Download biology notes as a summary and more Cheat Sheet Biology in PDF only on Docsity!
UNIT – 1: FORCE, WORK, POWER AND ENERGY
CHAPTER-
FORCE
Topic-
Turning forces , Moment of force (Torque), Forces in
equilibrium
Revision Notes
Motion ¾ ¾ When a body changes its position with respect to time is considered to be in motion. ¾ ¾ Examples are translational, rotational, periodic and non-periodic. Translational Motion ¾ ¾ It is a motion in which all the particles of object move in a single direction and with same velocity. ¾ ¾ Examples a bus moving on a road, motion of rectangular block down on an inclined plane. Rotational Motion ¾ ¾ When a rigid body rotates about its centre of mass is called rotational motion. An object spinning about a fixed axis is said to be in rotational motion. ¾ ¾ Examples of rotational motion include a spinning top , motion of ceiling fan, motion of potter's wheel. Forces and its Types ¾ ¾ Force : A force is that physical cause which changes or tends to change the state of rest or motion or direction of a body. It can also change the shape or size of a body. ¾ ¾ The S.I. unit of force is Newton (N). It is a vector quantity. C.G.S unit is dyne and gravitational unit is gf or kgf. Where, 1 kgf = 9.8 N. ¾ ¾ Force can be classified into two broad categories: contact forces and non-contact forces. ¾ ¾ Contact force : A force that comes into play only when there is a direct contact between two objects is known as contact force. Pushing a car, kicking a ball, pulling an object etc. are the examples of contact force. ¾ ¾ Non-Contact force : A force that comes into play, even when there is no direct (physical) contact between the two objects is known as non-contact forces. Electrostatic, magnetic, gravitational and nuclear forces are examples of non-contact forces. Moment of Force (Torque)
¾ ¾ When forces changes the direction of motion and provide rotational effect in a body is called turning forces. Turning effect of a force acting on a body about an axis is called the moment of the force or torque. Torque is the measure of rotational tendency of a force.
¾ ¾ Torque is the product of force with the perpendicular distance of force from the point of rotation. ¾ ¾ Mathematically, ¾ ¾ Torque = Force × perpendicular distance from the axis of rotation. ¾ ¾ Torque is a vector quantity. Its S.I. unit is Newton metre (N-m). ¾ ¾ Couple : Two equal and opposite forces acting along parallel lines at different points of the body form a couple. The line along which the force acts is called line of action. Principle of Moments ¾ ¾ Principle of Moments : When an object is in equilibrium, then the sum of the anti-clockwise moments about a turning point must be equal to the sum of the clockwise moments.
Let the distance of the weight W 1 from the support be l 1 and the distance of weight W 2 from the support be l 2. Let the weight W 1 tries to rotate the scale in anti- clockwise direction. Then, Anti-clockwise moment = W 1 × l 1 And the weight W 2 tries to rotate the scale in clockwise direction. Then, Clockwise moment = W 2 × l 2 As the scale is in equilibrium, so Total anti-clockwise moment = Total clockwise moment W 1 × l 1 = W 2 × l 2 ¾ ¾ Positive moment: When couple of forces act and the rotates in an anticlockwise direction, the moment is said to be positive. ¾ ¾ Negative moment: When the couple of forces rotates in clockwise direction, the moment is considered to be negative.
Forces in Equilibrium ¾ ¾ When a number of forces acting on a body produces no change in its state of rest or of motion, the body is said to be in equilibrium. ¾ ¾ The condition for a body to be in translatory motion equilibrium is that net force acting on the body is zero. ¾ ¾ The condition for a body to be in rotational motion equilibrium is that net torque acting on the body is zero. ¾ ¾ The equilibrium of a body is of three types : (i) Stable equilibrium (ii) Neutral equilibrium. (iii) Unstable equilibrium. ¾ ¾ A body is said to be in stable equilibrium, if it has a tendency to return to its original position, after being slightly disturbed. ¾ ¾ A body is said to be in neutral equilibrium, if on being slightly disturbed, it continues to stay in equilibrium in its new position, in the same way as it was in its original position. ¾ ¾ A body is said to be in unstable equilibrium, if it has no tendency to come to its original position, after being slightly disturbed from that position. The necessary conditions for a body to be in equilibrium are : (i) The sum of all the forces acting on the body is zero. (ii) The algebraic sum of the moments of all the forces acting on the body about any arbitrary point is zero.
Mnemonics
Concept: Moment of force Mnemonics: Music was Played with a Flute and Drum. Interpretations: M : Moment of force P : Product of F : Force D : distance Moment of force = Force × distance
Examples
1. A body of mass 1.50 kg is dropped from the 2 nd^ floor of a building which is at a height of 12 m. What is the force acting on it during its fall? (g = 9.80 m/s^2 ) Ans. Force acting during its free fall is given by F = mg = 1.50 × 9.8 N = 14.7 N And this force is independent of the height of fall. 2. A uniform metre scale is kept in equilibrium when supported at the 60 cm mark and a mass M is suspended from the 90 cm mark as shown in the figure. State with reasons, whether the weight of the scale is greater than, less than or equal to the weight of mass M. Ans. 0 50 60 90 100
M ′ M Let the mass of the scale = M ′ Applying principle of moments, Anti-clockwise moment = clockwise moment ¾ ⇒¾ M ′ × (60 - 50) = M ×(90 - 60) ¾ ⇒¾ M ′ × 10 = M × 30 ¾ ⇒¾ M ′ = 3 M Hence, mass the scale is more than the mass suspended.
