{1}{3} \pi r^2 h$$
Where:
( V ) is the volume of the cone
( \pi ) is a mathematical constant approximately equal to 3.14159
( r ) is the radius of the base of the cone
( h ) is the height of the cone
Example Equations
Here are a few example equations related to cones:
Equation for calculating the slant height of a cone: $$l = \sqrt{r^2 + h^2}$$
Equation for calculating the radius of a cone given its slant height and height: $$r = \sqrt{l^2 – h^2}$$
Equation for calculating the height of a cone given its volume and radius: $$h = \frac{3V}{\pi r^2}$$
Sphere
Solid Sphere
Introduction – A solid sphere is a three-dimensional geometric figure in which all points inside the sphere are at the same distance from its center. – It is a type of 3D shape known as a “sphere” with a uniform density throughout.
Characteristics – The solid sphere has a well-defined volume, surface area, and mass. – It is completely filled with matter.
Volume of Solid Sphere The formula to calculate the volume (\(V_s\)) of a solid sphere is given by: \[ V_s = \frac{4}{3} \pi r^3 \] Where: \(V_s\) = Volume of the solid sphere, \(\pi\) (\(\pi\)) ≈ 3.14159, \(r\) = Radius of the sphere.
Surface Area of Solid Sphere The formula to calculate the surface area (\(A_s\)) of a solid sphere is given by: \[ A_s = 4 \pi r^2 \]
Where: \(A_s\) = Surface area of the solid sphere, \(\pi\) (\(\pi\)) ≈ 3.14159, \(r\) = Radius of the sphere
Mass of Solid Sphere The mass (\(m_s\)) of a solid sphere can be calculated using the formula: \[ m_s = \text{Density} \times V_s \] Where: \(m_s\) = Mass of the solid sphere, \(\text{Density}\) = Density of the material making up the sphere (usually in \(kg/m^3\)), \(V_s\) = Volume of the solid sphere (calculated using the previous formula)
Hollow Sphere
Introduction – A hollow sphere is also a three-dimensional geometric figure, but unlike a solid sphere, it has an empty space inside. – It consists of an outer shell or surface with a certain thickness and an inner empty region.
Characteristics – The hollow sphere has a well-defined outer radius (\(R\)), inner radius (\(r\)), volume, surface area, and mass. – It is partially filled with matter, mainly in the form of the outer shell.
Volume of Hollow Sphere The formula to calculate the volume (\(V_h\)) of a hollow sphere is given by: \[ V_h = \frac{4}{3} \pi (R^3 – r^3) \] Where: – \(V_h\) = Volume of the hollow sphere, \(\pi\) (\(\pi\)) ≈ 3.14159, \(R\) = Outer radius of the sphere, \(r\) = Inner radius of the sphere
Surface Area of Hollow Sphere The formula to calculate the surface area (\(A_h\)) of a hollow sphere is given by: \[ A_h = 4 \pi (R^2 – r^2) \] Where: \(A_h\) = Surface area of the hollow sphere, \(\pi\) (\(\pi\)) ≈ 3.14159, \(R\) = Outer radius of the sphere, \(r\) = Inner radius of the sphere
Mass of Hollow Sphere The mass (\(m_h\)) of a hollow sphere can be calculated using the formula: \[ m_h = \text{Density} \times V_h \] Where: \(m_h\) = Mass of the hollow sphere, \(\text{Density}\) = Density of the material making up the sphere (usually in \(kg/m^3\)), \(V_h\) = Volume of the hollow sphere (calculated using the previous formula)
Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Content … Key Terms Topic Terminology Term Important Tables Table: . Assessments Test Your Learning readmore
