PHYSICS UNIT - 02 PAGE NO. Index ELECTROSTATICS o1 CAPACITOR rs CURRENT ELECTRICITY 36 MAGNETISM 48 EMI & AC 60 GEOMETRICAL OPTICS 67 WAVE OPTICS 73 MODERN PHYSICS 84 ERROR IN MESUREMENT & 100 INSTRUMENTSElocrostties ELECTROSTATICS SUBJECTIVE TYPE 1. Figure shows. in cross section, two solid spheres with uniformly distributed charge throughout their volumes. Each has radius R. Point P lies on a line connecting the centres of the spheres, at radial distance R/2 from the center of sphere 1. If the net electric field at point P is zero and Q, is 64 uC, what is Qy(in uC). ‘Two infinite rods with linear charge density +2 are kept apart by distance d. An electron of mass ‘m’, charge ‘e” is kept at the midpoint between the two rod . On being given slight vertical displacement (in the plane perpendicular to the plane of rods), the time period of this oscillatory ml oy freynd . motion is any vO . Then x will be. xe 3. ‘Two particles of mass ‘m’ each and having charge +q and ~q respectively joined by a light rod of length 6a.as shown in the figure. The whole system is kept on a horizontal frictionless surface and two spring are connected to the rod. Rod is hinged at centre and assume no energy loss takes place in form of electromagnetic wave during the motion of particles, A uniform electric field exists in the region as shown in the figure in entire region. The rod is given a small angular displacement from equilibrium, then the frequency of small oscillation 5 k . [oven m = 5 she & Eq = 8ka| is f Hz, Fill the value of 4f in OMR sheet. A hollow non conducting sphere A and a solid non conducting sphere B_of equal radius ‘R’ and masses m and 2m are kept at a large distance apart ona rough horizontal surface. Charge on the two spheres A and B are Q and 2Q respectively. Charges are distributed uniformly and remain constant and uniform as the spheres come closer. Friction is sufficient to support pure rolling and the kinetic energy of the two spheres just before collision isKyandK, Find 10x Xa Kp5. Appoint charge q moves from point P to S along the path PQRS in a uniform electric field E. pointing parallel to the positive direction of the x-axis . The co-ordinates of the points P,Q. R.S are (a,b, 0), (2a, 0,0), (a,b, 0) & ((),0,0) respectively . The work done by the field in the above process is given by the expression 6. Figure shows the part of a hemisphere of radius (R) = 2m and surface charge density (6) Calculate the electric potential (in volt) at centre O. 2e, Chm’, 7. A point charge +2e is placed on the top of a cone of semi vertex angle 6. The electric flux through the wef 9 Fi base of the cone is [sin] . Determine the value of («+B +7) 8 Aninfinitely long solid cylinder of radius R has a uniform volume charge density p. Tthas a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure, The magnitude of the electric field at the point P, which is at a distance 2 from the axis of the cylinder, is given 230K, by the expression 7, The value of n is ALS V battery of variable EMF of negligible resistance is connected to a wire with a resistance of 900 ©. Figure shows the potential difference across battery as function of time. Find total charge (in C) transferred by battery during these two hours. AVY) 10, A small rigid object carries positive and negative charge of magnitude 4 coulomb each. Itis oriented so that the positive charge has coordinates (-1.2mm, 1.1 mm) and negative charge has coordinates 0003) NIC. (1.4mm, ~1.3 mm). The object is kept in an electri Field of (25004 ‘nd the magni- tude of torque (in N-m) acting on the dipole.Elocrostties SINGLE CORRECT ANSWER TYPE ‘harge density 7,,x and ~2,,x (where x is the ia distance from their respective centres C, and C,) are placed close = Gat teesesestt and parallel to each other in such a way that distance between their | FFT FT TATE centres is a. Find out the electric field intensity at a point P distant A 11. Twolong thin rods ha r r from this system [k= kava py 2 2 (D) 12, The electric field intensity at the centre of a uniformly charged hemispheris (A) data insut ‘at © shell is E,, Now two por- tions of the hemisphere are cut from either side and remaining portion is shown in figure. If == 3, then electric field intensity at centre due to remaining portion is ( £, ) OBA) 13. In the given figure, ABC is a nonconducting semicircular wire of radius a carrying total charge Q uniformly distributed on it and a point charge q is at its centre. Ends of the wire are attached to, two CN) separate springs, each having spring constant k as shown in the figure. In the given position, system is in equilibrium. Now the point charge q is suddenly removed, The amplitude of resulting oscillation is (ignore any force other than spring force and electrostatic force) —__ a + ar ®) Greak © Brea ©) grea 14, Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in. =~JEE-Physics 15, 16. 17. 18, 19. 20, “Two equal point charges are fixed at x =—a and x = +a on the x-axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q. when it is displaced by a small distance x along the x-axis, is approximately proportional to (Ax (Bx? Ox (D) Ux Figure showsa solid hemisphere with a charge of SnC distributed uniformly through its volume. The hemisphere lies on a plane and point P is located on this plane, along a radial line from the centre of curvature at distance 15cm, The electric potential at point P due to the hemisphere, is —15cm—H (A) 150V (B) 300 V (©) 450V (D) 600 V Consider the following conclusions regarding the components of an electric field at a certain point in space given by BE, =—KyE, = Kx E (1) The field is conservative. (ID) The field is non-conservative. (ID) The lines of force are staright lines (IV) The line s of force are circles. Of these conclusions (A) ILand IV are valid (B) Land Il are valid (©) Land IV are valid (D) Hand IL are valid On an imaginary planet the acceleration due to gravity is same as that on Earth but there is also a downward electric field that is uniform close to the planet’s surface. A ball of mass m carrying a charge q is thrown upward ata speed v and hits the ground after an interval t. What is the magnitude of potential difference between the starting point and the top point of the trajectory ? ~st) my( gt my 2my #) © 5, Wat) wD) q\ 2q q w ™ ae 2g Figure shows a charge configuration with its equipotential surfaces and electric field ines placed in x- y plane. Mark INCORRECT statement :- (A) Potential gradient is positive along (CD) (B) Potential gradient is negative along (EF) (C) Ifa positive charge particle is constrained to move along line AB, it will have constant potential energy. (D)A positive charge particle released from rest at C will begin to move in direction (DC) Consider a circle of radius R.A point charge lies at a distance 'a' Irom its center and on its axis such that R = a3. Ielectric flux passing through the circle is then the magnitude of the point charge is:- (A366 (B) 25,6 (C) 4e,6/ V3 (D) 45,Elocrostties 21, Ahemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface? Hitt (AO (B) 4nR2E/3 (C) 2nR?E (D) xRE 22, ‘The diagram shows a uniformly charged hemisphere of radius R. It has volume charge density p. If the electric field at a point 2R distance above its center is E then what is the electric field at the point which is 2R below its center? n (A) pRi6e, +E (B) pR/12e, -E (C)-pRi6e, +E (D) pR/245, +E 23, Hight point charges having magnitude q are fixed at vertices of a cube. The electric flux through square surface ABCD of the cube is ‘ ¢ ni “ B Ur NG rg qF 4 4 4 4 te, ®) 2 OF. O36 24, The volume charge density as a function of distance X from one face inside a unit cube is varying as shown in the figure. The total flux (in S.1. units) through the cube if (p, = 8.85 x 10°? C/m’) is density (in em’) (in m) aya (B) 2 (3/4 @)125, Aring of radius R having a linear charge density 2. moves towards a solid imaginary sphere of radius 26. 