3. A force ‘F’ acts on a body such that line of action of force passes through the point of rotation of the body. Find the magnitude of moment of force. Ans. Here, force = F Perpendicular distance of force from point of rotation = 0 Moment of force = F × 0 = 0
Key Formula
¾ ¾ Principle of Moments : Anti-clockwise moment = Clockwise moment W 1 l 1 = W 2 l 2 ¾ ¾ Torque = Force × perpendicular distances from the axis of rotation
F r
Topic-
Centre of Gravity, Uniform Circular Motion
Concept covered: Centre of gravity, Uniform circular motion
Revision Notes
Centre of Gravity : ¾ ¾ Centre of gravity of a rigid body is a point at which the entire weight of the body acts and algebraic sum
of moments of weights of particles constituting the body is zero about this point. Its position depends on the distribution of mass. It may be within the body or
¾ ¾ If the angle between force and the displacement is acute, then work is said to be positive. ¾ ¾ If the angle between force and the displacement is 90° i.e., displacement is perpendicular to the force applied, work is said to be zero. ¾ ¾ If the angle between force and the displacement is obtuse, the work is said to be negative. ¾ ¾ When a coolie walks horizontally while carrying a load on his head, no work is done against the force of gravity. ¾ ¾ When a body rotates in a circular path, no work is done against the centripetal force, as force and displacement are normal to each other. ¾ ¾ Work done can be zero if : (i) force applied is zero i.e_._ , no force acts on the body. (ii) displacement of body is zero. (iii) angle between force and displacement is 90°. ¾ ¾ C.G.S. unit of energy or work is erg. 1 joule = 10^7 erg ¾ ¾ One joule of work is said to be done when a force of 1 Newton displaces a body through a distance of 1 metre in its own direction. ¾ ¾ 1 erg of work is said to be done when a force of 1 dyne displaces a body through a distance 1 cm in its own direction. Energy ¾ ¾ Energy is the capacity of a body to do work. Its S.I. unit is joule. ¾ ¾ One kilowatt hour (1 kWh) is the energy spent (or work done) by a source of power 1 kW in 1 hour. Different types of energy ¾ ¾ Energy exists in different forms like mechanical energy, chemical energy, nuclear energy, sound energy, light energy. ¾ ¾ Mechanical energy is of two types i.e.,
(i) Kinetic energy =
mv^2
(ii) Potential energy = mgh ¾ ¾ Kinetic energy is the energy possessed by a body by virtue of its motion. Examples include a moving train, a running boy, etc. ¾ ¾ Types of kinetic energy : (i) Translation kinetic energy (e.g., a car moving in straight path, a freely falling body posses translational kinetic energy) (ii) Rotational kinetic energy (e.g., a spinning top, a rotating fan posses rotational kinetic energy) (iii) Vibrational kinetic energy (e.g., a wire clamped at both the ends when struck in the middle vibrates, possessing vibrational kinetic energy)
¾ ¾ Derivation of expression of Kinetic energy, K =^1 2
mv^2
A body of mass ‘ m ’ moving with initial velocity ‘ v ’ is acted upon by a constant opposing force ‘ F ’ which produces retardation and the body is brought to rest. Force, F = mass × retardation …(i)
Using 2nd^ kinematic equation of motion, v^2 = u^2 + 2 as …(ii) Where, initial velocity, u = v Final velocity, v = 0 Acceleration, a = – a So, the equation (ii) becomes 02 = v^2 + 2 × (– a ) × s
s = v a
2 2
… (iii)
Kinetic energy will be equal to the amount of work the body does before coming to rest. Kinetic energy = F × s
= (^) ma × v a
2 2 [Using equation (i) and (iii)]
K =
mv^2
¾ ¾ Relation of Kinetic energy with momentum Momentum = P = mv Kinetic energy K^ =^12 mv^2
Or, K m vm
2 2 = 2
Or, K Pm
2 = 2
P^2 = 2 mK ¾ ¾ Potential energy is the energy possessed by a body by virtue of its position or configursation. ¾ ¾ Potential energy is of two types : (i) Elastic potential energy (ii) Gravitational potential energy ¾ ¾ Derivation of expression of potential energy, U = mgh Let a body of mass ‘ m ’ be lifted upwards to a height ‘ h ’ above the ground. Then, work done on the body against the force of gravity = force × displacement Force, F = mg Work done, W = mg × h This work done will be stored in the body in form of potential energy, U = mgh ¾ ¾ Law of conservation of energy : According to the law of conservation of energy, energy can neither be created nor be destroyed but it can be changed from one form to another. In a closed system, i.e., a system that is isolated from its surroundings, the total energy of the system is conserved. ¾ ¾ Work-energy theorem According to the work-energy theorem, the work done by a force on a moving body is equal to increase in its kinetic energy.
