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### Capacitance IITJEE TEST Series

(A) Multiple choice questions with one or more then one correct answers

1. Which one of the following statement(s) is true
a. When the space between conductors of a capacitor is filled by dielectric it's capacitance decreases.
b. When the space between conductors of a capacitor is filled by dielectric it's capacitance increases.
c. When the space between conductors of a capacitor is filled by dielectric it's capacitance is increased by a factor known as dielectric constant of the dielectric
d. On introduction of dielectric between the conductors of capacitor , dielectric will reduce both electric field and potential difference

2 A parallel plate air capacitor is charged by cinnecting both of it's plates to the battery now a dielectric of dielectric constant k is inserted without disconnecting the battery which causes
a. Increase in potential difference across the plates and reduction in stored energy and no change in charge of plates.
b. The battery to supply the more charge to maintain the original potential difference and charge on plates increases.
c. Reduction of charge on the plates and increase of potential difference across the plates.
d None of the above.

3. For the arrangement shown below in the figure 1

total effective capacitance between the terminals is
a. 12.5 μF
b. 4.4 μF
c. 15.2 μF
d. 14 μF

4. The two plates of a capacitor are given charges ±Q and then they are immersed in a tank of oil . the electric field between the plates
a. increases
b. decreases
c. remain same
d. none of the above

ans b

5. The net capacitance of capacitors in figure 2 beetween points a and b is

a. 1 μF
b. 3μF
c. 4 μF
d 2 μF

(A) A parallel plate capacitor of area A and separation d is charged to a potential difference V and is removed from the charging source. A dielectric slab of dielectri constant k=2 , thickness d and area A/2 is inserted between the plates of the capacitor as shown below in the fig.

1. Which one of the following statement(s) is correct
a. Electric field have different values inside the dielectric as in the free space between the plates.
b. Electric field have same values inside the dielectric as in the free space between the plates.
c. There will be diferent potential difference between the portion of the plate separated by dielectric slab an between the portion separated by the vacuum.
d. none of the above.

2. If τ1 be the surface charge density at the conductor-dielectric surface and τ2 be the charge density at the conductor vacuum-surfacethen ratio betwen the two charge densities is
a. τ12=2:1
b. τ12=1:2
c. τ12=2:2
d. τ12=4:1

3. If C is the capacitance of the capacitor without the dielectric slab and V is the potential diffrence then capacitance and potential diffrence of capacitor on introduction of dielectric is
a. 3C/2 ; 3V/2
b. 2C/3 ; 2V/3
c. 2C/3 ; 3V/2
d. 3C/2 ; 2V/3

(B) The space between the plates of a parallel plate capacitor is filled consicutively with two dielectric layers having thickness d1 and d2 and permitivities ε1 and ε2 respectively and area of each plate is A.

1. After the introduction of dielectric slabs the capacitance of the capacitor is
a. ε0A/[(d11)+(d21)]
b. ε0/A[(ε1/d1)+(ε2/d2)]
c. ε0d1d2/A(ε12)
d. ε0A/d1d212)

2. If the voltage across the capacitor is V and electric field is directed from layer 1 to layer 2 then density of boundary charge on boundary plane is
a. (ε2d11d2)/ε0V(ε12)
b. ε0V(ε12)/(ε2d11d2)
c. ε0V/(ε2d11d2)
d. ε0V(ε12)/(ε2d11d2)

### IITJEE TestSeries Mechanics -1

Multiple choice question with one answer

1.A IITJEE text book of mass M rests flat on a horizontal table of mass m placed on the ground.Let RX->Y be the constant force exerted by the body x on body Y.According to Newton third law,which of the following is an action-reaction pair of forces?

a. (M+m)g and Rtable->book
b. Rground->table and mg+Rbook->table
c. Rground->table and Rtable->ground
d Mg and Rtable->book

2. there are two statements
A Newtons first law in valid from the pilot in an aircraft which is taking off
B Newtons first law in valid from the observer in a train moving with constant velocity
Which of the following is correct

