KENDRIYA VIDYALAYA SANGATHAN
RAIPUR REGION
STUDY MODULES CLASS-XII
PHYSICS
2012-13
Symbols used in Physics
a acceleration (m/s2)
A Amplitude (m), Ampere (fundamental unit of current)
b y-intercept
B magnetic field strength (T = 104 G), Bulk Modulus (N/m2)
c speed of light (3 x 108 m/s), specific heat (J/(kg•K))
C Coulomb (unit of charge = A•s), center of curvature (m), Celcius (unit of Temperature), Capacitance (F)
cal calories (unit of heat energy = 4.186 J)
d distance (m), deci (prefix = 10-1)
dB decibels (unit of sound intensity)
e symbol for charge of an electron (1.6 x 10-19), efficiency (dimensionless)
eV electron-Volt (unit of energy = 1.6 x10-19 J)
E energy (J), electric field intensity (N/C)
f frequency (Hz = s-1), femto (prefix = 10-15), force of friction, focal length (m), final value (subscript)
F force (N), farad (unit of capacitance = A2•s4/(kg•m2), Farenheit (unit of Temperature)
g acceleration due to gravity (9.8 m/s2), gram (unit of mass)
G giga (prefix = 109) Universal Gravitational Constant (6.67 x 10-11 m3/(kg•s2)
h Planck’s constant (6.626 x 10-34 J•s), height (m)
H Henry (unit of inductance)
Hz Hertz (unit of frequency)
i current (A), initial value (subscript)
I moment of inertia (kg•m2), Luminous Intensity (W/m2)
J Joule (unit of energy / work), impulse (N•s)
k kilo (prefix = 103)spring constant (N/m = kg/s2), thermal conductivity (W/(m•K)), Boltzman constant (J/K)
kg kilogram (fundamental unit of mass)
K Kelvin (fundamental unit of temperature), kinetic energy (J)
l length (m)
L liter (unit of volume), latent heat (J/kg), angular momentum (J•s), inductance (H), latent heat (J/kg)
m mass (kg), meter (fundamental unit of distance), slope, milli (prefix = 10-3)
M mega (prefix = 106)
n nano (prefix = 10-9), index of refraction (dimensionless), number of moles
N Newton (unit of force), Normal Force (N), number of particles
NA Avogadro’s number (6.022 x 1023 particles / mole)
o subscript - initial
p momentum (N•s), pico (prefix = 10-12), proton
P power (W), pressure (N/m2, atm, mmHg, psi, Pa)
Pa Pascals (unit of pressure = N/m2)
q charge (C)
Q charge (C), Heat (J)
r radius (m)
R ideal gas constant (8.31 J/mol K), resistance (Ω)
rms root – mean – square
s seconds (fundamental unit of time)
S entropy (J/K)
t time (s)
T temperature (°C, K), period (s), tension (F), Tesla (unit of magnetic field)
u atomic mass unit (also amu, 1.6 x10-27 kg)
U potential energy (J)
v velocity or speed (m/s)
V Volt (unit of potential difference), Voltage or Potential Difference, volume (L or m3)
w weight (N)
W work (J), Watt (unit of power)
x distance – usually horizontal
X reactance – capacitive or inductive (Ω)
y distance – usually vertical
Y Young’s Modulus (N/m2)
z distance – usually 3rd dimension
Z impedance (Ω)
Greek Letters
α (alpha) - angular velocity (rad/s2), proportional symbol, temperature coefficient of linear expansion (K-1)
α – type of radiation
β (beta) – temperature of area expansion (K-1), type of radiation, electron
γ (gamma) – relativistic gamma factor (dimensionless), type of radiation
δ (delta)– instantaneous change
∆ (capital delta) – finite change
ε (epsilon) – electrical permittivity
θ (theta) – angle (rad or °)
κ (kappa) – dielectric constant (dimensionless)
λ (lambda) – wavelength (m), ), linear charge density (C/m)
µ (mu) – coefficient of friction (dimensionless), micro (prefix = 10-6), magnetic permeability
ν (nu) – frequency (Hz, s-1)
π (pi) – ratio of circumference to diameter (3.1416..)