27. 28. 29, R/2, so that the centre of ring to line joining the centers of is passes through the centre of sphere. The axis of the ring is perpendicular 1g and the sphere. The maximum flux through the sphere in this process aR aR Ae B) ze = 2 An ) 3 ‘Three uniformly charged wires with linear charge density A are placed along x. y and zaxis respectively. ‘What is flux of electric field through Gaussian surface given by x? +y?+72=1:x>0:y>0:2>0 6a 32. O) Fe nis given by & = 200) NIC for x >0 and —2997 NIC for x <0. A closed. cylinder of length 2m and cross-section area 10° m? iskeptin such a way that the axis of cylinders along ‘X-axis and its centre coincides with origin. The total charge inside the cylinder is [Take : e, =8.85 x 10” = CmN) (A) zero (B) 1.86 x 10°C. (C) 1.77 x 10"C (D) 35.4 x 10°C Fora system of two dipoles B and Pas shown in the figure, both dipole are at origin and perpendicular to each other along x and y axes respectively then (A) work done in taking electron from P to R on QPR is zero Eis resultant electric field (c) na= -f Bar = SET ire Anelectric dipole ( dipole moment p) is placed at a radial distance r >> a (where a is dipole length) from a infinite line of charge having linear charge density +A. Dipole moment vector isaligned along radial vector f force experienced by dipole is dp ap ap dp (A) Free, g? attractive (B) Zp ,F attractive (C) F5 ,F tepulsive (D) Fp ;° FepulsiveElocrostties 30. 31. 33. Two short dipoles p(i+K) & api are located at (0,0, 0) & (1 m, 0, 2m) respectively. The resultant ‘ctric field due to the two dipoles at the point (1 m, 0,0) is Bp D © Pre ©) te, a OW te ®) me, Ina standard YDSE setup if the screen is kept tilted as shown, find the distance OA if first maximum is formed at A. Wavelength of light emitted by source is 4. Seyeen ay Daseed o) Davos py Déseeduand \ Tehtand © Thad "T+ tand A system consists of uniformly charged sphere of radius R and a surrounding medium filled by a charge a with the volume density p=“, where ois a positive constant and ris the distance from the centre of the sphere. The charge of the sphere for which electric field intensity E outside the sphere is independent ofris a 2 WIS Bye (©) 2naR? (D) aR? Choose the CORRECT alternative : Three identical metallic uncharged spheres A, B and C of radius ‘a’ are kept of the corners of an equilateral triangle of side ‘d’. The fourth sphere of radius ‘a’ (d >a) which has a charge ‘q’ touches ‘A and is then removed to a position far away. B is earthed and then the earth connection is removed. Cis then earthed, The charge on C is ga(2d-a)) ow #24 2d) aad) Aconducting sphere A of radius r, carries a charge Q. Another conducting sphere B of radius r, is uncharged initially. Both the spheres are separated by a very large distance. Sphere A is connected with sphere B through a long conducting wire of zero resistance through a switch S as shown, As the current flow through the wire vanishes, switch S is opened, sphere A is again charged to a total x 5 charge Q and then switch $ is again closed and the process is continued for infinite times. Ifq is the charge transferred to sphere B when the switch $ Q is closed for the first time, then total charge on the sphere B after large number of such processes is (W\Q (By) 22 (C¢) Q* (D) None of these Q-4 aJEE-Physics 35. 37. 38. 39. MULTIPLE CORRECT ANSWER TYPE Ina uniformly charged dielectric sphere a very thin tunnel has been made along the diameter as shown in the figure below. A charge particle—q having mass m is released from rest at one end of tunnel. For the situation described, mark out the correct statement (s) :- [Neglect gravity] (A) Charged particle will perform SHM about centre of the sphere as mean position (B) Time period of the particle is 2x 25 (©)Par will perform oscillation but not SHM. (D) Speed of the particle while crossing-mean pos A particle of mass m and charge q is fastened to one end of a string fixed at pi system lies on a frictionless horizontal plane, Initially, the mass is at rest at A. A uni in the direction shown is then switched on. Then int O. The whole orm electric field 4, [eae (A) the speed of the particle when it reaches B is JS _ (ee yy (B) the speed of the particle when it reaches B is (C) the tension in the string when particles reaches at B is 2qE An (D) the tension in the string when the particle reaches at Bis gE of B A thin dielectric rod of length / lies along the x -axis with one end at the origin and the other end at the point (£, 0) Ibis charged uniformly along its length with a total charge Q. The potential ata point (x,0) when x > Cis (x) Q 5 lo (2) © anege log, | (A) Grept ®) Frepl Assume that entire x7-plane is charged with a uniform surface charge density of 8.85 x 10 C/m?, The potential at origin is assumed to be zero. ff (A) The potential at (1, 0, 1) is 2V (B) The potential at (1,1, =I) is | 5 |” 1 (C) The potential at (1,-1,-1)is 5V (D) The potential at (-1,-1,—1) is A sphere of radius R, has charge density p uniform with in its volume, except for a small spherical hollow region of radius R, located a distance "a" from centre (Take zero potential at infinity), pai (A) Electric field at O' is 32> a a jeld at Oris © (B) Electr 3a) a ric potential at any point in hollow region is constant (C) Blectie potential at O' is sal ARF - (D) Ble 84. a2, 43. Electrostatic A large insulating thick sheet of thickness 2d carries a uniform charge per unit volume p. A particle of mass m, carrying a charge q having a sign opposite to that of the sheet, is released from the surface of the sheet. The sheet does not offer any mechanical resistance to the motion of the particle. Find the {lation frequency v of the particle inside the sheet. os 1 [ap Qn \me, 1 [ap fae 2a Yime, (A)v= The following figure shows a block of mass m suspended from a fixed point by means of a vertical spring. The block is oscillating simple harmonically and carries accharge q. There also exists a uniform electric field in the region. Consider four different cases. The electric field is zero, in case- mg 2mg upward in ease-3 and “]~ downward in cas 4, The speed at