(a) A only
(b) B only
(c) Both A and B are correct
(d) Both A and B are wrong

3.The horizontal and vertical displacement of the projectile at time t are
x=36t
y=48t-4.9t2
where x and y are in meters and t in second.Intial velocity of the projectile in m/s
a. 15
c. 30
b. 45
d. 60

4.A truck accelerates from rest at the constant rate a for some time after which it decelerates at a constant rate of b to come to the rest.If the total time elapsed is t ,then find out the maximum velocity attains by the truck
a. (ab/a+b)t
b.(a+b/ab)t
c. (a2+b2/ab)t
d.(a2-b2/ab)t

5.A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of 30 ° with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? take g = 10 m/s2
a. 5.20 m
b.4.33 m
c.2.60 m
d 8.66 m.

Multiple choice question with one or more answer

1. A body is projected horizontally from a point above the ground.The motion of body is defined as
x=2t
y=2t2
where x and y are horizontal and vertical displacement respectivley at time t.Which one of the following is true
a.The trajectory of the body is a parabola
b The trajectory of the body is a straight line
c.the velocity vector at point t is 2i+4tj
d the acceleration vector at time t is 4j

2.Mark out the correct statement
a)Instantaneous Velocity vector is always in the direction of the motion
b)Instantaneous acceleration vector is always in the direction of the motion
c)Acceleration of the moving particle can change its direction with any change in direction of velocity
d) None of the above

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

1. STATEMENT1: The Average velocity of a continously moving particle may be zero for some time interval but average speed will not be zero
STATEMENT: Displacement of a continously moving particle can decrease with time but distance will not

2. STATEMENT1: Two bodies of mass m and M will reach ground in same time when fallen at same time from the tower of height h
STATEMENT1: Same Acceleration due to gravity is experienced by the both body in fall from tower

3.STATEMENT1:In a projectile motion,acceleration vector is Perpendicular to Velocity vector at the highest point
STATEMENT:There is no horizontal acceleration present in the projectile motion

Matrix match type
In a free fall motion from rest,Match column I to column II
column I
A) Graph between displacement and time
B) Graph between velocity and time
C) Graph between velocity and displacement
D) Graph between KE and displacement

column II
P) Parabola
Q) Straight line
C) Circle
D) No appropiate match given

.A train is moving in the west direction with a velocity 15m/s.A monkey runs on the roof of the train against its motion with a velocity 5m/s with respect to train .Take the motion along west as positive
1.Velocity of train relative to its driver
a. 0
b. 15 m/s
c. -15 m/s
d. 20 m/s

2. What is the velocty of train with respect to monkey
a. 5m/s
b -5 m/s
c. 15 m/s
d -15 m/s

3. find the velocty of ground with respect to monkey
a. 5 m/s
b. -5 m/s
c. 10 m/s
d. -10 m/s

### AIEEE Mechanics Past year Question with Answers

1.A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
A x2
B ex
(C) x
(D) logex

Ans A

2.A ball is released from the top of a tower of height h metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?
(A) h/9 metres from the ground
(B) 7h/9 metres from the ground
(C) 8h/9 metres from the ground
(D) 17h/18 metres from the ground.

Ans C.

3.A projectile can have the same range R for two angles of projection. If T1 and T2be the time of flights in the two cases, then the product of the two time of flights is directly proportional to
(A) 1/R2
(B) 1/R
(C) R
(D) R2

Ans C

4.Which of the following statements is false for a particle moving in a circle with a constant angular speed?
(A) The velocity vector is tangent to the circle.
(B) The acceleration vector is tangent to the circle.
(C) The acceleration vector points to the centre of the circle.
(D) The velocity and acceleration vectors are perpendicular to each other.

ANs B.

5.An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 cm. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be
(A) 20 m
(B) 40 m
(C) 60 m
(D) 80 m

ANs D.

6.A machine gun fires a bullet of mass 40 g with a velocity 1200 m/s. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
(A) one
(B) four
(C) two
(D) three

Ans D.

7.A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that
(A) its velocity is constant
(B) its acceleration is constant
(C) its kinetic energy is constant
(D) it moves in a straight line.

Ans C.

