30 S. No. Q = Charge, N = Number of Charge particle Q1, Q2 are point charges F= Force E = Electric field k = , r= distance ds = small area = Electric Flux = Absolute permittivity F = Q E FORMULAE SYMBOLS APPLICATION 1. ELECTROSTATICS GIST IMPORTANT FORMULAE Q = + N e Q 2 F = k 2 r Q 1 V = V - V = A B q W AB V = potential difference V =Electric potentail at A A V =Electric potentail at B B q=charge 1 4 1. 2. 3. 4. 5. 6. 7. Quantization of charges To find force between tow point charges Relation between F and E Electric field due to a point charge. To find electric flux Gauss Theorem To find the potential difference using Work done from a point A to a point B 8. 9. 10. 11. 12. 13. V = k q r r = distance Electric potential due to a point charge Electric potential due dipole Relation between electric field and potential Potential energy of a system of two point Charges Filed intensity due to infinitely long straight uniformly charged wire Filed intensity du to uniformly charged spherical shell p = dipole moment dV / dr=potential gradient U = Potential Energy W = Work done = linear charge density l r = radius of Gaussian surface (outside the shell) R=radius of shell s =surface charge permittivity a) outside the shell: b) on the shell: d) inside the shell : E=0 E = k 2 r Q PHYSICS = q E R s Downloaded from www.studiestoday.com Downloaded from www.studiestoday.com
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Downloaded from Cla… · 12. 13. V = k q r r = distance Electric potential due to a point charge Electric potential due dipole Relation between electric field and potential Potential
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30
S. No.
Q = Charge, N = Number ofCharge particle
Q1, Q2 are point charges F=Force
E = Electric field
k = , r= distance
ds = small area
= Electric Flux
= Absolute permittivity
F = Q E
FORMULAE SYMBOLS APPLICATION
1. ELECTROSTATICS GISTIMPORTANT FORMULAE
Q = + N e
Q2F = k2r
Q1
V = V - V =A B qWAB
V = potential difference V =Electric potentail at AA
V =Electric potentail at BB
q=charge
14
1.
2.
3.
4.
5.
6.
7.
Quantization of charges
To find force between towpoint charges Relation between F and E
Electric field due to apoint charge.
To find electric flux
Gauss Theorem
To find the potential difference using Workdone from a point A to apoint B
8.
9.
10.
11.
12.
13.
V = k qr
r = distance
Electric potential due to a point charge
Electric potential due dipole
Relation between electricfield and potential
Potential energy of a system of two point Charges
Filed intensity due to infinitely long straightuniformly charged wire
Filed intensity du touniformly chargedspherical shell
p = dipole moment
dV / dr=potential gradient
U = Potential EnergyW = Work done
= linear charge density l
r = radius of Gaussiansurface (outside the shell)R=radius of shells =surface charge permittivity
Capacitance of parallelplate capacitor withconducting slab in between
Capacitance of parallelplate capacitor withdielectric slab in between
U = Electrostatic energystored in capacitor
E = electric field strength
V = Common potential
E - E Loss fo energy 1 2
K = dielectric constant c = electric susceptibility
t =thickness of slabd=distance between theplatesC =capacitance 0
K=dielectric constant
Grouped capacitors: a) In series.
b) In parallel: C =C +C +Cp 1 2 3
cK = 1 +
C =
C =
E = Electric field = electric permittivity
Field intensity due to thininfinite plane sheet of charge
E = 2s
2v
e0
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25. l Values of Different quantities after Introducing dielectric slab between the plates of the charged capacitor :
Description
Charge
Potential difference
Electric field
Capacitance
Energy
When Battery connected
K Q0
V0
E0
KC0
When Battery disconnected
Q0
V /K0
E /K0
KC0
K times [Energy
is supplied By battery
1/K time [Energy
used for Polarization
PHYSICSPHYSICS
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S. No. FORMULAE SYMBOLS APPLICATION
(I) V = E - lr
(ii) V = E + lrr = internal resistance
V = Potential difference
(I) Current is drawn
(ii) cell is being charged15.
I=current, Q=charged, t=time,e=charge of electron
V=Potential difference,R=resistance
V =Drift Velocityd
A=area of cross section
R = Resistance , = Resistivity = relaxation time, m= mass of electron
C=conducatine, =conductivity
j = current density, = conductivity
mobility of electron
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
To find the current in acurrent carrying wire.