W = 1 2
mv^2 – 1 2
mu^2
Examples
1. A body of mass 0.2 kg falls from a height of 10 m to a height of 6 m above the ground. Find the loss in potential energy taking place in the body. ( g == 10 ms - -^2 ) Ans. Mass, m = 0.2 kg Initial height, h 1 = 10 m final height, h 2 = 6 m P.E. 1 = 0.2 × 10 × 10 = 20 J P.E. 2 = 0.2 × 10 × 6 = 12 J ∴ Loss in potential energy = (20 - 12) J = 8 J 2. A moving body weighing 400 N possesses 500 J of kinetic energy. Calculate the velocity with which the body is moving. ( g == 10 m/s^2 ) Ans. Weight of body = 400 N Let mass of body = m kg ⇒ mg = 400 ⇒ m × 10 = 400 ⇒ m = 40 kg Given, kinetic energy = 500 J Let its velocity be v m/s
∴ 1 2
mv^2 = 500 J
× 40 × v^2 = 500
⇒¾ v^2 = 500 20 ⇒¾ v^2 = 25 ⇒¾ v = 5 ms-^1
Mnemonics
Concepts: Positive, Negative and Zero work done. Mnemonics : Appu Planned On a Day to visit New Zealand. Interpretation : A : Acute P : Positive O : Obtuse N : Negative N : Ninety Z : Zero When angle between the force and displacement is acute , the work done is positive. When angle between the force and displacement is obtuse , the work done is negative. When angle between the force and displacement is ninety degree, the work done is zero.
Key Equations
¾ ¾ Work = Force × displacement (in the direction of force) ¾ ¾ Work = Fs cos θ ¾ ¾ Gravitational potential energy, P = mgh or Work done by the force of gravity = mgh ¾ ¾ Kinetic energy = 1 2
mv^2 ¾ ¾ 1 joule = 107 ergs ¾ ¾ 1 eV = 1.6 × 10 -^19 J ¾ ¾ p^2 = 2 mK Where, p = Momentum and K = Kinetic energy Work-energy theorem : W = 1 2
mv^2 – 1 2
mu^2
where, v = final velocity and u = initial velocity
Topic-
Power and Transformation of energy
Concepts covered: Power, Sources of energy, Conversion of energy
from one form to another
Revision Notes
Power ¾ ¾ Power is the rate of doing work. Its S.I. unit is Watt. ¾ ¾ 1 Watt = 1 Js-^1 ¾ ¾ If one Joule of work is done in 1 second, the power spent is said to be 1 Watt. ¾ ¾ 1 horse power = 746 Watts = 0.746 kW ¾ ¾ 1 kW = 1000 W, 1 MW = 106 W and 1 GW = 109 W ¾ ¾ The C.G.S unit of power is erg per second. ¾ ¾ 1 Watt = 1 J s -^1 = 107 erg s -^1
¾ ¾ Transformation of Energy Energy exists in different forms. The change of one from of energy into another form of energy is called transformation of energy. ¾ ¾ Solar energy is the energy radiated by the Sun. ¾ ¾ Solar panels, solar furnaces and solar cells use solar energy to do useful work. ¾ ¾ The energy released on burning coal, oil, wood or gas is the heat energy.
¾ The velocity ratio is also defined as the ratio of the displacement of effort to the displacement of load. ¾ Velocity ratio is a ratio. Hence, it has no unit. ¾ A machine in which there is no loss of energy is called an ideal machine. ¾ The efficiency of an ideal machine is 100% but in practice, it is not possible. ¾ No machine does work by itself. For an ideal machine, output = input. ¾ A machine is a device that makes work easier for us. It does so by enabling us to (i) multiply force
(ii) apply force at a convenient point or in a convenient direction and (iii) obtain gain in speed. ¾ The efficiency of a machine is the ratio of the useful work done by the machine (the output) to the total work done on the machine (input) Efficiency, η = output input
× 100%
¾ For a practical machine, Efficiency = Mechanical advantage Velocity ratio
Topic-
Pulley Systems
Concepts covered: Pulley, Block and Tackle
Revision Notes
¾ A pulley is simply a grooved wheel that is used along with a rope or a chain.
¾ A pulley which has its axis of rotation fixed in position is called a fixed pulley.
¾ For a pulley, mechanical advantage (^) = Load Effort
¾ For a single fixed pulley, ideal M.A. = 1 and V.R. = 1.
¾ A pulley whose axis of rotation is movable is called a movable pulley. A single movable pulley can act as a force multiplier.
¾ For a single movable pulley, ideal M.A. = 2 and V.R. = 2.
¾ We use single fixed pulley to change the direction of application of effort.
¾ A combination of pulleys enables us to multiply force by a factor that is dependent on the number of strands used to support the load.
¾ The block and tackle system of pulleys is made by having two blocks of pulleys in which the lower block is movable but the upper one is attached to a fixed support.
¾ When the weight of the lower movable block of pulley is negligible as compared to that of load and there is no friction, then M.A. = V.R. = n = number of strands of tackle supporting the load.