8. The relation between time t and distance x is t=ax2+bx where a and b are constants.
The acceleration is
(A) −2abv2
(B) 2bv3
(C) −2av3
(D) 2av2

Ans (C)

9. A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity
‘v’ that varies as v = a x1/2 . The displacement of the particle varies with time as
(A) t3
(B) t2
(C) t
(D) t1/2

Ans: (B)

10. A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity
of the 12 kg mass is 4 m/s. The kinetic energy of the other mass is
(A) 96 J
(B) 144 J
(C) 288 J
(D) 192 J

Ans: (C)

### IIT Chemistry Syllabus

Physical chemistry

General topics: Concept of atoms and molecules; Dalton’s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.

Gaseous and liquid states: Absolute scale of temperature, ideal gas equation; Deviation from ideality, van der Waals equation; Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; Law of partial pressures; Vapour pressure; Diffusion of gases.

Atomic structure and chemical bonding: Bohr model, spectrum of hydrogen atom, quantum numbers; Wave-particle duality, de Broglie hypothesis; Uncertainty principle; Qualitative quantum mechanical picture of hydrogen atom, shapes of s, p and d orbitals; Electronic configurations of elements (up to atomic number 36); Aufbau principle; Pauli’s exclusion principle and Hund’s rule; Orbital overlap and covalent bond; Hybridisation involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond; Polarity in molecules, dipole moment (qualitative aspects only); VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral).

Energetics: First law of thermodynamics; Internal energy, work and heat, pressure-volume work; Enthalpy, Hess’s law; Heat of reaction, fusion and vapourization; Second law of thermodynamics; Entropy; Free energy; Criterion of spontaneity.

Chemical equilibrium: Law of mass action; Equilibrium constant, Le Chatelier's principle (effect of concentration, temperature and pressure); Significance of DG and DGo in chemical equilibrium; Solubility product, common ion effect, pH and buffer solutions; Acids and bases (Bronsted and Lewis concepts); Hydrolysis of salts.

Electrochemistry: Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to DG; Electrochemical series, emf of galvanic cells; Faraday's laws of electrolysis; Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch's law; Concentration cells.

Chemical kinetics: Rates of chemical reactions; Order of reactions; Rate constant; First order reactions; Temperature dependence of rate constant (Arrhenius equation).

Solid state: Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, alpha, beta, gamma), close packed structure of solids (cubic), packing in fcc, bcc and hcp lattices; Nearest neighbours, ionic radii, simple ionic compounds, point defects.

Solutions: Raoult's law; Molecular weight determination from lowering of vapour pressure, elevation of boiling point and depression of freezing point.

Surface chemistry: Elementary concepts of adsorption (excluding adsorption isotherms); Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants and micelles (only definitions and examples).

Nuclear chemistry: Radioactivity: isotopes and isobars; Properties of alpha, beta and gamma rays; Kinetics of radioactive decay (decay series excluded), carbon dating; Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions.

Inorganic Chemistry

Isolation/preparation and properties of the following non-metals: Boron, silicon, nitrogen, phosphorus, oxygen, sulphur and halogens; Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur.

Preparation and properties of the following compounds: Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium; Boron: diborane, boric acid and borax; Aluminium: alumina, aluminium chloride and alums; Carbon: oxides and oxyacid (carbonic acid); Silicon: silicones, silicates and silicon carbide; Nitrogen: oxides, oxyacids and ammonia; Phosphorus: oxides, oxyacids (phosphorus acid, phosphoric acid) and phosphine; Oxygen: ozone and hydrogen peroxide; Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate; Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.

Transition elements (3d series): Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment; Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).

Preparation and properties of the following compounds: Oxides and chlorides of tin and lead; Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+; Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate.

Ores and minerals:Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminium, zinc and silver.

Extractive metallurgy: Chemical principles and reactions only (industrial details excluded); Carbon reduction method (iron and tin); Self reduction method (copper and lead); Electrolytic reduction method (magnesium and aluminium); Cyanide process (silver and gold).

Principles of qualitative analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide.