Relation between V and I
Relation between current and drift velocity
Relation for resistivity and relaxation time
To find C and
Relation between j with V and j with E d
To find from Vd
Variation of P with temperature
Formula for
Series combination
Parallel combination
Relation for P with V, I and R
Relation for E and V
Unit-2 : CURRENT ELECTRICITY
V = IR (Ohms law)
I= neAVd
(n = number density of free electron)
I = =
Relation between (i) R and (ii) R and relaxation time
R =
= e=charge of electron =conductance,
C =
J = = neVd
j = E
IA
= =
T - T = temperature difference 1 2
R = equivalent resistance in s
series combination
= temperature coefficient ofresistance
R = R + R + R + ....s 1 2 3
R = equivalent resistance in p
series combination
P = electrical power
E = emf of cell,
1/R = 1/R + 1/R + 1/R +...p 1 2 3
2 2P = VI = I R=V /R
E = V +Ir = I (R + r)
16.
17.
To find internal resistance by potentiometer
Current drawn when n cellsare connected in series
r = internal resistance R = External resistance
n = number of cells in seriesR = External resistance
PHYSICSPHYSICS
Vd
E
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v
algebraic sum of charge algebraic sum of potentialdifference
P, Q, R, S are resistences in fourarms of Wheatstone Bridge
S = Unknown resistance R = Known resistance
V= Potential drop a wireL= Balancing length
E and E , emf of two cells1 2
I and I balancing length 1 2
20.
21.
22.
23.
24.
Kirchhoff' s law
Balanced condition of Wheatstone Bridge
Working condition for Wheatstone Bridge
Principle of Potentiometer Cell.
Comparison of emf's of two cell.
= 0 (loop rule) = 0 (junction rule)
S =
V = K L
19. For max. current theexternal resistance must be equal to the total internal resistance
m = number of rowsn = number of cells in each row.
18. Current drawn when n cellsare connected in parallel
m = number of cells in parallel
Unit-3 : MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
SL. No.
1.
2.
3.
4.
5.
APPLICATIONS
To find magnetic field at apoint due to current element.To find magnetic field due toa straight conductor.
Magnetic field at centre, x = 0
magnetic field due to a straight conductor of infinite length
Force acting on a chargeparticle in magnetic field.
FORMULAE
Biot - Savart Law
SYMBOLS
B= magnetic field due to a circular coilof N turns at distance X from its center.a = Radius of coil
B = magnetic field r = perpendicular distance from wire to point of observation.
= Line integral of magnetic field in a closed path.
F = Force oV= velocity of charge particle q = charge of the particle
dB = magnetic field at a point at distance r due to a current element. = permeability of free spaceI = current through wire = angle between current element IdI and position vector r.
B=
B=
Ampere's circuitallaw
magnetic field due to a solenoid B =
PHYSICSPHYSICS
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6.
7.
Lorentz force
To find force acting on acurrent carrying conductor in a magnetic field.
Force on charged particle insimultaneous Electric and magnetic fields
F = Magnetic force on a current carrying conductor of length IB = magnetic field.
9.
10.
11.
12.
13.
magnetic field due to a straight conductor of infinite length
Conversion fo Galvanometerinto Ammeter.
Conversion fo Galvanometerinto Voltmeter.
To find the radius of circular path of chargedparticle moving perpendicular to themagnetic field.
To find the frequency of cyclotron.
= torque experienced by a current loop of area A in magnetic field B N = Number of turns of coil. I = current
R = high resistance in series
r = radius of circular path in magnetic field
n = Cyclotron frequency
= BINA Sin
S = shunt required, G = Galvanometer Resistance, = maximum current throughgalvanometer(0-i) = range of ammeter
S = G
R = - G
r =
u =
8. Force per unit length between two parallel current carrying conductors.
= Force per unit length betweentwo parallel current carrying I 1
and I r = distance between the2
conductors.
PHYSICSPHYSICS
v
v
L
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S. No. FORMULAE SYMBOLS APPLICATION
Unit-4 : ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT
1.
2.
3.
4.
5.
6.
Faraday's law of electromagneticinduction :
Motional emf
To find emf developed between the end of the rod rotating in the magnetic field.
Relation between and L
To find self-induced emf in a coil.
Self-induced of a solenoid
e = induced emf.