mean position — [7G is same in all cases. Select the correct alternative(s). (A) Time periods of oscillation are equal in case-1 and case-3 (B) Amplitudes of displacement are same in case-2 and case-3 (C) The maximum elongation (increment in length from natural length) is maximum in case-4, (D) Time periods of oscillation are equal in ease-2 and case-4 Ina system of two dipoles placed in the way as shown in figure: oe (A) Itis possible to consider a spherical surface of radius aand whose centre | lies within the square shown, through which total flux is +ve. (B) [tis possible to consider a spherical surface of radius a and whose centre —gé.. lies within the square shown through which total flux is —ve (C) There are two points within the square at which EP is zero. (D) Itis possible to consider a spherical surface of radius a and whose centre lies within the square shown, through which total flux is zero, A point charge q is placed at P(0, 0, a). Then = eater than 4 (A) Flux through surface formed by joi Be, ing points (0, 0, 0) ; (0, a, 0); (a, 0, 0) is (B) Flux through surface formed hy joining points (0, a, 0) : (a, 0.0): q a 0) is greater than 34 0): Ca.a, 0) is (C) Flux through surface formed by joining points (0, a, 0) : (0.—a, 0) 3 q equal 0 54" (D) Flux through surface formed by joining points (0,0, 0) : (0. 0, a) :(0,a.a) : (0, a, 0) is equal to 4 Be,JEE-Physics [ARLEN 44, An electric dipole moment 6=(2.01+3.0)) "Cm is placed in a uniform electric field 45. E=(3.01+2.08)x10°NC1. (A) The torque that E exerts on Pis (0,61-0.4 j-0.98)Nm (B) The potential energy of the dipole is 0.6 (C) The potential energy of the dipole is~0.6 3 (D) If the dipole Four charges are arranged as shown in figure. A point P is located at distance r from the centre of the configuration Assume r >> the field at point P, rotated in the electric field, the maximum potential energy of the dipole is 1.33 (B) is of magnitude 4negr® (C) makes an angle tan“! (2) with x - axis (1) (D) makes an angle tant | ] with x - axis There isa spherical conductor of radius a. A point charge is plac the spherical conductor as shown in figure. ke (A) The electric field at'c’ due to spherical conductor is —+(-i) ata distance 4a from the centre of : (kq_ka (B) Potential at P due to induced charge on spherical conductors |." (C) Net electric field at 'P'is ZERO. (D) Now the conductor is earthed then charge on the spherical conductor is ( 1) COMPREHENSION TYPE Paragraph for Q.No. 47 to 49 A device shown in the figure may be used as an energy analyzer. It separates identical charged particles moving with different kinetic energies. For example B-rays are electrons emitted by some radioactive materials. If we placed a beta emitter at O, all the electrons emitted in direction OA will concentrate at same spot C on the sereen if they have same energy. But if they are emitted with different energies, they will be spread over a region on the screen, Itis this situation that is found experimentally. On the other hand, if a nucleus emits o-particle, itis found that they all have same energies. 1047. 49. 50, Electrostatic For the analysis of the situations, we will ignore gravity and assume that BD can be ignored in comparison to CX. The parallel arrows represent constant electric field Choose the INCORRECT statement, (A) the path of charged particle in region AD is circul: (B) the charged particle shown is positively charged. (C) the speed v of charged particle alter coming outof the electri Ve (D) if source emits neutrons, they will pass through without deflection, Choose the CORRECT statement about displacement d. (A) Itis inversely proportional to the length a, field is more than the initial speed (1) (B) Itis directly proportional to the kinetic energy of incident particle | imi} (©) tis directly proportional to the electric field E. gher 4 (D) For lesser a (charge to mass ratio), itis hi Choose the CORRECT statement. (A) dis a fixed value if'we use a B-emitter _ (B) dis variable if we use a neutron-emitter (C)dis fixed value if we use ana-emitter (1D) dis variable if we use a y-ray source Paragraph for Q.No. 50 & 51 ‘A small, charged bead can slide on a citcular, frictionless, insulating wire frame. A short electric dipole is fixed at the centre of the circle with the dipole’s axis lying in the plane of the circle. Initially the bead is on the plane of symmetry of the dipole, as shown in fig. Ignore the effect of gravity, assuming that the electric forces are much greater than the gravitational ones. (Take : mass of bead = m, 1 charge of bead = Q, radius =r, K = . dipole moment = j5) Mark the CORRECT statement :- (A) Speed of bead at angle 0 is given by v= re | (B) Speed of bead at angle 8s given by v= PRQcoss| initial position mr of bead [pRQcosn] (©) Speed of head at angle @ is given by v= | (D) Speed of bead at angle 0 is given by v pa 11JEE-Physics 51. 52, 35. 56. 37. Mark the CORRECT statement aac aig 2QPK cos (A) Normal reaction between bead and wire as function of 8 is ——s—— (B) Bead will execute periodic and oscillatory motion (C) If wire frame is not present bead will move along electric field lines (D) If wire frame is not present bead will move radially outward Paragraph for Q.No. 52 to 54 Accharge qis moving in XZ plane in acircle of radius ‘a’ centered at origin and another charge 4q is moving in plane y = in acircle of radius ‘b’ centered at (0, ¢, 0) with same angular speed. Such that electric field is zero ata point on y axis at every instant. Choose the CORRECT statement :- b. (A) The ratio is (B) If thei angular speed is doubled then neutral point will shift towards origin (C) The sense of rotation of both the particles must be same (D) Initial X and Z coordinates of both the particles are same The coordinate of neutral point, where electric field is zero is ~ 0.) r . ( a 0.—,0 0.5.0 >) | 0,=,0 oT e o( 4 @)|%5-) O(%3 } (D) Depends on a & b b The ratio of — is a (Ay4e (B) 11 2:1 (D)l4 Paragraph for Q.No. 55 to 57 Two non-conducting plates A & B of radii 2R and 4R respectively are kept at distances x and 2x from the point charge g. A surface cutout of a non conducting shell A is kept such that its centre coincides with the point charge. Each plate and spherical surface carries surface charge density 6. IF, F,, and F be the forces on plate (A) plate (B) and spherical surface (C) due to charge q respectively then ON (B) Fo Pye Py D)Fy If; is lux through surface of (B) due to electric field of (A) and p, be the flux through (A) due to electric field of (B) then (A) 6, = (B) 6, > 65 ©), Fy! (B) Py! > Fy (COP. > Fy (D) none of these Ble 'y becomes F,' then the correct option 12Elocrostties 58, 59, 60. 61. 