Organic Chemistry

Concepts: Hybridisation of carbon; Sigma and pi-bonds; Shapes of simple organic molecules; Structural and geometrical isomerism; Optical isomerism of compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded); IUPAC nomenclature of simple organic compounds (only hydrocarbons, mono-functional and bi-functional compounds); Conformations of ethane and butane (Newman projections); Resonance and hyperconjugation; Keto-enol tautomerism; Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds: definition and their effects on physical properties of alcohols and carboxylic acids; Inductive and resonance effects on acidity and basicity of organic acids and bases; Polarity and inductive effects in alkyl halides; Reactive intermediates produced during homolytic and heterolytic bond cleavage; Formation, structure and stability of carbocations, carbanions and free radicals.

Preparation, properties and reactions of alkanes: Homologous series, physical properties of alkanes (melting points, boiling points and density); Combustion and halogenation of alkanes; Preparation of alkanes by Wurtz reaction and decarboxylation reactions.

Preparation, properties and reactions of alkenes and alkynes: Physical properties of alkenes and alkynes (boiling points, density and dipole moments); Acidity of alkynes; Acid catalysed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination); Reactions of alkenes with KMnO4 and ozone; Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions; Electrophilic addition reactions of alkenes with X2, HX, HOX and H2O (X=halogen); Addition reactions of alkynes; Metal acetylides.

Reactions of benzene: Structure and aromaticity; Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation; Effect of o-, m- and p-directing groups in monosubstituted benzenes.

Phenols: Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation); Reimer-Tieman reaction, Kolbe reaction.

Characteristic reactions of the following (including those mentioned above): Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution reactions; Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and ketones; Ethers:Preparation by Williamson's Synthesis; Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation; aldol condensation, Perkin reaction; Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard addition); Carboxylic acids: formation of esters, acid chlorides and amides, ester hydrolysis; Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction; Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution).

Carbohydrates: Classification; mono- and di-saccharides (glucose and sucrose); Oxidation, reduction, glycoside formation and hydrolysis of sucrose.

Amino acids and peptides: General structure (only primary structure for peptides) and physical properties.

Properties and uses of some important polymers: Natural rubber, cellulose, nylon, teflon and PVC.

Practical organic chemistry: Detection of elements (N, S, halogens); Detection and identification of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino and nitro; Chemical methods of separation of mono-functional organic compounds from binary mixtures.

### IITJEE MATHEMATICS SYLLABUS

Algebra:

-Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

-Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

-Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

-Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
-Logarithms and their properties.
-Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.

-Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.

Trigonometry:

-Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.

-Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).

Analytical geometry:

-Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.

-Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.

-Equation of a circle in various forms, equations of tangent, normal and chord.

-Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.

-Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus Problems.

-Three dimensions: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.

Differential calculus:

Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.

Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.
Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus:

Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.

Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.

Vectors:
Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.

### PARTICAL PROPERTIES OF WAVES

Photoelectric effect
-Photoelectric effect is the emission of electrons from metal surface when they absorb energy from an electromagnetic wave.

-These electrons emitted from metal surface are known as photo electrons.

(a) Observed features:
-For a given metal or photosenstive surface there is a minimum frequency ν0 of incident radiation , below which there is no emission of photo electrons and this frequency is called threshold frequency of that metal surface.
-Electronic emission increases with the intensity of radiation falling on the metal surface , since more energy is available to the release of electrons but maximum kinetic energy KEmax (=eV where V is the cut off voltage) is independent of the intensity of light.
-There is no time delay between the arrival of light on the metal surface and the emission of electrons.
-The maximum kinetic energy of photoelectrons and frequency of incident light are related linearly as
KEmax=eV ∝ (ν-ν0)
(b) Theoretical explaination:
-Classical theory which assumes light as an EM wave fails to explain photoelectric effect.
-Einstein first gave correct explaination of photoelectric effect using Plank's idea of energy quantization.
-Einstein in his theory considered that radiation of frequency ν consists of a stream of discrete quanta (photons) each of energy hν , where h is the plank's constant. The photons moves through space with the speed of light.
-When a quanta of energy hν is incident on a metal surface , the entire energy of the photon is absorbed by a single electron without any time lag.
-The minimum amount of work or energy necessary to take a free electron just out of metal against attractive forces of surrounding positive ions is called work function of the metal and is denoted by φ0.
-Appliying principle of conservation of energy to the absorption of photon by an electron in the metal surface we get,
hν=KEmax0
writing φ0=hν0 , we get
KEmax=h(ν-ν0)
-thus maximum kinetic energy is same as observed KEmax with the proportionality constant equal to Plank's constant.