B = magnetic fieldv = velocityI = metal rod of length
V = emf developed between the ends of the rod. = angular velocityI = length of the rod
e =
= Magnetic fluxL = Self-inductance of the coil.
= L I
M =Coefficient of mutual12
inductance
dl /dt=Rate of charge of 2
current in th secondary coil
L = Self-inductance of the coil.
n = no of turns of the solenoid B = magnetic fieldA = area of the solenoidv = frequency of AC
9. To find energy stored in the inductor in its magnetic field.
Equation of a. c generator
U = Energy stored in inductor
8.
7. Equation of a.c generator = Realtive permeability = permeability of free spacen = no of turns of the solenoidA = area of the solenoidL = length of the solenoid
PHYSICSPHYSICS
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S. No. FORMULAE SYMBOLS APPLICATION
Unit-5 : ELECTROMAGNETIC WAVES
1.
2.
c is the speed of electromagneticwave in vacuumpermeability constant and is the permittivity constant
n is the speed of electromagnetic wave inmaterial medium
To find speed of e.m. wave in vacuum
To find speed of electromagnetic wave in material medium
Laws at a glance :
(Gauss's Law for electricity)
(Gauss's Law for magnetism)
(Faraday's Law)
(Ampere - Maxwell Law)
1.
2.
3.
4.
Unit-6 : RAY OPTICS
S.No.
1.
2.
3.
4.
APPLICATIONS FORMULAE SYMBOLS
u - object distance v - image distance,f - focal length of the mirror
m = magnificationm is negative for real images and +ve for virtual images
A = Angle of prismn = refractive index of prism2
n = refractive index of medium1
D = angle of minimum deviation.m
R = Radius of curvature V = image distance, u = object distance
To find focal length of mirror
To find magnification
To find refractive index
To find Rad. ofcurvature of lens
m =
PHYSICSPHYSICS
n
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38
S. No. FORMULAE SYMBOL APPLICATION
S.No. APPLICATIONS FORMULAE SYMBOL
5.
6.
7.
8.
R , R = Radius of curvature1 2
f = focal length of the lensn , n = Refractive index of 1 2
medium 1 and respectively
f = effective focal legnth of combination f , f , f = focal length of each lens in 1 2 3
contact.
m: magnifying power of a compoundmicroscope f = focal length of objective 0
f = focal length of eyepiecee
m: magnifying power of a telescopef = focal length of objective 0
f = focal length of eyepiecee
b = angle subtended at the eye by the imagea = angle subtended at the eye by the object
Lens makers formulaTo find focal length of lens
To find effective focallength of combinationof lenses
To find magnifying power of a compound
To find magnifying power of a telescope
WAVE OPTICS
1.
2.
3.
To find refractive index of the material
To find intensity of light
To find fringe width forinterference fringes
b = fringe width = wavelength of lightD = distance between the slits and the screend = distance between the lists
Y
I = intensity of light passing 0
through the polarizer, = angle between polarizer and analyzer.
= relative refractive index of the denser medium = polarizing angle.
PHYSICSPHYSICS
1f
���n -�n2� 1
������n1
������1�����1������R ����R1 2
=(�������������) (�������������)
f0
fe
m
ip
ip
L= Distance between objective lens and eye lens
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39
S.No. APPLICATIONS FORMULAE SYMBOL
4.
5. Imax = Max. intensityImin = Min. intensitya, b = respective amplitudes
To find width of central maxima for diffractionfringes
To find ratio of max. and min. intensity
= wavelength of light used, D = distance between the slits and the screenw= width of central maxima in diffraction
Y
2(a + b)2(a - b)
=ImaxImin
UNIT 7 : DUAL NATURE OF MATTER
1.
2.
3.
4.
5.
6.
7.
E = energy of photon, h = Plank'sconstant, v = frequency
W = work function0
v = threshold frequency0
= threshold wavelength
K Maximum kinetic energy max =
of emitted electronsV = maximum velocity max
e = charge of electronV = stopping potential0
= wave length of matter waveh = Plank's constant
E= kinetic energyV = accelerating potential
V = accelerating potential
To find the energy of photon
Relation between work function and V , 0
Einstein's photoelectric equation.
Relation between maximumkinetic energy and stopping potential.
De Broglie wavelength formatter wave.