62, 63. @ a aD) Paragraph for Q. No. 58 to 60 A sphere of radius R has total charge Q. Ifa sphere has volumetric charge distribution as a function of radial distance r the electric field is considered to be radial. Consider a charge density that decreases fr) linearly from p, at the centre to zero at the surface of sphere =p, | 1 = oR) Electric field inside sphere is given by r Qf, r) Me t)o© 4a3e 2 RW) Ome RR) Pee Rw _—Q- 4 AW trek ®) gre, © Bre, R ©) 3ane,R° What is expression for the volume charge density p(t) inside the ball as a function of r:- 3Q r° 4Qr 2Qr° 30 A) ae B) ots D) \FEQ ® aE Re (SER te) Paragraph for Q.No. 61 to 63 An electric dipole (AB) consisting of two particles of equal and opposite charge and same mass is released in an electric field. In the figure are shown field lines without considering effect of field of dipole. es = be ‘The mass centre of the dipole (A) Has no acceleration (B) Has acceleration with positive x and y components (C) Has acceleration with positive x component and negative y-component (D) Has acceleration with negative x component and positive y-component Angular acceleration of the dipole, immediately afterit is released (A) is zero. (B) is clockwise. (Chis Read the following statement anticlockwise. (D) cannot be determined from the given information. Presence of the dipole affects the total electric field at points A and B therefore to calculate force on it the new value of electric field at points A and B should be used Presence of the dipole affects the total electric field at points A and B, Itdoes not matter while calculating force on it because this effect is negligible. Presence of the dipole affects the total electric at points A and B. Itdoes not matter while calculating force on it because a body cannot exert force on itself. Correct statement is/are CTO) (yap j@an (D) Mand (I) 13JEE-Physics MATRIX MATCH TYPE 64. _Ineach figure of column-I, a spherical uniform charge distribution is given in column-II, direction of electric field is represented by arrows. Match the direction of electric field due to charge distribution at given pointin figures of column-1 Column - I Column-I (A) A solid hemisphere, uniformly positive charged direction of (P) [ resultant electric field at point P must be (point P lies on diameter AB as shown) (B) A solid uniformly positive charged hemisphere with a hemispherical cavity and C, and C, are the centres of hemispheres, direction of resultant electric field at point C, can be (C) A solid uniformly positive cha .d hemisphere with a ®) \ hemispherical cavity and C, and C, are the centres of R Where R is radius of hemispheres, C,P = C; R hemisphere and radius of cavity is 5. Direction of (s) | resultant electric field at point P must be (D) A solid hemisphere, uniformly charged, direction of om | resultant electric field at centre C can beBy © ©) Electrostatic Column-1 Electrically neutral thick conducting (P) spherical shell, with point charge at its center.conductoris zero. Electrically neutral thin conducting (Q) spherical shell, with point charge to the right of its center. Electrically neutral thick conducting () spherical shell, with point charge to the right of its centre, Shell is earthed, Electrically neutral thick conducting (S) spherical shell with point charge atitcentre and another identical (T) charge is located outside the conductor Column-II Electric field every where inside the cavity due to charges induced on the inner surface of Electric field everywhere inside the cavity due to charges present on the outer surface of conductor is zero. Electric potential at the center of the cavity due to charges present on inner & outer surface of conductor is zero, Outer surface charge on the conducting shell is zero, Net electric field outside the shell is directed radially away from centre, 15ANSWER KEY 1 4073) 2 % © 4. (84) 5. (-qEa) 6 1 © 8% ©) % © 10. (28) u © 12 © 13. (B) 14. (©) 15. (B) 16. (B) 17, (A) 18, (A) 1%. (D) 20. (D) 21. (D) 22. (B) 23. (C) 24. (C) 25. (D) 26. (D) 27. ) 28. (C) 29, (A) 30. (B) 31. (A) 32. C) 33. ©) 34. (B) 35. ( ) 36. (B.C) 37. ©) 38. (BD) 3% (AC) 40. (A.D) 41. (A,B.C.D) 42. (A.B.D) 4. (AC) 9 44 (ACD) 45. (B.D) 46. (A,B.C.D) 47. (A) 48. (C) 49. ©) 50. (A) 51. (B) 52.) 53. (B) 54. (C) 55. (D) 56. (A) 57.) 58. (C) 59. (B) 60. (D) 61. (B) 62. (B) 63. (D) 64, ASR:BOR:C>R:D>ST 65. A>PQT:BQRT:CQS; DoP 16Capacitor CAPACITOR 2 - SUBJECTIVE TYPE QUESTIONS Figure shows two concentric conducting spherical shell, Ratio of their radii is2. Equivalent capacitance of the system between two shells is found to be N 4a. Find the value of N. In the given network if potential difference between p and q is 2V and C potential difference between a & b. 3C,. Then find the ¢ ¢ The figure shows a circuit consisting of four capacitors. Find the effective capacitance between X and Y. {| AF MMF KE + De Five identical capacitor plates, each of area A, are arranged such that adjacent plates are at a distance ‘d’ apart, the plates are connected to a source of emf V as shown in figure. The charge on plate | is, and that on plate 4 i qy44 _ ye In the circuit shown in figure, initially K, is closed and K, is open. What are the charges on each capacitors. Then K, was opened and K, was closed (order is important), What will be the charge on each capacitor now? [C= IF] faa 1710. 11. In the circuit shown in the f ure, intially SW is open. When the switch is clos through the switch is in the direction to oy 2uF eae ov Find heat produced in the circuit shown in figure on closing the switeh S. 2uF 201C —20nC 50uC | -S0uC! Sp ‘The two identical parallel plates are given charges as shown in figure. Ifthe plate area of either face of each plate is A and separation between plates is d, then find the amount of heat liberate after closing the switch, 3q +4 at ‘The plates of a parallel plate capacitor are given charges +4Q and -2Q. The capacitors then connected across an uncharged capacitor of same capacitance as first one (= C). Find the final potential difference between the plates of the first capacitor Figure shows three concentric conducting spherical shells with inner and outer shells earthed and the middle shell is given a cl the electrostatic energy of the system stored in the region I and Il. Find the capacitance of the system shown in figure, Pte aeCapacitor 12. The plates of a parallel plate capacitor are charged upto 100 volt, A 2mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates increased by 1.6mm. Find the dielectric constant of the plate. 13. Find the ratio between the energy stored in 5 UF capacitor to the 4 uF capacitor in the given circuit in steady state. © 14, Inthe connection shown in the figure the switch K is open and the —— capacitor is uncharged. Then we close the switch and let the capacitor charge up to the maximum and open the switch again. Then (Use the[ "8, R 0 V, R,=10 KO, R,=5 kQ,) i Ni K (i the current through R, be I, immediately after closing the switch (i) the current through R, be I, a long time after the switch was closed (ii) the current through R, be I, immediately after reopening the switch I Find the value of 7 (in ampere”). 