### Capacitance II

(a) Parallel combination of capacitors-Capacitors connected in parallel combination have same potential difference across their terminals shown below in fig

where
V=potential difference across terminals of capacitors c1, c2, c3
and Q1, Q2 and Q3 resp. are charges on capacitors c1, c2, c3.
-In parallel combination system of capacitors is equivalent to a single capacitor of capacitance
C=Q/V= C1+C2+C3
where, C1=Q1/V
C2=Q2/V
C3=Q3/V
-Thus for capacitors connected in parallel combination their resultant capacitance C is the sum of their individual capacitances.
-Also for parallel combination of capacitors their resultant capacitance C is greater then the capacitance of greatest individual one.

(b) Series combination of capacitors
-Figure above shows three capacitors connected in series combination
-In series combination of capacitors potential difference across each capacitor is different but charge on each capacitor is same.
-The resultant capacitance of capacitors connected in series combination is the ratio of charge stored to the applied potential difference V and is given by
C=Q/V
or 1/C=V/Q
now V=V1+V2+V3
=Q(1/C1+1/C2+1/C3)
Thus,
1/C=1/C1+1/C2+1/C3
-Resultant capacitance Cof the capacitors connected in series combination is equal to the sum of reciprocals of their individual capacitances. Here in case of series combination C is less then the capacitance of smallest individual capacitor.

(c) Energy stored in capacitor-Energy stored in capacitor is
E=QV/2
or E=CV2/2
or E=Q2/2C
factor 1/2 is due to average potential difference across the capacitor while it is charged.
-Battery supply QV amount of energy during charging a capacitor but energy stored in capacitor is QV/2 , the another half of energy is transferred into the circuit resistance in the form of heat.
thus,
heat in the wire=energy supplied by battery-energy stored in the capacitor
=QV-QV/2 = QV/2

### Thermodynamics AIEEE Past year questions with answer

1.

“Heat cannot by itself flow from a body at lower temperature to a body at higher temperature” is a statement of consequence of
(A) second law of thermodynamics
(B) conservation of momentum
(C) conservation of mass
(D) first law of thermodynamics.

Ans Second law of thermodynamics.

2. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio Cp/CV for the gas is
(A) 4/3
(B) 2
(C) 5/3
(D) 3/2

Ans A.

3. Which of the following parameters does not characterize the thermodynamic state of matter?
(A) temperature
(B) pressure
(C) work
(D) volume

Ans C.

4.
One mole of ideal monoatomic gas ( Cp/CV= 5/30) is mixed with one mole of diatomic gas (Cp/CV = 7/5). What is Cp/CV for the mixture?
(A) 3/2
(B) 23/15
(C) 35/23
(D) 4/3

Ans A.

5 If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be
(A) 4
(B) 16
(C) 32
(D) 64.

Ans D.

6. Which of the following statements is correct for any thermodynamic system?
(A) The internal energy changes in all processes.
(B) Internal energy and entropy are state functions.
(C) The change in entropy can never be zero.
(D) The work done in an adiabatic process is always zero.

Ans B.

### Solution for IITJEE test series SHM

Mulitiple choice questions with one answer
1.

Ans c

2.
Ans b

3. Ans (d)
4. ANs (b)

5. Ans (d)
Mulitiple choice questions with more then one answer

6.
Ans b,c

7.
Ans c,d

8.
Ans c,d

9.

Ans a,c

10.

Ans a,c

Assertion and Reason

11.

Ans (d)

12.

Ans (b)

13.

Ans (c)

14.

Ans (b)

MAtrix match type

15.