Relation between and E, V
De Broglie wavelegth for electron
E = h v = hcl
W = hv = hc/0 0 l0
PHYSICSPHYSICS
Kmax2= mvmax
= hv - w0
= h (v - v )0
12
12= mKmax
2v max eV0=
l0
l
l0
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40
S.No. APPLICATIONS FORMULAE SYMBOL
UNIT 8 : ATOMS AND NUCLEI
2.
3.
4.
5.
6.
7.
8.
thV = speed of an electron in norbit
To find the impact parameter
Bohr's radius (Z =1, n =1) r =000.53A
, c = speed of light
th= Radius of n orbit
b = impact parameter = scattering angle
1. To find the distance of closestapproach r .0
, z = Atomic number ofelement. m = mass of electron,v = velocity of electron.
E = Total energy of electron inn
thn orbit.
En = - Total energy of electron in nth orbit forhydrogen.
Kinetic energy of electronRelation between K. E. and totalenergy
Potential energy of electronRelation between P.E. and total energy
k = , Z = Atomic number of element
= Wavelength of emittedradiation.R = Rydberg's constant
= Wave numberLyman series : n = 1, n = 2,3,4..1 2
Balmer series: n = 2, n = 3,4,5..1 2
9.
10.
11.
12.
13.
14.
-15R = 1.2 x 10 m0 Relation between Radius of nucleus and mass number
Relation between binding energy and mass defect.
Relation between binding energy and mass defect.
Relation active decay law
N = Number of active nuclei leftafter time t.
To find half life period
1/3R = R A0
E = Binding EnergyB
m = mass defect1 a.m.u. = 931.5 Mev
N = Number of radioactive0
nuclei present initially
T = half life of a radioctive1/2
substance
= Nuclear density, m = averagemass of a nucleon.
= Rate of dacay of radioactive substances = decay constant
PHYSICSPHYSICS
E = Total Energyn
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15.
16.
17.
Number of radioactive nuclei leftin a sample after n half - lives.
N0 = Number of radioactive nuclei present initially
R = activity of a radioactive sample
Relation between R and
= Mean life.
S.No.
1.
2.
3.
4.
5.
6.
7.
APPLICATIONS FORMULAE SYMBOL
n = free electron density e
n = hole density h.
Intrinsic semiconductors
p - type semiconductors
n - type semiconductors
Relation between charge carriers
Current through a semiconductor
Relation between currents
through the transistor
Output voltage through
transistor amplifier
UNIT 9 : ELECTRONIC DEVICES
n = density of Intrinsic carriers i
I = current through electronse
I = current though holesh
V = Derift velocity of electronsd
V = Drift velocity of holes h
L = emitter currente
I = Base currentb
I = Collector current c
V = Output Voltagece
Vc = Collector voltagec
I R = Potential drp through c l
load resistance
8.Current gain of a CB transistor Ie = Emitter current
Ib = Base currentIc = Collector current
Input Resistance V = Base emitter Voltage be
9.
10.
11.
12.
13.
Current gain of a CE transistor
AC Voltage GainR = Load resistance (Output)i
R = input resistancei
AC Power Gain
= CB current gain = CE current gain
Relation between and
V Constant ce
PHYSICSPHYSICS
∆ cI
∆ eIα = vce(���)
∆ cI
∆ bIβ = vce(���)
∆vbe
∆ bI(���)
V Constant ce
V Constant ce
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To find modulation index
To find modulation index
Equation of modulating signal
Equation of carrier signal
Equation of AM wave
To find upper and lowerside frequencies
To find band width
To measure the lengthh ofdipole antenna
To find range of antenna
To find maximum line ofLOS distance
= Modulation factor = Amplitude ofmodulating signal = Amplitude of carrier wave
A = Maximummax
amplitudeA = Minimummin
amplitude
m (t) = modulating signal
C (t) = carrier signal
C (t) = AM wavem
USB = Upper side bandLSB = Lower side band
Length of dipole antenna
d = The range of TVtransmissionR = Radius of earth
d = Maximum line of LOSm
distance
USB = F + fc m
LSB = f - fc m
= band width
C (t) = Am c
S.No.
1.
2.
3.
4.
APPLICATIONS SYMBOL
UNIT 10 : COMMUNICATION SYSTEMS
6.
7.
8.
9.
10.
Output Resistance Vce = Collector Emitter voltage 14.