Example 1
A woman draws water from a well using a fixed pulley. The mass of the bucket and water together is 6 kg. The force applied by the woman is 70 N. Calculate the mechanical advantage. (take g = 10 ms -^2 ) [ICSE 2004] Ans. Given, Load, L = mg = 6 × 10 = 60 N Effort, E = 70 N Mechanical Advantage M.A. = Load Effort M.A = 60 70
Mnemonics
Key Equation
Mechanical advantage = Load Effort For single fixed pulley, M.A. = 1, V.R. = 1 For single movable pulley, M.A. = 2, V.R. = 2 For block and tackle system, M.A. = V.R. = n ( n = number of strands of tackle system supporting the load)
UNIT – 2: LIGHT
CHAPTER-
LIGHT
Topic-
Refraction of Light at Plane Surface and Total
Internal Reflection
Concepts covered: Refraction of light through a glass block and
a triangular prism, Total internal reflection
Revision Notes
¾ ¾ The speed of light in air/vacuum is 3 × 10^8 m/s. ¾ ¾ A medium is said to be optically denser if light slows down in it. ¾ ¾ A medium is said to be rarer if light speeds up in it. ¾ ¾ When a ray of light travels from a rarer medium to a denser medium, it bends towards the normal. ¾ ¾ When a ray of light travels from a denser medium to a rarer medium, it bends away from the normal. ¾ ¾ The conditions when light travelling from one medium to another goes undeviated : (i) Optical densities of both the media are the same. (ii) Angle of incidence is zero. i.e ., light falls normally on the surface. ¾ ¾ Refractive index has no unit. ¾ ¾ When light passes from one medium to another, its frequency does not change but wavelength, speed and direction changes. ¾ ¾ When light passes from rarer to denser medium, its wavelength decreases. ¾ ¾ When light passes from denser medium to rarer medium, its wavelength increases. ¾ ¾ In case of minimum deviation of light while passing through the prism, the refracted ray inside the prism is parallel to the base of the prism. ¾ ¾ Factors affecting the angle of deviation of light travelling through the prism are : (i) the angle of incidence. (ii) the material of the prism (i.e., refractive index). (iii) the angle of prism ( A ). (iv) the colour or wavelength (λ) of light used. ¾ ¾ Factors affecting lateral displacement of light passing through a rectangular glass block : (i) The thickness of glass block (ii) The angle of incidence (iii) The refractive index of the glass and (iv) the wavelength of light used. ¾ ¾ Cause of refraction is that light has different speeds in different media. ¾ ¾ The refractive index of a transparent medium is always greater than 1. ¾ ¾ Factors affecting refractive index of a medium : (i) Nature of medium (ii) Physical conditions such as temperature (iii) The colour or wavelength of light ¾ ¾ Speed of light in glass is 2 × 10^8 m/s and in water is 2.25 × 10^8 m/s. ¾ ¾ Refractive index of glass is 1.5, of water is 1.33 and of diamond is 2.41.
¾ ¾ Refraction of light through a rectangular glass block.
¾ ¾ Refraction of light through a glass prism
¾ ¾ Applications of refraction of light (a) Real and apparent depths of object in water
Key Terms
¾ ¾ Refraction : The change in direction of the path of light, when it passes from one transparent medium to another transparent medium is called refraction. It is a surface phenomenon. ¾ ¾ Denser medium : A medium is said to be optically denser if the speed of light in it decreases. ¾ ¾ Rarer medium : A medium is said to be optically rarer if the speed of light in it increases. ¾ ¾ Angle of incidence : It is the angle between incident ray and the normal to the surface at point of incidence. ¾ ¾ Angle of refraction : It is the angle between the refracted ray and the normal at the point of incidence. ¾ ¾ Laws of refraction : ¾ ¾ 1 st^ Law : The incident ray, the refracted ray and the normal at the point of incidence, all lie in the same plane. ¾ ¾ 2 nd^ Law : The ratio of the sine of the angle of incidence i to the sine of the angle of refraction r is constant for the pair of given media and for a monochromatic light. This constant is called refractive index. This law is also called Snell’s Law. ¾ ¾ Refractive index : The refractive index of the second medium with respect to the first medium is defined as the ratio of the sine of the angle of incidence in the first medium to the sine of the angle of refraction in the second medium. ¾ ¾ Lateral displacement : The distance between the incident ray extrapolated and the emergent ray when light travels through a rectangular glass slab is called lateral displacement. ¾ ¾ Angle of deviation : The angle between the emergent ray and the incident ray extrapolated when light passes through a prism is called angle of deviation.
¾ ¾ Frequency, f = Speed of light in medium, Wavelength of light in that med
v iium, λ ¾ ¾ Refractive index (or absolute refractive index), m = Speed of light in air, Speed of light in that medium,
c v ¾ ¾ Refractive index of second medium with respect to first medium = Absolute refractive index in medium 2, Absolute refracti
μ 2 vve index in medium 1, μ 1 ¾ ¾ A + d = i + e ,where A is angle of prism d is the angle of deviation, i is the angle of incidence and e is the angle of emergence ¾ ¾ m = (^) Apparent depthReal depth
¾ ¾ m =
sin C ,where^ C^ is the critical angle.
Mnemonics
Concept: Movement of light ray when refracted from rarer to denser medium. Mnemonics: Watch RD’s Movie ToNight. Interpretation: R : Rarer to D : Denser M : Moves T : Towards N : Normal
Topic-
Refraction Through a Lens
Concepts covered: Lenses (convex and concave)
Revision Notes
¾ ¾ A lens is a transparent refracting medium bounded by two surfaces, both of which are either spherical in shape or one is plane and other is spherical. A lens may be regarded as being made up of a set of prisms. (A lens is not made up of prisms.) ¾ ¾ There are mainly two types of lenses : (i) Convex or converging lens. (ii) Concave or diverging lens. ¾ ¾ Convex or converging lenses are thin at the edges and thick at the middle. ¾ ¾ Concave or diverging lenses are thick at the edges and thin at the middle. ¾ ¾ The principal axis of a lens is the line joining the centres of the two spheres of the two surfaces of which lens is a part. ¾ ¾ Optical centre of a thin lens is the point on the principal axis of the lens through which a ray of light passes undeviated.
