PHYSICS

IMPORTANT FORMULAE
UNIT 1. ELECTROSTATICS
S. No. FORMULAE SYMBOLS APPLICATION

1. Q=+Ne Q = Charge, N = Number of Quantization of charges

Charge particle
2. Q2Q1 Q1, Q2 are point charges F= To find force between tow
F=k
r2 Force point charges
3. F=QE E = Electric field Relation between F and E

E=k
Q k = 41 , r= distance Electric field due to a
4. point charge.
r2 = Absolute permittivity
5. ds = small area To find electric flux

6. q = Electric Flux Gauss Theorem

=

7. V = potential difference To find the potential

W AB VA=Electric potentail at A difference using Work
V=V-V= VB=Electric potentail at B done from a point A to a
A B q q=charge point B
q
8. V=k Electric potential due
r to a point charge
r = distance
9. p = dipole moment Electric potential due
dipole

10. dV / dr=potential gradient Relation between electric

 field and potential

11. U = Potential Energy Potential energy of a

W = Work done system of two point
Charges
12. = linear charge density Filed intensity due to
infinitely long straight
R uniformly charged wire
13. a) outside the shell: r = radius of Gaussian Filed intensity du to
surface (outside the shell) uniformly charged
R=radius of shell spherical shell
b) on the shell:  =surface charge permittivity

d) inside the shell : E=0

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14.  E = Electric field Field intensity due to thin

E=
2 = electric permittivity infinite plane sheet of
charge

15. C=capacitance Capacity of isolated

r=radius of conductor spherical conductor
16. A = area of plates Capacitance of a parallel
d = distance between the plate capacitor
plates

17. Grouped capacitors: Cs= equivalent capacitance To calculate equivalent

a) In series. in series capacitance of a circuit
Cp=equivalent capacitance
in parallel
b) In parallel:
Cp=C1+C2+C3

18. U = Electrostatic energy Energy stored in a

v2 stored in capacitor capacitor

19. E = electric field strength Energy density of a

 parallel plate capacitor

20. V = Common potential To find Common

potential due to sharing of
charge

21. E1 - E2 Loss fo energy Loss of energy due sharing

charges

22. K=1+ K = dielectric constant Relation between

 = electric susceptibility dielectric constant &
electric susceptibility

23. t =thickness of slab Capacitance of parallel

C= d=distance between the plate capacitor with
plates conducting slab in
C0=capacitance between

24. K=dielectric constant Capacitance of parallel

C= plate capacitor with
dielectric slab in between
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25. l Values of Different quantities after Introducing dielectric slab between the plates
of the charged capacitor:

Description When Battery connected When Battery disconnected

Charge K Q0 Q0
Potential V0 V0/K
difference
Electric E0 E0/K
field
Capacitance KC0 KC0
Energy K times [Energy 1/K time [Energy
is supplied By battery used for Polarization
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Unit-2: CURRENT ELECTRICITY

S. No. FORMULAE SYMBOLS APPLICATION

I=current, Q=charged, t=time, To find the current in a
1. I= = e=charge of electron current carrying wire.
2. V=Potential difference, Relation between V
V = IR (Ohms law)
R=resistance and I

3. = neAVd Vd=Drift Velocity Relation between

(n = number density of A=area of cross section current and drift velocity
free electron)
4. R = Resistance, = Resistivity Relation between
R= = relaxation time, m= mass of (i) R and (ii) R and
electron relaxation time
5. e=charge of electron Relation for resistivity
= =conductance, and relaxation time

6. C=conducatine, =conductivity To find C and

C=

7. I j = current density, Relation between j with

J =A = neVd = conductivity Vd and j with E
j= E
8. Vd = mobility of electron To find from Vd
=

9. = temperature coefficient of Variation of P with
resistance temperature
10. T1 - T2 = temperature difference Formula for

11. Rs = R1 + R2 + R3 + .... Rs = equivalent resistance in Series combination

series combination

12. 1/Rp = 1/R1 + 1/R2 + 1/R3 +... Rp = equivalent resistance in Parallel combination
series combination