Ans
A->A
B->B
C->A
D->B

16

Ans (a)

17.

ans (a)

18.

Ans (b)

### IIT JEE Test series (ELectricty) solutions

Multiple choice question with only one answer
1.

Ans (a)

2.

Ans (a)

3.

Ans (A)

4.

Ans (b)

5.
Ans (A)

Multiple choice question with more than one answer

6)

Ans (all)

7)

Ans a,c

8)
Ans a,b,c

9.

Ans a,b

10.

Ans (a)

11.

Ans (c)

12.

Ans (c)

13.

Ans (a)

Matrix Match type

Ans
A-P,R
B-Q,R
C-P,R
D- P,S

1)
Ans (a)

2)
Ans (b)

3)

Ans (a)

### Capacitors

-Capacitors are important components used in electronics and telecommunication devices for example radio , television recivers , transmitter circuits etc.

-Capacitor is a device used for storing electronic charge.

-All capacitors consists of two metal plates(or conductors) separated by an insulator(air, vacuum or any other dielectric medium).

-Conventional symbol of capacitor is where T is the terminal (positive or negative) of battery joined to the plates.

-Capacitor gets charged when a battery is connected to it or when there is a potential difference between two metal plates of the capacitor.

-Capacitor gets discharged on joining two of it's plates.

-If V is the potential difference between two plates of the capacitor and q is the amount of charge developed on each plate then q/V is constant for the capacitor since q∝V.

-The ratio of charge on either plate to the potential difference between the plates is called capacitance C of the capacitor. Thus,
C=q/V
or q=CV

-Unit of capacitance is Farads(F) or CV-1.

-1F is very large unit of capacitance. Practically capacitors with capacitance of the order of micro farads (μF) are used in circuits of radio recivers , transmitters etc. Thus,
1μF=10-6 (micro)
1nF=10-9 (nano)
1pF=10-12 (pico)

-For any capacitor it's capacitance is constant and depends on shape , size , separation f the two conductors and also on insulating medium being used for making capacitor.

- Capacitance of parallel plate capacitor havinf vacuum or air acting as dielectric or insulating medium is
C=(ε0A)/d
where,
C= capacitance of capacitor
A= area of conducting plate
d= distance between plates of the capacitor
ε0=8.854× 10-12 and is known as electric permitivitty in vacuum.
-If k is the relative permittivity of the dielectric medium then
ε=ε0k
thus capacitance of parallel plate air capacitor in presence of dielectric medium of electric permitivity ε is
C=εA/d
-Capacitance of spherical capacitor having radii a, b (b>a) with
(a) air as dielectric between them
C=(4πε0ab)/(b-a)
(b) dielectric with relative permitivity ε
C=(4πεab)/(b-a)

### IITJEE Test series Electric Potential

Multiple choice question with only one answer

1.The elctrical potential energy of an islolated metal sphere of radius R and total Charge Q
a. Q2/4πεR
b. Q2/8πεR
c. Q2/2πεR
d. Q2/16πεR

2. A electric dipole is placed at +q(-a,0) and -q(a,o) in the xy plane.Find the workdone by the electric lines on charge which is moved from point (0,a) to (0,-a).
a. zero
b. p/4πεr2
c. -p/4πεr2
d. none of the above

3.Find the electric field at the centre of the uniformly charged semicircular arc of of Radius R and linear charge density λ
a.λ/2πεa
b.λ/4πεa
c. λ/πεa
d. none of these

4.An electric dipole placed in a uniform electric field experiences
a. A torque but no force
b A force but no torque
c. Both force and torque
d neither a force and torque

5.A charge q is placed at the center of the line joining two equal charges Q.The system of three charges will be in equilibrium if q equal is
a. -Q/2
b. Q/2
c. Q/4
d. -Q/4

Multiple choice questions with one or more answer

6.Choose the correct statement
a.if electric field is zero at the point then electric potential must be also zero at that point
b.Two diffrent equipotential surface can intersect
c.if electric potential is constant in a given region then electric field must be zero in that region
d. Electrons move from higher potential to lower potential