¾ ¾ For a convex lens, the first focal point is a point F 1 on the principal axis of the lens such that the rays of light coming from it, become parallel to the principal axis of the lens after refraction from the lens.
¾ ¾ For a concave lens, first focal point is a point F 1 on the principal axis of the lens such that the incident rays of light appearing to meet at it, become parallel to the principal axis of the lens after refraction from the lens.
¾ ¾ For a convex lens, the second focal point is a point F 2 on the principal axis of the lens such that the rays of light incident parallel to the principal axis passes through it after refraction from the lens.
¾ ¾ For a concave lens, the second focal point is a point F 2 on the principal axis of the lens such that the rays of light incident parallel to the principal axis appear to be diverging from this point after refraction from the lens.
2
¾ ¾ A concave lens always produces a virtual, erect and diminished image of a real object. ¾ ¾ The power of a lens is the reciprocal of its focal length measured in metre. It is measured in units of dioptre (D). ¾ ¾ A convex lens of small focal length may be used as a simple magnifying glass or a reading lens. For this, the object is kept between the optical centre and the focus of the lens. When it is used in this manner, it is also known as a simple microscope. ¾ ¾ The magnification produced by a lens is the ratio of a size of the image produced by it to the size of the object. ¾ ¾ Refraction of an oblique parallel beam by a convex lens :
¾ ¾ Refraction of an oblique parallel beam by a concave lens :
¾ ¾ A convex lens is made up of a large number of prisms and a glass slab: A convex lens may be considered to be a combination of a large number of truncated prisms. The prisms in the upper half have their bases downwards and the prisms in the lower half have their bases upwards with continuously changing angle of each prism. The central part of the lens is like a glass slab. Rays of light passing through the prisms tend to deviate towards the base. The central rectangular glass slab allows the incident ray to pass undeviated.
¾ ¾ A concave lens is made up of a large number of prisms and a glass slab: A concave lens may be considered to be a combination of a large number of truncated prisms. The prisms in the upper half have their bases upwards and the prism in the lower half have their bases downwards with continuously changing angle of each prism. The central part is like a rectangular glass block. Rays of light passing through the prisms tend to deviate away from the base. The central rectangular glass slab allows the incident ray to pass undeviated.
¾ ¾ Focal Length of Lens: The distance between focus and optical centre of the lens is called focal length of a lens. ¾ ¾ Focal Plane: The plane passing through the focus and perpendicular to the principal axis is called Focal plane. ¾ ¾ Aperture: The effective diameter of the circular outline of a spherical lens is called its aperture. ¾ ¾ Centre of Curvature: Centre of curvature of a surface of a lens is the centre of the sphere of which lens is a part. A lens having two spherical surfaces has two centres of curvature. ¾ ¾ Radius of Curvature: Radius of curvature is the distance between the optical centre and centre of curvature. ¾ ¾ Sign Conventions : All distances are measured from the optical centre of the lens. Distances measured in the direction of the incident ray are taken as positive and opposite
to the direction of the incident ray are taken as negative. Distances measured upwards and perpendicular to principal axis are taken as positive, whereas distances measured downwards and perpendicular to principal axis are taken as negative. ¾ ¾ Lens formula 1 1 v u
− =^
f Where, u = Object distance (always negative) v = Image distance (may be positive or negative) f = Focal length (positive the for convex lens and negative for the concave lens) ¾ ¾ Lenses are used for eye defect correction, magnifying glass, telescope, camera.
Topic-
Spectrum
Concept covered: Electromagnetic spectrum, Dispersion
Revision Notes
¾ ¾ The phenomenon of splitting of white light by a prism into its constituent colours is known as dispersion. ¾ ¾ The band of colours seen on passing white light through a prism is called the spectrum. ¾ ¾ Cause of dispersion : ¾ ¾ The cause of dispersion is the change in speed of light with wavelength in dispersive medium. When white light enters the first surface of a prism, light of different colours due to their different speeds in the glass gets deviated toward the base of prism through different angles. ¾ ¾ Dispersion by a prism :
¾ ¾ The angle of deviation depends upon, (i) angle of incidence at first surface (ii) angle of prism (iii) refractive index of the material.
¾ ¾ Wavelengths and frequencies of different colours in white light :
Colour Wavelength range (nearly)^ Frequency range in 10 (^14) Hz
Violet Indigo Blue Green Yellow Orange Red
4000 Å to 4460 Å 4460 Å to 4640 Å 4640 Å to 5000 Å 5000 Å to 5780 Å 5780 Å to 5920 Å 5920 Å to 6200 Å 6200 Å to 8000 Å
¾ ¾ The complete electromagnetic spectrum in the increasing order of their wavelength (or decreasing order of their frequency ) is given below: (1) Gamma rays, (2) X-rays, (3) Ultraviolet rays, (4) Visible light, (5) infrared radiations, (6) Microwaves, and (7) Radio waves. Thus, infrared spectrum is the part of the spectrum just beyond the red end while the ultraviolet spectrum is the part of the spectrum just before the violet end.