13. P = VI = I2 R=V2/R P = electrical power Relation for P with V, I and R

14. E = V +Ir = I (R + r) E = emf of cell, Relation for E and V

15. (I) V = E - lr r = internal resistance (I) Current is drawn

(ii) V = E + lr V = Potential difference (ii) cell is being charged

16. r = internal resistance To find internal resistance

R = External resistance by potentiometer

17. n = number of cells in series Current drawn when n cells

R = External resistance are connected in series
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18. m = number of cells in parallel Current drawn when n cells

are connected in parallel
19. m = number of rows For max. current the
n = number of cells in each row. external resistance must be
equal to the total internal
resistance
20. = 0 (loop rule) algebraic sum of charge Kirchhoff' s law
= 0 (junction rule) algebraic sum of potential
difference

21. P, Q, R, S are resistences in four Balanced condition of

arms of Wheatstone Bridge Wheatstone Bridge

22. S = Unknown resistance Working condition for

S=
R = Known resistance Wheatstone Bridge

23. V=KL V= Potential drop a wire Principle of Potentiometer

L= Balancing length Cell.
24. E1 and E2, emf of two cells Comparison of emf's of two
I1 and I2 balancing length cell.

Unit-3: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM

SL. No. FORMULAE SYMBOLS APPLICATIONS
1. Biot - Savart Law dB = magnetic field at a point at To find magnetic field at a
distance r due to a current element. point due to current element.
= permeability of free space To find magnetic field due to
I = current through wire
= angle between current element a straight conductor.
IdI and position vector r.

B= magnetic field due to a circular Magnetic field at centre, x = 0

2. B= coilof N turns at distance X from its
center.
a = Radius of coil

3. B = magnetic field magnetic field due to a

B= r = perpendicular straight conductor of infinite
distance from wire to length
point of observation.
4. Ampere's circuital magnetic field due to a
law = Line integral of solenoid B =
magnetic field in a closed path.

F = Force o
5. v V= velocity of charge particle
Force acting on a charge
particle in magnetic field.
q = charge of the particle
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6. Force on charged particle in

v Lorentz force
simultaneous Electric and
magnetic fields
7. F = Magnetic force on a current To find force acting on a
L carrying conductor of length I current carrying conductor
B = magnetic field. in a magnetic field.

8. = Force per unit length between Force per unit length

two parallel current carrying I1 between two parallel
and I2 r = distance between the current carrying
conductors. conductors.

9. = BINA Sin = torque experienced by a magnetic field due to a

current loop of area A in straight conductor of
magnetic field B infinite length
N = Number of turns of coil.
I = current

10. S= G S = shunt required, Conversion fo

G = Galvanometer Resistance, Galvanometer
= maximum current through into Ammeter.
galvanometer
(0-i) = range of ammeter
R = high resistance in series Conversion fo
11. R= -G Galvanometer
into Voltmeter.
v r = radius of circular path in To find the radius of
12. r=
magnetic field circular path of charged
particle moving
perpendicular to the
magnetic field.

13. =  = Cyclotron frequency To find the frequency

of cyclotron.
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Unit-4: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

S. No. FORMULAE SYMBOLS APPLICATION

1. =  = induced emf. Faraday's law of

electromagnetic
induction:
2. B = magnetic field Motional emf
v = velocity
I = metal rod of length
3. V = emf developed To find emf developed
between the ends of the rod. between the end of the rod
= angular velocity rotating in the magnetic field.
I = length of the rod
4. =LI = Magnetic flux Relation between and L
L = Self-inductance of the coil.
5. L = Self-inductance of the coil. To find self-induced emf
in a coil.
6. M12 =Coefficient of mutual Self-induced of a solenoid
inductance
dl2/dt=Rate of charge of
current in th secondary coil
7. = Realtive permeability Equation of a.c generator
= permeability of free space
n = no of turns of the solenoid
A = area of the solenoid
L = length of the solenoid

8. n = no of turns of the solenoid Equation of a. c generator

B = magnetic field
A = area of the solenoid
v = frequency of AC
9. U = Energy stored in inductor To find energy stored in the
inductor in its magnetic field.
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Unit-5: ELECTROMAGNETIC WAVES

S. No. FORMULAE SYMBOLS APPLICATION

c is the speed of To find speed of e.m.

