This document summarizes key concepts in electricity and magnetism, mechanics, and waves and sound. It defines Coulomb's inverse square law, electric field intensity, electric potential, electric current, electric current density, Ohm's law, electric resistivity, conductivity, Kirchhoff's laws, and other important electrical concepts. It also outlines Newton's laws of motion, the law of universal gravitation, and defines gravitational field. Finally, it discusses types of motion, simple harmonic motion, defines key wave properties like period, frequency, and wavelength, and distinguishes between mechanical and non-mechanical waves.

1. COULOMB’S INVERSE SQUARE LAW
Figure:
Statement: “The magnitude of the electrostatic force of interaction betn
two point charges is
directly proportional to the scalar multiplication of the magnitudes of charges and
inversely proportional to the square of the distance between them.”
Math. Formula:
Fα q1q2/r2
F = kq1q2/r2
(where k= Coulomb’s constan
= 1/4πε0
= 8.98 x 109
Nm2C-2)
ε0 = 8.85x 10-12 farad/m
= 8.85x 10-12 C2N-1m-2
ELE. FIELD OR ELE. FIELD INTENSITY OR ELE. FIELD STRENGTH (E)
Defin
:“Ele. field or ele. field intensity is defined as the ele. force per unit charge.”
- The diren
of field is taken to be the diren
of the force it would exert on a +ve test charge.
- The ele. Field is radially outward from a +ve charge &radially in toward a –ve point charge.
Formula:
Ele. Field intensity (E) =
( )
( )
S. I. unit:
( )
( )
= NC-1
or
( )
( )
= Vm-1
[NC-1
= =
∙
∙
= ∙
= =Vm-1
]
ELE. POTENTIAL OR ELE. POTENTIAL DIFFERENCE
Defin
:“The work required to transfer a unit +ve charge from an infinite distance to a given point
against an ele. Field.”
Formula:
Ele. Potential =
( )
( )
S. I. unit:
Volt (V) =
( )
( )
= J∙C-1
ELE. CURRENT (I)
Defin
: “Ele. Current is defined as the rate at which charge flows through the cross section of a wire.”
Formula:
Ele. Current (I) =
( )
( )
S. I. unit:

2. Ampere (A) =
( )
( )
= C∙S-1
ELE. CURRENT DENSITY (J)
Defin
: “It is simply defined as the ele. Current (I) per unit cross sectional area (A).”
Formula:
Ele. Current density (J) =
. ( )
( )
S. I. unit:
Ampere/meter2
= A∙m-2
OHM’S LAW
Circuit diagram:
Statement: “Ohm’s law states that in certain physical circumstances (constant temp.) the ele.
Current flowing through the circuit is directly proportional to the potential difference &
inversely proportional to the impedence or resistance.”
Math. Formula:
I α V or V α I
V = RI (Where R = Resistance of conductor)
Graph:
Limitation: With changing temp. the ratio of V to I changes resulting in changing R.
ELE. RESISTIVITY (ρ)
Defin
:“The resistance of a material having unit length & unit cross sectional area is known as
resistivity of the material.”
or

3. “The inverse of the conductivity of the material is known as resistivity.”
Formula:
Resistivity (ρ) =
∙
[̣ ˙ ̣˙ Rα =ρ ]
or
Resistivity (ρ) = 1/conductivity (σ)
S. I. unit:
Ohm ∙ meter = Ω∙m
ELE.CONDUCTIVITY (σ)
Defin
: “It is the reciprocal of ele. resistivity& measures a material’s ability to conduct an ele.
current.”
Formula:
conductivity (σ) = 1/Resistivity (ρ)
S. I. unit:
∙
= (Ω∙m)-1 = Ʊ∙m-1 = mho∙m-1
JUNCTION
Defin
: “Junction is a circuit points at which currents divide.”
Figure :
LOOP
Defin
: “A closed circuit formed with conductors is known as a loop.”
Figure :
KIRCHHOFF’S 1ST
LAW OR KIRCHHOFF’S CURRENT LAW (KCL) OR KIRCHHOFF’S JUNCTION/NODAL
RULE
Statement: “The algebraic sum of currents in a network of conductors meeting at a junction (node)
is zero.”
or
“At any node (junction) in an ele. circuit, the sum of currents flowing into that node is
equal to the sum of currents flowing out of that node.”
Formula:
At any junction O
I1 - I2 + I3 - I4 - I5 = 0
SI = 0
KIRCHHOFF’S 2ND
LAW OR KIRCHHOFF’S VOLTAGE LAW (KVL) OR KIRCHHOFF’S LOOP RULE
Statement: “The algebraic sum of the product of the resistance of the conductors & the currents in
them in a closed loop is equal to the total emf available in that loop.”
or
“The sum of the emfs in any closed loop is equivalent to the sum of the potential
drops in that loop.”