Electromagnetic spectrum
Name of the wave Frequency in Hz Discoverer Source Method of detection Gamma rays above 3 × 1019 Paul Villard In cosmic rays, In radiations from radioactive substances.
By their large penetrating power
X-rays 3 × 1019 – 3 × 1016 Roentgen When highly energetic electrons are stopped by a heavy metal target of high melting point.
By the fluorescence produced on a zinc sulphide screen. The photographic film gets affected. Ultraviolet 3 × 1016 – 7.5 × 1014 Ritter Sunlight, arc-lamp or spark
By their chemical activity on dyes. Photographic plates get affected. It causes fluorescence. Visible light 7.5 × 1014 – 3.75 × 1014
Newton Sunlight, light from electric bulb, flame, white hot bodies.
Other objects can be seen in its presence.
Infrared waves 3.75 × 1014 - 3 × 1011 Herschel Lamp with thoriated filament, heated silicon carbide rod, red hot bodies
Heating effect is more. The mercury rises rapidly when a thermometer with the blackened bulb is kept in these radiations. Microwaves 3 × 1011 - 3 × 109 Hertz Electronic devices such as crystal oscillators
Oscillatory electrical circuit. Radio waves below 3 × 109 Maxwell predicted the existence of radio waves.
TV and radio transmitters
Aerials of radio and TV receiver.
Properties common to all electromagnetic spectrum : (i) The electromagnetic waves of the entire wavelength range do not require any material medium for their propagation. (ii) They all travel with the same speed in vacuum which is the same as the speed of light in vacuum i.e. , 3 × 108 m/s. (iii) They exhibit the properties of reflection and refraction. (iv) These waves are not deflected by the electric and magnetic fields. (v) These waves are transverse waves. Properties and uses of the electromagnetic spectrum : ¾¾ ¾¾ γγ -rays These rays are the most energetic electromagnetic waves of wavelength less than 0.001 nm. Properties of γ -rays are as follows : (i) They cause fluorescence when they strike on the fluorescent materials as zinc sulphide. (ii) They can easily penetrate through the thick metallic sheets. (iii) γ-rays can easily penetrate through the human body. Uses of γ -rays are as follows : (i) They are used in the treatment of cancer and tumours.
(ii) γ-rays are used to preserve the foodstuffs for a long time. (iii) It provides valuable information about the structure of the atomic nucleus. ¾ ¾ X-rays X-rays, discovered by German physicist W Roentgen, having a range of wavelength from 0.001 nm to 1 nm. They are produced when highly energetic cathode rays are stopped by a heavy metal target of high melting point. Properties of X-rays are as follows : (i) They have high penetrating power. (ii) They strongly affect the photographic plate. (iii) They cause fluorescence in certain material such as zinc sulphide, etc. Uses of X-ray are as follows : (i) For detection of fracture, foreign bodies like bullets, stone in a human body, etc. (ii) For detecting faults, cracks, flaws and holes in the final product of metals. (iii) For curing untraceable skin diseases and malignant growths. (iv) For investigation of the structure of crystals, arrangement of atoms, etc. ¾ ¾ Ultraviolet Radiation It was discovered by Ritter in 1801. They are produced by some special lamps and very hot bodies. Ultraviolet rays coming from the Sun are absorbed by the ozone
¾ ¾ The sound of frequencies lower than 20 Hz are known as infrasonic sounds or infrasound, which cannot be heard by human beings. It is generated during earthquake. ¾ ¾ Ultrasonic sound : The sounds of frequencies higher than 20000 Hz are called as ultrasonic sounds or ultrasound which cannot be heard by human beings. Dogs can hear ultrasonic sounds of frequency upto 50000 Hz. This is why dogs are used for detective work by the police. Monkeys, bats, cats, dolphins, leopard and tortoise can also hear ultrasonic sounds. Dolphins, tortoise and rats can also produce ultrasonic sounds as well as hear ultrasonic sound. ¾ ¾ Reflection of sound waves : The returning back of the sound wave on striking a surface such as wall, metal sheet, etc., is known as reflection of sound wave. It does not require a smooth and shining surface like mirror. The reflection of sound takes place in accordance with the same laws those governing the reflection of light. The condition for reflection of sound wave is that the size of the reflecting surface must be bigger than the wavelength of the sound wave. ¾ ¾ Echo : It is a reflection of sound, arriving at the listener sometime after the original sound. Basically, a reflected sound from an (distant) object is heard after the original sound has ‘‘died down.’’ e.g., The echoes are produced by the bottom of a well, by a building or by the walls of an enclosed room and an empty room. ¾ ¾ Bats and dolphins make use of the phenomenon of echoes in nature. ¾ ¾ Trawlerman makes use of echoes for finding the depth of ocean beds or for detecting submerged objects. ¾ ¾ RADAR and SONAR also make use of echoes for finding the position and distance of an enemy airplane, under water dangers. ¾ ¾ A tuning fork is made by shaping a metal piece in the form shown alongside. It enables us to produce a pure sound note. ¾ ¾ Conditions for formation of echo/hearing the echo distinctly : (i) The size of the obstacle/reflector must be large compared to the wavelength of the incident sound (for reflection of sound to take place). (ii) The distance between the source of sound and the reflector should be atleast 17 m ( so that the echo is heard distinctly after the original sound is over). (iii) The intensity or loudness of the sound should be sufficient for the reflected sound reaching the ear to be audible. The original sound should be of short duration. ¾ ¾ Echoes also find use in medical field for imaging of human organs (womb, liver, uterus). ¾ ¾ Echoes find application in SONAR (Sound navigation and ranging). In order to find the distance of obstacle from ship, waves are transmitted and then reflected waves are received by the receiver. Let the distance of the obstacle from source of sound be “ d ” then,
