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

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

a) outside the shell:

b) on the shell:

d) inside the shell : E=0

E = k2r

Q

PHYSICSPHYSICS

=q

E

R

s

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31

PHYSICSPHYSICS

14.

C=capacitancer=radius of conductor

A = area of plates d = distance between theplates

C = equivalent capacitance s

in series C =equivalent capacitancep

in parallel

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

Capacity of isolatedspherical conductor

Capacitance of a parallel plate capacitor

To calculate equivalent capacitance of a circuit

Energy stored in acapacitor

Energy density of aparallel plate capacitor

To find Common potential due to sharing of charge

Loss of energy due sharingcharges

Relation betweendielectric constant &electric susceptibility

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



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

32



33

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



34

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



35

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



36


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



37


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



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



39


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



40


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



41

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



42

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.

I Constant b

5.

FORMULAE

PHYSICSPHYSICS

Am

Ac

m�(t)�=�A Sinw tm m

c�(t)�=�A Sinw tc c

x 100%m�=A - Amax min

A + Amax min

∆vce

∆ cI(��)r =0 Ib

m�=�Am

�Ac



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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