4. or
“The directed sum of the ele. pote. diff.s (voltage) around any closed network is zero.”
Figure :
Formula:
-I1R1 + E1 + I2R2 - E2- I3R3 + I4R4 + I5R5= 0
-I1R1+ I2R2- I3R3 + I4R4 + I5R5 = - E1 + E2
SIR = SE
ELE. ENERGY (W) OR (E)
Defin
: “The work done by the battery to keep flow of charges continuously is known as ele. energy.”
Formula:
W = VQ [˙ ̣˙ V = W/Q ]
W = V It [ ˙ ̣˙ Q = It ]
W = IR It [ ˙ ̣˙ Ohm’s law, V = IR ]
Ele. energy W = I2
Rt (1)
Eqn
(1) is known as Joule’s law.
S. I. unit: Joule (J)
Other :-Ele. pote. energy is a pote. energy that results from conservative Coulomb forces and is
associated with the configuration of a particular set of point charges within a defined system .
- The term “Electric pote. energy” is used to describe the pote. energy in systems with time-
variant ele. fields, while the term “Electrostatic pote. energy” is used to describe the pote.
energy in the systems with time invariant electric fields.
ELE. POWER (P)
Defin
: “Ele. power is the rate at which ele. energy is transferred (converted to other forms) by an
ele.
circuit.”
or
“ Ele. power is the rate of energy consumption in an ele. circuit.”
or
“The ele. power (P) is equal to the energy consumption (E) divided by the consumption time
(t).
Formula:
Ele. Power (P) = Work done per unit time = =

5. P =
= I2
Rt/t
= I2
R
= IV [ ˙ ̣˙ Ohm’s law, IR = V ]
= V2
/R [ ˙ ̣˙ Ohm’s law, I = V/R ]
S. I. unit:
( )
( )
= Watt (W)
JOULE CONSTANT
- To convert heat energy and mechanical energy into eachother.
Formula:
W = JH W = Mechanical energy in Joule
H = Heat energy in Calorie
J = Joule constant
Where J is known as Joule’s constant.
It is also known as the mechanical equivalent of heat.
Application of Joule Heating :
1. Common application in fuse used in ele. circuit.
2. Ele. Iron, bread toaster, ele. kettle, ele. heater etc.
3. Producing light in incandescent bulb.
THERMO ELECTRIC EFFECT
THERMO ELE. SERIES
- The thermo ele. series is a set of elements that can be used to build thermocouples & which
participate in the Seeback effect & it’s inverse, the Peltier effect.
- As you move the two elements you are using closer in the table, the thermoele. Yield goes
down, as it does when you reduce the temp. difference.
- So the ele. production depends on, (1) Types of the metal used from thermo ele. series.
(2) Temp. diff. betn
junctions of the thermocouple.
SEEBECK EFFECT
- The Seebeck effect is the conversion of tem. differences directly into electricity & is named
after the BALTIC GERMAN PHYSICIST THOMAS JOHANN SEEBECK, who, in 1821, discovered
that a compass needle would be deflected by a closed loop formed by two different metals
joined in two places, with a temp. differencebetn
the junctions. This was a thermoele.
Circuit composed
FIGURE
of materials of different Seebeck co-efficient (P-doped & n-doped semiconductors),
configured as a thermoele. Generator. If the load resistor at the bottom is replaced with a
voltmeter the circuit then functions as a temp. sensing thermocouple because the metals

6. responded to the temp. difference in different ways, creating a current loop & a magnetic
field.
- Seebeck did not recognize ther was an ele. current involved, so he called the phenomenon
the “THERMOMAGNETIC EFFECT”.
- DANISH PHYSICIST HANS CHRISTIAN ORSTED rectified the mistake and coined the term
“THERMOELECTRICITY”.
Formula:
J = s(-VV + Eemf)where J = Ele. current density
s= Local conductivity
V = Local voltage
Eemf = -S∙VT where S = Seebeck co-efficient also known as thermopower, a
property of the local material.
VT= Temperature gradient
- Seebeck co-efficients generally vary as fn
of temp. , and depend strongly on the composition
of the conductor.
- For ordinary materials at room temp. , the Seebeck co-efficient may range in value from -
100mV/K to +1000mV/K.
PELTIER EFFECT
- The Peltier effect is the presence of heating or cooling at an electrified junction of two
different conductors and is named for FRENCH PHYSICIST JEAN CHARLES ATHANASE
PELTIER, who discovered it in 1834.
FIGURE
- When a current is made to flow through a junction betn
two conductors A & B, heat may be
generated (or removed) at the junction. The Peltier heat generated at the junction per unit
time,𝑄̇, is equal to
𝑄̇= (πA – πB)I Where πA andπB are the Peltier Co-efficient of conductor A & B
respectively and I is the electric current (from A to B).
- Note that the total heat generated at the junction is not determined by the Peltier effect
alone, as it may also be influenced by Joule heating & thermal gradient effects.
- The close relationship betn
Peltier&Seebeck effects can be seen in the direct connection betn
their co-efficients : π = T∙S
- A typical Peltier heat pump device involves multiple junctions in series, through which a
current is driven. Some of the junctions lose heat due to the Peltier effect, while others gain
heat. Thermoele. Heat pumps exploit this phenomenon, as dothermoele. Cooling devices
found in refrigerators.
THOMSON EFFECT