2 d = v × t Where, v is the velocity of ultrasonic waves in water and t is the time between sending and receiving of waves. ¾ ¾ The periodic vibrations of a body of decreasing amplitude in presence of a resistive force are called the damped vibrations. Examples : oscillations of simple pendulum in air. ¾ ¾ The periodic vibrations of a body of constant amplitude in the absence of any external force on it, are called the free vibrations. Examples : vibration in instruments like sitar, violin when they are plucked. ¾ ¾ The vibrations of a body which take place under the influence of an external periodic force acting on it are called the forced vibrations. ¾ ¾ The frequency of vibrations of a body executing forced vibrations equals to the frequency of the applied periodic force. Examples : vibrations produced in the diaphragm of microphone sound box with frequency matching the speech of speaker. ¾ ¾ Resonance is a special case of forced vibrations. When the frequency of an externally applied periodic force on a body is equal to its natural frequency, the body readily begins to vibrate with an increased amplitude. This phenomenon is known as resonance. The vibrations of large amplitude are called the resonant vibrations. For example, tuning of a radio is based on resonance. ¾ ¾ Condition for resonance : Resonance occurs only when the frequency of the applied force is exactly equal to the natural frequency of the vibrating body.
Example 1
Two pendulums C and D are suspended from a wire as shown in the figure given below. Pendulum C is made to oscillate by displacing it from its mean position. It is seen that D also starts oscillating.
C D
wire
(i) Name the type of oscillation, C will execute. (ii) Name the type of oscillation, D will execute. (iii) If the length of D is made equal to C, then what difference will you notice in the oscillations of D? (iv) What is the name of the phenomenon when the length of D is made equal to C? [ICSE 2019] Ans. (i) Free vibration / damped vibrations (ii) Forced vibrations (iii) D vibrates with the same amplitude as C or C and D vibrate with maximum amplitude alternately. (iv) Resonance. [ICSE Marking Scheme, 2019]
¾ ¾ Difference between the free and damped vibrations : S. No. Free vibrations Damped vibrations 1.
The amplitude of free vibrations remains constant and the vibrations continue forever.
There is no loss of energy in free vibrations.
No external force acts on the vibrating body. The vibrations are only under the restoring force. The frequency of vibrations is nearly equal to the natural frequency and it remains constant.
The amplitude of damped vibrations gradually decreases with time and ultimately the vibrations cease. In each vibration, there is some loss of energy in the form of heat. The frictional or damping force acts to oppose the motion.
The frequency of vibrations is less than the natural frequency.
¾ ¾ Difference between the free and forced vibrations : S. No. Free vibrations Forced vibrations 1.
The vibrations of a body in absence of any resistive force are called the free vibrations. The frequency of vibration depends on the shape and size of the body. The frequency of vibration remains constant.
The amplitude of vibration is constant.
The vibrations of a body in presence of an external periodic force are called the forced vibrations. The frequency of vibration is equal to the frequency of the applied force. The frequency of vibration changes with change in the frequency of the applied force. The amplitude of vibration depends on the frequency of applied force.
¾ ¾ Difference between the forced and resonant vibrations :
S. No. Forced vibrations Resonant vibrations 1.
The vibrations of a body under an external periodic force of frequency different than the natural frequency of the body are called the forced vibrations. The amplitude of vibration is usually small. The vibrations of the body are not in phase with the external periodic force. These vibrations last for a very small time after the periodic force has ceased to act.
The vibrations of a body under an external periodic force of frequency exactly equal to the natural frequency of the body are called the resonant vibrations. The amplitude of vibration is very large. The vibrations of the body are in phase with the external periodic force. These vibrations last for a long time after the periodic force has ceased to act.
Mnemonics
Concept: Relation of frequency and wavelength of sound with its velocity. v = fλ. Mnemonics: S eagull E gg is F amous in M alaysia and W ashington. Interpretation: S : Speed E : Equal to F : Frequency M : Multiplied by W : Wavelength
4. The sound level is low (between 10 dB and 30 dB).
The sound level is high (above 120 dB).
5. The wave form is regular. Example : The sound produced by the musical instruments.
The wave form is irregular. Example : The sound produced by an aeroplane, road roller, industrial machines, etc.