ρ (rho) – density (kg /m3), resistivity (Ω•m)
σ (sigma) – surface charge density (C/m2), Stefan Boltzmann constant (5.6704 × 10-8 kg s-3 K-4)
∑ (capital sigma) – summation or sum of
τ (tau) – torque (N•m), time constant (s)
φ (phi) – angle (rad)
Φ (capital phi) – flux – either magnetic or electric
Ψ (psi) – wave function (dimensionless)
ω (omega) – angular velocity (rad/s)
Ω (capital omega) – Ohms (unit of resistance = V/A)
KENDRIYA VIDYALYA SANGATHAN
RAIPUR REGION
STUDY MATERIAL
FOR LOW ACHIEVERS
PHYSICS
CLASS XII
SESSION : 2012-13
GUIDANCE : KVS REGIONAL OFFICE
RAIPUR
Prepared By :
NAGENDRA SHARMA
PRINCIPAL
KENDRIYA VIDYALAYA AMBIKAPUR
IN CONSULTATION WITH PGTs
OF
KV AMBIKAPUR, KV KUSMUNDA, KV DURG &KV BILASPUR
CONTENTS
PART - I
Electrostatics* Unit – 1* Marks – 8* KV Ambikapur
1 (a) Electrostatic Charges
1 (b) Electrostatic Field
1 (c) Electrostatic Potential and Flux
1 (d) Capacitance
Current Electricity* Unit – 2* Marks – 7* KV Kusmunda
2 (a) Electric Current and Resistance
2 (b) Electric Measurement
Magnetic Effects of* Unit – 3* Marks – 8* KV Kusmunda
Current and Magnetism
3 (a) Magnetic Field Due to Current
3 (b) Forces on Charged Particles in Electric & Magnetic Fields
3 (c) Magnets and Earth’s Magnetism
Electromagnetic Induction* Unit – 4* Marks – 8* KV Ambikapur
& Alternating Currents
4 (a) Electromagnetic Induction
4 (b) Alternating Currents & Electrical Devices
Electromagnetic Waves* Unit – 5* Marks – 3* KV Ambikapur
5. Electromagnetic Waves 142 - 146
PART - II
Optics* Unit – 6* Marks – 14* KV Durg
6 (a) Reflection, Refraction & Dispersion of Light
6 (b) Optical Instruments
6 (c) Huyghens Principle and Interference
6 (d) Diffraction and Polarization
Dual Nature of Matter* Unit – 7* Marks – 4* KV Durg
7. Dual Nature of Matter and Radiation
Atoms and Nuclei* Unit – 8* Marks – 6* KV Bilaspur
8. Atoms and Nuclei
Electronic Devices* Unit – 9* Marks – 7* KV Bilaspur
9 (a) Conductors, Insulators and Semi-conductors
9 (b) Semi-conductor Devices
9 (c) Logic Gates
Communication Systems* Unit – 10* Marks – 5* KV Bilaspur
10 (a) Analog and Digital Communication
10 (b) Space Communication
1(a) ELECTROSTATC CHARGES
IMPORTANT CONCEPTS
1. Electrostatics (Static Electricity or Frictional Electricity): The branch of Physics, which deals with the study of electric charges at rest, the forces between the static charges, fields and potentials due to these charges is called Electrostatics or Static Electricity or Frictional Electricity.
2. Electrification: When certain pair of substances are rubbed together, they acquire a property of attracting small bits of paper, light feathers etc. towards them. The substances are said to have been electrified or charged and the process is known as electrification.
3. Electric Charge: Charge is something possessed by material object that makes it possible to exert electrical force and to respond to electrical force. Excess or deficiency of electron on a material object constitutes an electric charge.
4. Polarity of Charge: The property which differentiates the two kinds of charges is called the polarity of charge. When a body possesses no charge, it is said to be neutral. Conventionally two kinds of charges are said to be positive & negative.
5. Dielectrics: Insulating materials which transmit electric effects without conducting are known as dielectrics. Insulators are the materials which can not conduct electricity and are also called Dielectrics.
6. Conductor: A substance which can be used to carry or conduct electric charge from one place to the other is called a conductor.
7. Charging by Induction: In charging by induction, a charged body A imparts to another body B, some charge of opposite sign without any actual contact between A and B. Obviously, body A shall not lose any charge as it is not in contact with body B.
8. Quantization of Electric Charge: The property by virtue of which all free charges are integral multiple of a basic unit of charge represented by e is known as the quantization of electric charge, where e = 1.6×10−19coulombs.
Thus charge q of a body is always given by
q = ne
where n is any integer, positive or negative.