1. electromagnetic wave in vacuum
wave in vacuum
permeability constant and
is the permittivity constant
2.  is the speed of To find speed of
 electromagnetic wave in electromagnetic wave in
material medium material medium

Laws at a glance:
1. (Gauss's Law for electricity)

2. (Gauss's Law for magnetism)

3. (Faraday's Law)

4. (Ampere - Maxwell Law)

Unit-6: RAY OPTICS

S.No. FORMULAE SYMBOLS APPLICATIONS

1. u - object distance To find focal length of
v - image distance, mirror
f - focal length of the mirror
2. m = magnification To find magnification
m=
m is negative for real images
and +ve for virtual images
3. A = Angle of prism To find refractive index
n2 = refractive index of prism
n1 = refractive index of medium
Dm = angle of minimum deviation.

4. R = Radius of curvature To find Rad. of

V = image distance, curvature of lens
u = object distance
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S. No. FORMULAE SYMBOL APPLICATION

n2 - n1 1 1
1
( )(R )
5. R1, R2 = Radius of curvature Lens makers formula
= f = focal length of the lens To find focal length of
f n1 1 R 2 n1, n2 = Refractive index of lens
medium 1 and respectively
6. f = effective focal legnth of To find effective focal
combination length of combination
f1, f2, f3 = focal length of each lens in of lenses
contact.
7. m: magnifying power of a compound To find magnifying
microscope power of a compound
f0 = focal length of objective
fe = focal length of eyepiece
L= Distance between objective
lens and eye lens

8. f0 m: magnifying power of a telescope To find magnifying

m f0 = focal length of objective power of a telescope
fe fe = focal length of eyepiece
 = angle subtended at the eye
by the image
 = angle subtended at the eye
by the object

WAVE OPTICS

S.No. FORMULAE SYMBOL APPLICATIONS

1. ip = relative refractive index of To find refractive index

the denser medium of the material
ip = polarizing angle.
2. I0 = intensity of light passing To find intensity of light
through the polarizer,
= angle between polarizer
and analyzer.

3.  = fringe width To find fringe width for

= wavelength of light interference fringes
D = distance between the slits
and the screen
d = distance between the lists
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4. = wavelength of light used, To find width of central

D = distance between the slits maxima for diffraction
and the screen fringes
w= width of central maxima in
diffraction
5. max = a + b)2 max = Max. intensity To find ratio of max. and
( min = Min. intensity
min (a - b)
2 min. intensity
a, b = respective amplitudes

UNIT 7: DUAL NATURE OF MATTER

S.No. FORMULAE SYMBOL APPLICATIONS

1. c E = energy of photon, To find the energy of photon

E=hv=h
 h = Plank's
constant, v = frequency
2. W0 = work function Relation between work
W0 = hv0 = hc/  v0 = threshold frequency function and V0, 
 = threshold wavelength
3. Kmax = 1 mv2 Kmax = Maximum kinetic energy Einstein's photoelectric
2 max
= hv - w0 of emitted electrons equation.
= h (v - v0) Vmax = maximum velocity
4. Kmax = 1
mv2 = eV e = charge of electron Relation between maximum
2 max 0 V0 = stopping potential kinetic energy and stopping
potential.

5.  = wave length of matter wave De Broglie wavelength for

h = Plank's constant matter wave.

6. E= kinetic energy Relation between and E, V

V = accelerating potential

7. V = accelerating potential De Broglie wavelegth for

electron
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UNIT 8 : ATOMS AND NUCLEI

S.No. FORMULAE SYMBOL APPLICATIONS

1. , z = Atomic number of To find the distance of closest

element. m = mass of electron, approach r0.
v = velocity of electron.