7. - In many materials, the Seebeck co-efficient is not constant in temperature, and so a spatial
gradient in temperature can result in a gradient in the Seebeck co-efficient. If a current is
driven through this gradient then a continuous version of the Peltier effect will occur.
- This Thomson effect was predicted & subsequently observed by LORD KELVIN in 1851. It
describes the heating or cooling of a current –carrying conductor with a temperature
gradient.
- If a current density J is passed through a homogeneous conductor, the Thomson effect
predicts a heat production rate 𝑞̇ per unit volume of :
𝑞̇= -κJ∙VT Where 𝑞̇ = Heat production rate
κ= Thomson co-efficient
J = Ele. current density
VT = Temp. gradient
- The Thomson co-efficient is related to the Seebeck co-efficient as
κ= T
This eqn
however neglects Joule heating, and ordinary thermal conductivity.
MECHANICS
NEWTON’S 1ST
LAW OF MOTION
Statement: “Every body continues its state of rest or of uniform motion in a straight line unless
compelled by some external force to act otherwise.”
(The mass of a body is defined as the quantity of matter contained in a body & is a
measure of the inertia of the body)
NEWTON’S 2ND
LAW OF MOTION
Statement: “The rate of change of momentum of a body is α the applied force & takes
place in the diren
in which the force acts.”
Formula: α F
( )
α F

8. m α F
m∙a α F
or
“ Whenthe body is acted upon by a force its resulting acceleration is α the force &
inverselyα the mass.”
Formula: a α
NEWTON’S 3RD
LAW OF MOTION
Statement: “This law states that to every action there is always an equal & opposite reaction.”
Formula: F = -F’
NEWTON’S LAW OF GRAVITATION
Statement: “Every particle of matter in this universe attracts every other other particle and this
force of attraction is directly α the product of their masses & inversely α the squares of
thedistancebetn
Them.
Formula: F α M1∙M2/r2
= GM1∙M2/r2
( Where G = Gravitational constant
= 6.67 x 10-11
N∙m2
/kg2
= 6.67 x 10-8
dyne∙cm2
/gm2
)
If we take mass of any object on Earth (M) as M1, mass of Earth (ME) as M2& Radius of Earth
(RE) as r
F = G M∙ME/RE
2
= Mg [ G
GRAVITATIONAL FIELD
Defin
: “The region round about a material body in which its gravitational attraction is experienced
by
others is called the gravitational field.”
WAVES & SOUND
THERE ARE MAINLY FIVE TYPES OF MOTION
(1) Rectilinear (motion in straight line)
(2) Curvilinear (motion in curve)
(3) Circular (motion in circular orbit)
(4) Simple harmonic motion (S.H.M.- to & from from its mean position)
(5) Random motion (movement of smoke in air)
HARMONNIC MOTION
Few examples of harmonic (oscillatory) motion are as under.
- Motion of simple pendulum bob
- Motion of sewing m/c needle
- Motion of piston in engine cylinder
- Motion of planets around the sun
SIMPLE HARMONIC MOTION (S.H.M.)

9. Defin
: “S. H. M. is a motion in which the acceleration of the body is directly α it’s displacement from
a
fixed point & is always directed towards the fixed point.”
WAVE
Defin
: “Wave is a disturbance propagating in a medium in which medium particles are in S.H.M..”
- Disturbance progresses but medium particles do not leave their position they execute
S.H.M. on their places.
TYPES OF WAVE (REGARDING TO MEDIUM)
Mechanical waves Non-mechanical waves
MECHANICAL WAVES
- These waves need elastic medium to propagate.
- The medium particles take part in propagation of wave.
- E.g. - wave in a string (Melde’s experiment)
- sound waves in air.
- sound waves in glass or water (liquid).
NON-MECHANICAL WAVES
- No need of medium is required for these waves.
SOME DEFIN
S ASSOCIATED WITH THE WAVE
PERIODIC TIME (T)
Defin
: “It is the time required to complete one vibration/cycle/wave.”
Formula: Periodic time T =
S. I. unit: Second
FREQUENCY (f OR n)
Defin
: “It is the number of vibration/cycles/waves performed by the particle in one second.”
Formula: Frequency f =
S. I. unit: Second-1
= Hertz
WAVELENGTH (l)
“ The distancebetn
two consecutive particles in the same phase is called wavelength.”
Formula: lα
S. I. unit: meter
- “For transverse wave wavelength is the distance betn
two consecutive crests or troughs.”
- “For longitudinal wave wavelength is the distance betn
two consecutive compressions or
rarefactions.”