15. In the circuit shown in figure R, = R. 10V. The switch is closed at t= 0, find 6R, = 300 MQ, C = 0.01 WF and (a) Charge on capacitor as a function of time. ne Ky (b) energy of the capacitor at t= 20s. ; ll U1 16, _ For the arrangement shown in the figure, the key is closed at t= 0. C, is initially uncharged while C has a charge of 2uC. xe G (a) Find the current coming out of the battery just after switch is closed. Et (b) Find the charge on the capacitors in the steady state condition. on ee eB 17. In the circuit shown in figure the capacitance of each capacitor is equal to C and resistance R. One of the capacitors was charged to a voltage V and then at the moment t = 0 was shorted by means of the switeh S. Find: (a) the current in the circuit as a function of time t. (b) the amount of generated heat. 18, The diagram shows four capacitors with capacitances and break down voltages as mentioned. What should be the maximum value of the external emf source such that no capacitor breaks down? 3CIRV 2C:2kV TCV 3C;2KV 1920, 21. 22, 23. ‘The acitors of 2UF, 3HF and 5yF are independently charged with batteries of emf’s 5V, 20V and 10V respectively. After disconnecting from the voltage sources. These capacitors are connected as shown in figure with their positive polarity plates are connected to A and negative polarity is earthed Now a battery of 20V and an uncharged capacitor of 4uF capacitance are connected to the junction A as shown with a switch S. When switch is closed, find (a) the potential of the junction A. (b) final charges on all four capacitors. ‘The connections shown in figure are established with the switch $ open. How much charge will flow through the switch if itis closed ? TF] uF uv s aura A potential difference of 300 V is applied between the plates of a plane capacitor spaced 1 em apart. A plane parallel glass plate with a thickness of 0.5 cm and a plane parallel paraffin plate with a thickness of 0.5 em are placed in the space between the capacitor plates find (Intensity of electric field in each layer. (i) The drop of potential in each layer. (iii) The surface charge density of the charge on capacitor the plates Given that : kyo, = 6 Kyattin= 2 ‘Two parallel plate capacitors A & B have the same separation d=8.85 x 10 m between the plates. The plate areas of A & B are 0.04 m? & 0.02 m? respectively. A slab of di-electric constant (relative permittivity) K=9 has dimensions such that itcan exactly fll the space between the plates of capacitor B. ee « o © () The di-electtic slab is placed inside A as shown in the figure (a) A is then charged to a potential difference of 110 volt. Calculate the capacitance of A and the energy stored in it. (i) The battery is disconnected & then the di-electric slab is removed from A . Find the work done by the external agency in removing the slab from A (iii) The same di-electric slab is now placed inside B, filling it completely. The two capacitors A & Bare then connected as shown in figure (c). Calculate the energy stored in the system. 2025, 27. 28. 29, Capacitor ‘Two square metallic plates of 1 m side are kept 0.01 m apart, like a parallel plate capacitor, in air in such a way that one of their edges is perpendicular, to an oil surface in a tank filled with an insulating il. The plates are connected to a battery of e.m.f. 500 volt. The plates are then lowered vertically into the oil ata speed of 0.001 m/s. Calculate the current drawn from the battery during the process. [di-electric constant of oil = 11, <,=8.85 x 10-1? C/N? m*] A 10 pF and 20 uF capacitor are connected to a 10 V cell in parallel for some time after which the capacitors are disconnected from the cell and reconnected at t= 0 with each other , in series, through wires of finite resistance. The +ve plate of the first capacitor is connected to the ve plate of the second capacitor. Draw the graph which best describes the charge on the +ve plate of the 20 wF capacitor with increasing time. A capacitor of capacitance C, is charged to a potential V, and then isolated. A small capacitor C is then charged from C,, discharged & charged again, the process being repeated n times. The potential of the large capacitor has now fallen to V, Find the capacitance of the small capacitor. If'V, = 100 volt, V=35volt, find the value of n for Cy =0.2 UF & C=0,01075 uF . Is it possible to remove charge on , this way? In the figure shown initi ly switch is open for a long time. Now the switch is closed at t= 0. Find the charge on the rightmost capacitor as a function of time given that it was intially uncharged. ¥ 5 fries + ‘Two capacitors A and B with capacities 3 uF and 2 uF are charged to a potential difference of 100 V and 180 V respectively. The plates of the capacitors are connected as shown in figure with one wire from each capacitor free. The upper plate of A is positive and that of B is negative. An uncharged 2 uF capacitor C with lead wires falls on the free ends to complete the circuit, Calculate: cy pat tho = uF ov pi (The final charges on the three capacitors (ii) The amount of electrostatic energy stored in the system before and after the completion of the circuit In the circuit shown in the figure initially switch S is open and capacitor is uncharged, Internal resistances of the cells are r, and r,, thei emf’s are equal to © . The potential difference across the cell of internal resistance r, becomes zero long time after closing the switch. Find the value of R in terms of other known physical quantities. All symbols have their usual meaning.JEE-Physics 30. Find the charge which flows trom point A to B, when switch is closed. a aT uF SuF | OuF SUF SMP |__| 31. The capacitors each having capacitance C=2uF are connected with a battery of emf 30V as shown in figure. When the switch § is closed. tn ra (i the amount of charge flown through the battery c i 5 c (ii) the heat generated in the circuit © (iii) the energy supplied by the battery (iv) the amount of charge flown through the switch 306 Jn) & C, (4uF & initial uncharge) are joined in 32, Two capacitors C, (6 uF & initial charge qg = (: series with resistance R (80 ©) as shown in figure. Switch $ is closed at t = 0. Find charge on C, (in HC) at t= 192 ps. 33. If anelectron enters into a space between the plates of a parallel plate capacitor at an angle 8, with the plates and leaves at an angle 8, to the plates the ratio of its kinetic energy while entering the capacitor to that while leaving will be 34, Calculate the capacitance of a parallel plate condenser, with plate area A and distance between plates 4, when filled with a medium whose permittivity varies as ; (x)= ey +Bx fordHF © 15 uF (D) none An infinite number of identical capacitors each of capacitance 1}. F are connected as in adjoining figure. Then the equivalent capacitance between A and B is 1 1 fal Faecal HHHKSHH HH Sam H] TH Hibapaatoh HY A B (A) lwk (B) uF (©) 12 uF yx Four identical capacitors are connected in series with a battery of emf 10V. The point X is earthed. Than the potential of point A is (A) 10 (B)1SV k ©-15V Mov For the circuit shown here, the potential difference between points A and B is (A) 2.5V (B)75V @Wwv (D) Zero 23JEE-Physics 40. a2. 4B. 44, 45. 46. 47. 