9. Conservation of Electric Charge: The property by virtue of which total charge of an isolated system always remains constant is known as the conservation of electric charge.
10. Additivity of Charge: This is a property by virtue of which total charge of a system is obtained by adding algebraically all the charges present anywhere on the system.
Charges adds up like real numbers i. e., they are Scalars more clearly if any system has n number of charges q1, q2, q3, qn then total charge of the system is
q = q1 + q2 + q3 + ...... qn
Proper sign have to be used while adding the charges for example if
q1 = +1C
q2 = -2C
q3 = +4C
then total charge of the system is
q = q1 + q2 + q3
q = (+1) + (-2) + (+4) C
q = (+3) C
11. Coulomb’s Law: The force of interaction between any two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The force acts always along the line joining the two charges.
Consider two point charges q1 and q2 at points with position vector r1 and r2 with respect to the origin
vector r21= r2 - r1 is the difference between r2 and r1 and the distance of separation r is the magnitude of vector r21.
Point wise it can be written as
r1 = position vector of charge q1 with respect to origin
r2 = position vector of charge q2 with respect to origin
r21 = vector from 1 to 2 (r2 - r1)
r12 = -r21 = vector from 2 to 1 (r1 - r2)
r = r12 = r21 = distance between 1 and 2.
Coulomb's law can then be expressed as
F21 = force on q2 due to q1
= K [(q1 q2) / r2] (r21/r) (2a)
F12 = force on q1 due to q2
= -F21 = K [(q1 q2) / r2] (r12/r)
(2b)
K = some position constant
From these two equation we see that electric forces exerted by two charges on each other are equal in magnitude but are opposite in direction
In above equation, we find a positive constant K and experimentally found value of K is
K = 8.98755 × 10 9 Nm2/C2
K ≅ 9 × 10 9 Nm2/C2
sometimes K is written as 1/4π ε0 where ε0 is the permittivity of the vacuum whose value is
K = 1/4πε0
(ε0 = 9 × 10 -12 C2/Nm2)
12. Unit of Charge: Unit charge in SI (i.e. one coulomb) is that charge which when placed in vacuum at a distance of one metre from an equal and similar charge would repel it with a force of 9 × 10 9 Newton.
13. Dielectric Constant: Dielectric constant of a medium is defined as the ratio of absolute electrical permittivity of the medium (ε) to the absolute permittivity of vacuum or free space (ε0).
Dielectric Constant, also called relative electrical permittivity of the medium and denoted by εr, is thus given by
εr = ε/ ε0
14. Principle of Superposition (Forces between Multiple Charges): Force on any charge due to a number of other charges at rest is the vector sum of all the forces on that charge due to other charges, taken one at a time. The forces due to individual charges are unaffected due to presence of other charges.
If a system of charges has n number of charges say q1, q2, ...... , qn, then total force on charge q1 according to principle of superposition is
F = F12 + F13 + ...... F1n
Where F12 is force on q1 due to q2 and F13 is force on q1 due to q3 and so on.
15. Charge Density: The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume per unit length, per unit area or per unit volume respectively.. It is measured in coulombs per metre (C/m), square metre (C/m²), or cubic metre (C/m³), respectively. Since there are positive as well as negative charges, the charge density can take on negative values. Like any density it can depend on position. It should not be confused with the charge carrier density. As related to chemistry, it can refer to the charge distribution over the volume of a particle, molecule, or atom. Therefore, a lithium cation will carry a higher charge density than a sodium cation due to its smaller ionic radius.
IMPORTANT FORMULAE, UNITS AND CONSTANTS
1. q = ne, where q is the amount of the charge, n is an integer and e is electronic charge. The constant e is given by: e = 1.6×10−19coulombs.
2. F = K [(q1 q2) / r2], where F is the force of interaction between q1 & q2 , the two point charges separated by a distance r in vacuum or free space. The constant K here is given by: K ≅ 9 × 10 9 Nm2/C2 in vacuum or free space.
3. The constant K above for any medium (other than vacuum or free space) is given by: K = 1/4πε, where ε is known as the absolute permittivity of that medium
4. εr = ε/ ε0, where εr is the relative permittivity or the dielectric constant of the medium, ε is the absolute permittivity of the medium and ε0 is the absolute permittivity of free space or vacuum. ε0 = 8.854 × 10 -12 C2/Nm2 ≅9 × 10 -12 C2/Nm2