Mnemonics
Concepts: Characteristics of sound. Mnemonics: W e A re S et F ree T oday. Interpretation: W : Wavelength A : Amplitude S : Speed F : Frequency T : Time period
UNIT – 4: ELECTRICITY AND MAGNETISM
CHAPTER-
CURRENT ELECTRICITY
Topic-
Current, E.M.F., Resistance and Ohm’s Law
Concepts covered: Ohm's law, limitation of Ohm's law, factors
affecting resistances, combination of resistances, internal
resistance; EMF and potential difference, simple electrical
circuits
Revision Notes
¾ ¾ A sustained electric current flows through a conductor only when it is connected to a source of emf. ¾ ¾ The electric current, in a given conductor is simply the rate of flow of charge across its cross section. Thus, I = Q/t ¾ ¾ The unit of current is ampere (A). We have 1 A = 1 Coulomb per second = 1 Cs – ¾ ¾ The current, flowing through a wire, is said to be one ampere when one Coulomb of charge flows across its cross-section in one second. ¾ ¾ Potential is the electrical state of a conductor which determines the direction of flow of charge when two conductors are either kept in contact or joined by a metallic wire. The potential at a point is defined as the amount of work done in bringing a unit positive charge from infinity to that point. The potential difference (p.d.) between two points is simply the work done in transporting a positive charge of one Coulomb from the first point to the second point. W = QV ¾ ¾ The unit of potential difference is Volt ( V). We have 1 volt = 1 joule per Coulomb = 1 JC-1. The potential difference between two points equals one volt if the work done in transporting a charge of one coulomb between these points equals one joule.
¾ ¾ Electromotive Force: When no current is drawn from a cell, then the potential difference between the terminals of the cell is called electromotive force. It is denoted by e. Its unit is Volt (V). The electromotive force of a cell depends upon (i) the material of the electrodes. (ii) the electrolyte used in the cells. ¾ ¾ According to Ohm’s Law : The current flowing through a given conductor is directly proportional to the potential difference across its ends, provided the physical conditions of the conductor (e.g. , its length, its area of cross-section, its temperature, etc.) remain constant. The resistance of a conductor equals the ratio of the potential difference across its ends to the current flowing through it. Thus, the resistance of the conductor is numerically equal to the potential difference across its ends when unit current flows through it. R = V/I or V = IR or I = V/R
I ~ V characteristics for metallic conductors ¾ ¾ The obstruction offered to the flow of current by the conductor (or wire) is called its resistance. The unit of resistance is ohm (Ω). A conductor has a resistance of one ohm when a potential difference of one volt across its ends causes a current of one ampere to flow through it. ¾ ¾ The resistance associated with the electrolyte of a cell—within its electrodes—is known as the internal resistance of the cell. ¾ ¾ When a cell of emf e or E , and internal resistance r , is connected across an external resistance R , current flows through the circuit, which is given by I = E /( R + r ) and V = 'p.d.' across V = IR
Simple electrical circuits containing E, I, R and r ¾ ¾ The internal resistance of a cell depends on (i) the nature, concentration and temperature of its electrolyte. (ii) the surface area of the (‘dipped within the electrolyte’ part) electrodes. (iii) the distance between the electrodes. ¾ ¾ An increase in the surface area of the electrodes causes the internal resistance to decrease, whereas an increase in the distance between the electrodes causes the internal resistance to increase. Internal resistance decreases with increasing temperature or concentration of an electrolyte. ¾ ¾ Factors Affecting the Resistance of a Conductor The electrical resistance of a conductor depends on the following factors : (i) Length of the conductor : The resistance of a conductor R is directly proportional to its length l i.e., R ∝ l ∴ When the length of a wire is doubled or halved, then its resistance also gets doubled or halved respectively. (ii) Area of cross-section of the conductor : The resistance of a conductor R is inversely proportional to its area of cross-section A. i.e. , R A
∴ When the area of cross-section of wire is doubled, its resistance gets halved and if
area of cross-section of wire is halved, its resistance will get doubled. (iii) Nature of the material of the conductor : The resistance of a conductor depends on the nature of the material of which it is made of. Some materials have low resistance whereas others have high resistance. Temperature dependence of resistance for metallic conductors (iv) Effects of temperature : (a) Resistance of a conductor increases linearly with increase in temperature. (b) Resistance of a semiconductor decreases with increase in temperature.
(c) Resistance of insulators (non-conductor) decreases with increase in temperature. (d) Resistance of electrolytes decreases with increase in temperature. From the above relation (i) and (ii), we can write (^) R A
or (^) R l A
where,^ ρ^ is the constant of proportionality
called resistivity or specific resistance of the conductor. ¾ ¾ Ohmic and non-ohmic resistor : The conductor which obeys Ohm’s law is called ohmic resistor (or linear resistance), e.g. , Silver, nichrome, copper, iron, etc. The graph of V vs I is a straight line. The conductor which does not obey Ohm’s law is known as non-ohmic resistor for non-linear resistance) e.g. , Triode valve, junction diode, transistor, etc. The graph of V vs I is a curved line. Resistivities of substances at room temperature Substances r (Ω m ) CONDUCTORS Silver Copper Aluminium
1.47 × 10–
1.72 × 10–
2.75 × 10–
ALLOYS
Nichrome 100 × 10– SEMICONDUCTORS Pure Germanium Pore Silicon
INSULATORS
Glass Wood
1010 – 10^14
108 – 10^11
¾ ¾ Superconductor : It is a substance of zero resistance at a very low temperature. e.g. , Mercury, niobium, etc. ¾ ¾ Resistivity of a material is the resistance of a wire of that material of a unit length and unit area of cross section.