48. Th the given cireuit it charge on On capacitor Is 10 nC, then charge on 4 nF capacitor will be (A) 40 uc i (B) 10 nC (©)20uc (D) 30nC Inthe citeuit shown, the energy stored in 114F capacitor is (A) 40 (B) 64 (C)32uI (D) none = SUF A capacitor of capacitance Cis initially charged to a potential difference of V volt, Now itis connected toa battery of 2V Volt with opposite polarity. The ratio of heat generated to the final energy stored in the capacitor will be (A) 1.75) (B) 2.25 (25 (D) 1/2 Three plates A, B and C each of area 0.1 m? are separated by 0.885 mm irom each other as shown in the figure. A 10 V battery is used to charge the system. B——4i +4 The energy stored in the system is — (A) Lu (B) 107 wy (C) 102 wW (D) 103 wh Five conducting parallel plates having area A and separation between them d, acs are placed as shown in the figure. Plate number 2 and 4 are connected wire and 12} 3) ss between point A and B, a cell of emf Eis connected. The charge flown through the ellis 3 egAE 4d 2 t9AE SHAE. py DAE 3 d Oa Ona A parallel plate capacitor has an electric field of 10°V/m between the plates. If the charge on the capacitor plate is IC, then the force on each capacitor plate is (A) 0.1Nt (B) 0.05Nt (C) 0.02Nt (D) 0.01Nt A paralle-plate capacitoris connected to aresistance less circuit with a battery until the capacitors fully charged. The hattery is then disconnected from the circuit and the plates of the capacitor are moved to half of their original separation using insulated gloves. LetV,,., be the potential difference across the capacitor plates when the plateshave moved. Let V,,, be the potential difference across the capacitor plates when they were connected Yew to the battery 7" = old 1 1 Ay B) > © (D)2 A capacitor of capacitance C is charged to a potential difference V from acell and then disconnected. from it, A charge +Q is now given to its positive plate. The potential difference across the capacitor is now F Q sve Q > (ayy BV+G OV+ 5G W)V- G.ifV». Bodies 2 and 3 are initially uncharged. "Body 2 is touched with body 1. Then, body 2 is removed from body 1 and touched with body 3, and then removed." This process is repeated N times. Then, the charge on body 1 at the end must be (A) Q38 (B) QBN (© Qs (D) None Three long concentric conducting cylindrical shells have radii R, 2R and 2y2 R. Inner and outer shells are connected to each other. The capacitance across middle and inner shells per unit length i eee Re (A) aa (B) in2 (Cc) In2 (D) None A parallel plate capacitor is connected from a cell and then isolated from it, Two dielectric slabs of dielectric constant K and 2K are now introduce in the region between upper half and lower half of the plate (as shown in figure). The electric field intensity in upper half of dielectric is E, and lower half is B, then (A)E, = 26, (B) Electrostatic potential energy of upper half is less than that of lower half (C) Induced charges on both slabs are same (D) Charge distribution on the plates remains same after insertion of dielectric 25JEE-Physics or is 5d Let the positively charged plate is at x=0 and negatively charged plate is_at x=5d, Two slabs one of conductor and other of a dielectric of equal thickness d are inserted between the plates as shown in figure. Potential versus distance graph will look like o v v v “~ @) 7 © ©) ~ 55. A capacitor stores 60UC charge when connected across a battery. When the gap between the plates is filled with a dielectric , a charge of 1201C flows through the battery. The dielectric constant of the material inserted is 54, The distance between plates of a parallel plate capaci sO ed ead ERM Sd (al (B)2 3 (D) none 56. Condenser A has a capacity of 15 F when itis filled with a medium of dielectric constant 15. Another condenser B hasa capacity 1 4tF with air between the plates. Both are charged separately by a battery of 100V . After charging, both are connected in parallel without the battery and the dielectric material heing removed. The common potential now is (A) 400V, (B) 800V. (C) 1200V (D) 1600V 57. Inthe adjoining figure, capacitor (1) and (2) have a capacitance a ‘2 A 1 “C’ each, When the dielectric of dielectric consatntK is inserted ; < between the plates of one of the capacitor, the total charge a} ! 2 flowing through battery is KCE + ste © & (A) Faq itom Bio (B) AF HromCwB CO) from C to B + py (KRaDEE from B to (D) K+) CE K+ 58. A capacitor C 1kQ_ and a battery of emf 9V. The switch S has been closed for long time 00 AF is connected to three resistor each of resistance so as to charge the capacitor. When switch $ is opened, the capacitor discharges with time constant (A) 33 ms (B) Sms (C)3.3ms (D) 50 ms 59, Three capacitors 2 F, 3 F and 5 pF can withstand voltages to 3V, 2V and IV respectively. Their series combination can withstand a maximum voltage equal to (A) 5 Volts (B) B16) Volts (C) (26/5) Volts (D) None. 2660, 61. 62. 63. 64. 65. Capacitor In the circuit shown, the cell is ideal, with emf = 15 V, ach resistance is of 3Q. The potential difference across the capacitor is aisv i (A) zero. (B)9V. (C)12V (D)1SV In the circuit shown, the charge on the 3F capacitor at steady state will be 3 20 2 (A) 6 uC (B) 4uC (©) zue (D) 3 uC In the transient circuit shown the time constant of the circuit is : R © v. OR Na gk R 3 1 7 (A) = Src (B) SRC © re (by = RC In the R-C circuit shown in the figure the total energy of 3.6 x10 J is dissipated in the 10.Q resistor when the switch S is closed. The initial charge on the capacitor is, toa 60. (A) 60 wc (B) 120 pe (C) 60. JZ we @) Fue A capacitor of capacitan which potential differenc Cis charged by a battery whose internal resistance is R. The time after ross resistor becomes n times to that across capacitor is (#4) (_n) ( n_) inf Lt inf 2 + RCin{ , (A) RCEn- 7 (B) Rcin| -) (C) RCi‘n 7) (D) RCin(1+n) In the circuit shown initially C, & C, are uncharged. After closing the switch (A) The charge on C, is greater that on C, i oi (B) The charge on C, and C, are the same kc-SuF (C) The potential drops across C, and C, are the same (D) The potential drops a greater than that across C, a ross C 2767. 