7.A spherical conductor shell has charge Q on it and Radius of the spherical shell is R
a. Electric potential decrease with 0< r < infinity
b Electric field decrease with with 0< r < infinity
c Electric potential is non zero constant for 0< r < =R and decrease for R< r < infinity
d Electric field is zero for 0< r < =R and decrease for R< r < infinity

8.Electric potential V(x,y) of a electrostatic field E=a(yi +xj) where a is constant
a.V(x,y)-V(0,0)=-axy
b.V(x,y)-V(1,1)=-axy+a
c.V(x,y)-V(1,1)=-axy-a
d. None of the these

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

9.
STATEMENT I:Electrix flux through any closed surface around point charge is independent of the size and shape
STATEMENT II.φ=∫ E.da

10.
STATEMENT I:Electric potential inside the spherical conductor shell is nonzero constant
STATEMENT II:Electric field inside the shell is zero

11.
STATEMENT I:Electric Field on the surface of a conductor is less at the sharp corners

STATEMENT II: Surface charge density on conductor surface is inversely proportional to the radius of curvature

### Electric Flux and Gauss law

Electric Flux

dφ=E.da
da is the area vector to the surface and it is taken +ve along the outward normal to the surface
dφ=Edacosθ

φ=∫ E.da

For closed surface
φ=∫ E.da

Guass Theorem

Flux in closed surface is equal net charge inside divided by ε

E.da=qin

Some points:
a. E is the electric field present due to all charges in the ssystem not just the charge inside

b.Flux crossing a closed surface does not depend on the shapes and size of gaussian surface

Electric Potential energy of a charge
=qV where V is the potential there

Others important things
1. ∫ E.dl over closed path is zero
2.Electric potential in the spherical charge conductor is Q/4πεR where R is the radius of the shell and the potential is same everywhere in the conductor
3 Conductor surface is a equipotential surface

### Electric Potential

Electric Potential Energy

ΔU=-W

Where ΔU = Change in Potential energy
W= Workdone by the electric lines of forces

For a system of two particles

U(r)=q1q2/4πεr

where r is the seperation between the charges

We assume U to be zero at infinity

Similarliy for a system of n charges
U=Sum of potential energy of all the distinct pairs in the system

For example for three charges
U=(1/4πε)(q1q2/r12+q2q3/r23+q1q3/r13)

Another way to represent
U=1/2ΣqV

where V is the potential at charge q due to all the remaining charges

Electric Potential:
Just liken Electric field intensity is used to define the electric field,we can also use Electric Potential to define the field

Potential at any point P is equal to th workdone per unit test charge by the external agent in moving the test charge from the refrence point(without Change in KE)

Vp=Wext/q

So for a point charge

Vp=Q/4πεr

where r is the distance of the point from charge

Some points about Electric potential1. It is scalar quantity
2.Potential at point due to system of charges will be obtained by the summation of potential of each charge at that point

V=V1+V2+V3+V4

3.Electric forces are conservative force so workdone by the electric force between two point is independent of the path taken

4. V2-V1=-∫ E.dr

5 In cartesion coordinates system
E=Exi+Eyj+Ezk
dr=dxi+dyj+dzk

Now
dV=-E.dr

So dv=-(Exdx+Eydy+Ezdz)

So Ex=∂V/∂x

Similary
Ey=∂V/∂y and Ez=∂V/∂z

Also
E=-[(∂V/∂x)i+(∂V/∂y)j+(∂V/∂z)k]

4
Surface where electric potential is same everywhere is call equipotential surface
Electric field components parallel to equipotential surface is always zero

Electric dipole:
A combination of two charge +q and -q seperated by the distance d

p=qd
Where d is the vector joiing negative to positive charge

Electric potential due to dipole
V=(1/4πε)(pcosθ/r2)

where r is the distance from the center and θ is angle made by the line from the axis of dipole

Electric field
Eθ=(1/4πε)(psinθ/r3)

Er=(1/4πε)(2pcosθ/r3)

Total E=√Eθ2+Er2
=(p/4πεr3)(√(3cos2θ+1))

Torque on dipole=pXE

Potential Energy
U=-p.E