2. b = impact parameter To find the impact parameter

= scattering angle

3. = Radius of nth orbit Bohr's0 radius (Z =1, n =1) r0 =

0.53A
4. V = speed of an electron in nth , c = speed of light
orbit
5. En = Total energy of electron in En = - Total energy of
nth orbit. electron in nth orbit for
hydrogen.

6. k= , Z = Atomic number Kinetic energy of electron

of element Relation between K. E. and total
energy
En = Total Energy
7. Potential energy of electron
Relation between P.E. and total
energy
8. = Wavelength of emitted = Wave number
radiation. Lyman series : n1 = 1, n2 = 2,3,4..
R = Rydberg's constant Balmer series: n1 = 2, n2 = 3,4,5..
9. R = R0A1/3 R0= 1.2 x 10-15 m Relation between Radius of
nucleus and mass number

10. = Nuclear density, Relation between binding

m = average energy and mass defect.
mass of a nucleon.
11. EB = Binding Energy Relation between binding
m = mass defect energy and mass defect.
1 a.m.u. = 931.5 Mev
12. = Rate of dacay of radio Relation active decay law
active substances
= decay constant
13. N0 = Number of radioactive N = Number of active nuclei left
nuclei present initially after time t.
14. T1/2 = half life of a radioctive To find half life period
substance
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15. N0 = Number of radioactive Number of radioactive nuclei left

nuclei present initially in a sample after n half - lives.

16. R = activity of a radioactive Relation between R and

sample

17. = Mean life.

UNIT 9 : ELECTRONIC DEVICES

S.No. FORMULAE SYMBOL APPLICATIONS
1. ne = free electron density Intrinsic semiconductors
2. nh. = hole density p - type semiconductors
3. n - type semiconductors
4. ni = density of Intrinsic carriers Relation between charge
carriers
5. Ie = current through electrons Current through a
Ih = current though holes semiconductor
Vd = Derift velocity of electrons
Vh = Drift velocity of holes
6. Le = emitter current Relation between currents
Ib = Base current through the transistor
Ic = Collector current
7. Vce = Output Voltage Output voltage through
Vcc = Collector voltage transistor amplifier
IcRl = Potential drp through

( ∆∆ ) v
load resistance
α= Ie ce
Ic Ie = Emitter current Current gain of a CB transistor
8. Ib = Base current
Ic = Collector current
Vce Constant

9. β= (∆∆ ) v
Ic
Ib ce
Current gain of a CE transistor
Vce Constant
10. = CB current gain Relation between and
= CE current gain
11. Ri = Load resistance (Output) AC Voltage Gain
Ri = input resistance
12. AC Power Gain

( ∆v∆ )
13. be
Vbe = Base emitter Voltage Input Resistance
Ib
Vce Constant
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14.
( )
r0 = ∆v
∆ Ic
ce

b
Vce = Collector Emitter voltage Output Resistance

b Constant

UNIT 10 : COMMUNICATION SYSTEMS

S.No. FORMULAE SYMBOL APPLICATIONS
1. m = Modulation factor To find modulation index
= Am = Amplitude of
c modulating signal
Ac= Amplitude of carrier
wave
Amax - Amin Amax = Maximum To find modulation index
2. = x 100% amplitude
Amax + Amin
Amin = Minimum
amplitude

3. m (t) = AmSinmt m (t) = modulating signal Equation of modulating

signal

4. c (t) = AcSinct C (t) = carrier signal Equation of carrier signal

5. Cm (t) = Ac Cm (t) = AM wave Equation of AM wave

USB = Fc + fm USB = Upper side band To find upper and lower

6.
LSB = fc - fm LSB = Lower side band side frequencies

7. = band width To find band width

Length of dipole antenna To measure the lengthh of

8. dipole antenna

9. d = The range of TV To find range of antenna

transmission
R = Radius of earth

10. dm = Maximum line of LOS To find maximum line of

distance LOS distance