68, 69, 70. n. ‘A capacitor of capacity C is charged to a steady potential difference V and connected in series with an open key and a pure resistor 'R’. At time t= 0, the key is closed. If I = current at time t, a plot of log I against '! is as shown in (1) in the graph, Later one of the parameters i.e. V, R or Cis changed keeping the other two constant, and the graph (2) is recorded, Then (A) Cis reduced (B) C is increased (©) Ris reduced (D) Ris increased log! ‘As shown in circuit C, isi (A) Charge distribution will not take place inaaeeal (B) Charge & energy distribution will take place but total — energy & charge of system (circuit) will remain constant (C) Charge will decrease © (D) Circuit will release some energy MULTIPLE CORRECT ANSWER TYPE A circuit shown in the figure consists of a battery of emf 10 V and two capacitance C, and C of capacitances 1.0 uF and 2.0 uF respectively, The potential difference V, — Vp is SV (A) charge on capacitor C, isequal to charge on capacitor C, (B) Voltage across capacitor C, is SV. Ao Fa f-|Fes (©) Voltage across capacitor C, is 10V we (D) Energy stored in capacitor C, nes the energy stored in capacitor C,. The capacitance of a parallel plate capacitor is C when the region between the plate has air. This region is now filled with a dielectric slab of dielectric constant k. The capacitor is connected to a cell of emf E, and the slab is taken out (A) charge CE(k — 1) flows through the cell (B) energy E°C(k ~ 1) is absorbed by the cell. (C) the energy stored in the capacitor is reduced by E2C(k~ 1) 1 (D) the external agent has to do > E?C(k — 1) amount of work to take the slab out. A parallel plate air-core capacitor is connected across a source of constant potential difference. When a dielectric plate is introduced between the two plates then (A) some charge from the capacitor will flow back into the source. (B) some extra charge from the source will flow back into the capacitor. (C) the electric field intensity between the two plate does not change. (D) the electric field intensity between the two plates will decrease. A parallel plate capacitor of plate area A and plate seperation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and the work done on the system. in question, in the process of inserting the slab, then AV oKAV, ae @AV7f, 1) 7] ©E 7 d e & (A) Q= (B)Q= 28n. B. 14. 1. 16. 71. Capacitor A parallel plate capacitor has a parallel slab of copper inserted between and parallel to the two plates. without touching the plates. The capacity of the capacitor after the introduction of the copper sheet is (A) minimum when the copper slab touches one of the plates. (B) maximum when the copper slab touches one of the plates (C) invariant for all positions of the slab between the plates. (D) greater than that before introducing the slab. Two thin conducting shells of radii R and 3R are shown in the figure. The outer shell carries a charge +Q and the inner shell is neutral. The inner shell is earthed with the help of a switeh S. (A) With the switch S open, the potential of the inner sphere is equal to that of the outer. (B) When the switch $ is closed, the potential of the inner sphere becomes zero. (©) With the switch $ closed, the charge attained by the inner sphere is ~ Q/3. Sh (D) By closing the switch the capacitance of the system increases. The circuit shown in the figure consists of a battery of emf e = 10 V ; a capacitor of capacitance C 1.0 pF and three resistor of values R, =20, R, =2Q and R, = 1©. Initially the capacitor is completely ® (B) The current through resistor R, a long time after the switch closed is SA. (C) The ratio of current through R, and R, is always constant, (D) The maximum charge on the capacitor during the operation is SHC. In the circuit shown in figure C, = C, = 2uF. Then charge stored in uncharged and the switch $ is open, The switch S is closed at (= 0. ; (A) The current through resistor R, at the moment the switch closed is zero. ik tee } J RR To I (A) capacitor C, is zero (B) capacitor C, is zero +t LT) oT (C) both capacitor is zero (D) capacitor C, is 40 uC Lo A dielectric slab fills the space between the plates of a parallel-plate capacitor, The magnitude of the bound charge on the slab is 75% of the magnitude of the free charge on the plates. The capacitance of the capacitor is 480 wl’ with the slab inserted, The maximum charge that can be stored on the capacitor is 240 ey1F,,,.. where E,,,. is the breakdown field. Choose the CORRECT statement(s):~ (A) The dielectric constant for the dielectric slab is 4 (B) Without the dielectric, the capacitance of the capacitor would be 360 nF. (©) The plate area is 601? tric slab is having the same area as the capacitor plate but the width half that of the capacitance would be 192uF. Mark the CORRECT statement(s) regarding the current I through the battery in the circuit shown in figure. (A) Immediately after the key K is closed, I e (B) Immediately after the key K is closed, I (C) Long time after key K is closed, 1 (D) Long time after key K is closed, I= RR 29JEE-Physics EAALEEN 78. Figure shows two identical capacitors A & B with identical dielectric inserted between them and are connected to a battery, Now the slab of capacitor B is pulled out with battery connected (A) During the process current flows counter clockwise in the circuit (B) Finally charge on capacitor B will be less than that on capacitor A. (©) Blectric field in capacitor A reduces in magnitude. 4 (D) During the process, internal energy of the battery increases. 79. In the circuit shown in figure. initially key K, is closed and key K, is open, Then K, is opened and K, is closed (order is important). [Take Q’, and Q', as charges on C, and C, and V, and V, as voltage respectively. Then K, K (A) charge on C, gets redistributed such that V, (B) charge on C, gets redistributed such that Q’ (C) charge on C, gets redistributed such that C,V, + CV, Q 80. A parallel plate capacitor is connected to a battery as shown in figure, Consider two situations: (D) charge on C, gets redistributed such that Q', + Q’ A: Key K is kept closed and plates of capacitors are moved apart using insulating handle. B: Key K is opened and plates of capacitors are moved apart using insulating handle Choose the correct option(s). 5 (A) In: Q remains same but C changes. | (B) In B : Vremains same but C chan; (©) INA: Vremains same and hence Q changes. (D) InB : Q remains same and hence V changes. COMPREHENSION TYPE Paragraph for Q. No. 81 and 86 The charge across the capacitor in two different RC circuits 1 and 2 are plotted shown in figure. a nay 1 o! n 81. Choose the correct statement(s) related to the two circuits. (A) Both the capacitors are charged to the same charge. (B) The emf's of cells in both the (C) The emf of the cells may be different. cuit are equal, (D) The emf E, is more than E, 82. Identify the correct statement(s) related to the R,. R,,C, and C, of the two RC circuits, (A) R, > Rif E (BC, Q, @B)V>Vy (OE>E, (D)U 65 (B) E, > Ep (© Ep=By (D) 6, =6, Three identical capacitors A, B and C are charged to the same potential and then made to discharge through three resistances R,. Ry and Re. where R,>R,>R,. Their potential differences (V) are plotted against time t, giving the curves 1, 2 and 3. The relations between A, B, C and 1, 2, 3 is/are - (ISA (B) 258 @isc (D)35A Two identical capacitors, have the same capacitance C. One of them is charged to potential V, and the other to V,. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is © toby v,} Paragraph for Q. No. 87 to 89 In the circuit shown initially the switches are open and capacitors are uncharged. Switches S, and S, are closed simultaneously at t= 0. 6 Resa de Ne wae Lyd Charge on capacitor C, is (A) 12uc (B) 24 0c (©)48 nC (D) None of these Now switch S, is opened after a long time interval then charge flow through the S, is (A) 12uc (B) 24 uC (©) 36 nC (D) 48. uc Inabove question the amount of heat dissipated in r istors (A) 136 wt (B) 272 Wh (©)68 wh (D) None of these 31JEE-Physics EAALEEN 90, m1. 92. 93. 94, 95. Paragraph for Q. No. 90 to 93 Ahighway emergency flasher uses a 120 volt battery. a 1 MQ resistor, a Qreshiamp 1 WF capacitor anda neon flash lamp in the circuit shown in the figure. ‘The flash lamp has a resistance more than 10" Q when the voltage across Com itisless than 110V. Above 110, the neon gas ionizes, the lamp’s resistance drops to 10 Q, and the capacior discharges completely. Until the capacitor voltage reaches the breackdown voltage V,, = 110 V, the large resistance of the flash lamp ensures that it draws a negligible current. RIM: Rav The capacitor charges as ifthe lamp were absent. ALV,, however, the lamp resistance quickly becomes negligible, and the capacitor discharges through the lamp as if the battery and the series resistor were absent, The time between the flashes is the time for the capacitor to charge to V,, The flash duration is roughly the time for the capacitor to discharge through the lamp, or about 3 time constant of the capacitor—lamp circuit, The flash energy is the stored energy in the capacitor at 110 volt, The flash interval is found by solving for the time when the capacitor voltage is V, = 110 V. V,=e(1—e"%), fn 12 = 2.5), Flash interval is (A)2s (B) 25s (52s @)Is Time constant (7, of the capacitor-lamp circuit is- (A) 20 ps (B) 15 ps (©) 30 ps (D) 10 ps Flash duration is (A) 10 ps (B) 20 ps (C)30 ps (D) Sus The energy in the flash is (A) 6.1 mJ (B)6.1I ©3m (D) 12.2 mJ Paragraph for Q. No. 94 to 95 figure the switch is closed at t= Josing the switch (A) the battery del (B) no current flows through C (©) Voltage drop act (D) the current through the battery decreases with time finally becomes zero. fers maximum current, 88 R, is zero. Along time after closing the switch (A) voltage drop across the capacitor is E. E (B) current through the battery is RFR, (C) energy stored in the capacitor is, (D) current through the capacitor becomes zero, 3296. 97. (A) (B) © () Capacitor MATRIX MATCH Column-I Plates of an isolated, charged, parallel plate, air core capacitor are slowly pulled apart. A dielectric is slowly inserted inside an isolated and charged parallel plate air cored capacitor to completely fill the space between plates. Plates of a parallel plate capacitor connected across a battery are slowly pulled apart. A dielectric slab is slowly inserted inside a parallel plate capacitor connected across a battery to completely fill the space between, plates. TYPE Column-II Electric energy stored inside capacitor increases in the process. Force between the two plates of the capacitor remain unchanged ) @Q (R) Electric field in the region between plates remain unchanged. Total electric energy stored inside capacitor decreases in the process (S) (T) Electric field in the region decreases. Column—t shows some parameters after completion of event and Column—II shows tha arrangements to which these parameters belong. “ (B) © () Column-1 Work done by external agent is negative (P) Electric field between platesincreases — (Q) Energy of capacitor decreases (R) Force between plates remains constant (8) a Column—I Dielectric is being removed slowly from acharged capacitor t Dielectric being introduced slowly while battery is connected rf}: — Dielectric is being introudced slowly in acharged capacitor Plates of capacitor are being slowly moved closer v 4 Plates of capacitor are being moved slowly ina charged capacitor se | 33JEE-Physics EAALEEN ANSWER KEY AgV 2Aq)V 8 7 . 30 . HP . , 1) 2 30V 3 Hl 4. a 6 60 Nc, Ato B 0) ead 9 3Q/2C @) 264A se oe Ay 25 eA 10. FU, =2K@rq)y/35r We 5-4 12, 6) 13. (0.8) 14. (750) 15, (a) q= 0.05(1 ~e*) WC (b) 0.125 pT 20Re Loy 16. 17. eRe: Cb) FOV? 18, 100 20, (a) “>> volts: (b) 28.56 mC, 42.84 mC, 71.4 mC, 22.88 mC 21, 12 22, (i) LS x 104 Vim, 4.5 x 10! W/m, (i) 75 V, 225 V. (iii) 8 x 107 Chm? 23, (4) 0.2x LOB, 1.2.x 105J; (ii) 4.84% 105 J; Gii) LI x 10° J 24, 4.425 x 10° Ampere 25. Try.en , 26. | -1]= 0.01078 WF, n = 20, No 27. g | 28. Qy=90 UC, Qy = 150 WC, Qo = 210 UC, U, = 47.4 mJ, U;= 18 mJ 4 400 2 E ; 29. 7, rT) 30. 7 uC 31. (i) 20uC, (ii) 0.3 mJ, (iii) 0.6 mJ (iv) 60 WC ; BA /', (2&0 +Bd 32, 012 33. 08" @.,/c0s? 8, 2/ ee }Capacitor (B) 37. (B) 38. (B) 39. (B) 40. (A) 41. (A) 42. ©) 43. (B) 44. (B) 45. (B) 46. (B) 47. (B) 48. ©) 49. (D) 50. (C) 51. (A) 52. (B) 53. (B) 54. (B) 55. (C) 56. (B) 357. (D) 58. (D) 59. (B) 60. C) 61. (B) 62. ©) 63. (B) 64. (A) 65. (B) 66. (B) 67. (D) 68. (AD) 69% (ABD) 70. (B.C) 7. (ACD) 72. (GD) 73.(A.B.C.D) 74. (A,B.C.D) 75. (B,D) (A.C.D) 77. (AC) 78(ACD) 79 (AD) 80. (CD) BLL (AC) 82D) 83. (A) 84. (A) 85. (BCD) 86. © 87. ©) 88. (D) 89. (A) 9. (C) 91. (D) 92. ©) 93. (A) 94. (AC) 98. (BCD) 9. (AP.QR):(B) 9(Q.8,T) (OS. 97. (A) > (QI ) :(B) > (PS) 3 (C) > (RT) :(D) > (PRT)Physic ALLEN)” JEE-Physics EevAMen CURRENT ELECTRICITY SUBJECTIVE TYPE QUESTIONS 1, ind the current I & voltage V in the circuit shown. oy ind the equivalent resistance of the circuit between points A and B shown in figure (each branch is of resi 19) fa . Ia cell of constant E.M.F. produces the same amount of the heat during the same time in two independent resistors R, and R,, when they are separately connected across the terminals of the cell, one after the another, find the internal resistance of the cell. 4. Inthe circuit shown in figure, all wires have equal resistance r. Find the equivalent resistance between ‘Aand B. E ¢ / e . A For what value of R in circuit, current through 40 resistance is zero. [fle lov 6. Inthe circuit shown in figure the reading of ammeter is the same with both switches open as with both closed. Then find the resistance R. (ammeter is ideal) L000 ue Lb den OY Hav 7. Anelectrical circuit is shown in the figure. Calculate the potential difference across the resistance of 400 ohm, as will be measured by the voltmeter V of resistance 400 ohm, either by applying Kirchhoft’s rules or otherwise,8. 9. 10. 1 Current Electricity reoa_[ipna 3000 Ig L__4, J TV Ithe switches S,, S, and S, in the figure are arranged such that current through the batery is minimum, find the voltage across points A and B. Sth A battery of emf ¢) = 10 V is connected across a 1 m long uniform wire having resistance 10Q/m. Two cells of emfe, =2V and e, = 4V having internal resistances 1Q and 5Q respectively are connected as shown in the figure. If'a galvanometer shows no deflection at the point P, find the distance of point P from the point A A network of resistance is constructed with R, & R, as shown in the figure. The potential at the points 1, 2,3... Nate V,. V,. Vj. V, respectively each having a potential k time smaller than previous one, | id RV wi my in terms of k. The resistance of the galvanometer G in the circuit is 25Q. The meter deflects full scale for a current of 10 mA. The meter behaves as an ammeter of three different ranges. The range is 0-10A, if the terminals O and P are taken; range is 0-1 A between O and Q: range is 0-0.1 A between O and R. Calculate the resistance R,, R, and R,. 37