# Capacitance and Capacitor

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1 Capacitance and Capacitor 1. Choose the correct statement(s) about the point charge point charge is a concept (b) point charges do not exist in reality the field produced by a point charge in inversely proportional to the square of the distance (d) the concentration of a charge at a point is called a point charge. dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x = 0 and positive plate is at x = 3d. The slab is equidistant from the plates. The capacitor is given some charge. s x goes from 0 to 3d the magnitude of the electric field remains the same (b) the direction of the electric field remains the same the electric potential increases continuously (d) the electric potential increases at first, then decreases and again increases 3. small sphere of mass m and having charge q is suspended by a light thread tension in the thread may reduce to zero if another charged sphere is placed vertically below it (b) tension in the thread may increases to twice of its original value if another charged sphere is placed vertically below it tension in the thread is greater than mg if another charged sphere is held in the same horizontal line in which first sphere stays in equilibrium (d) tension in the thread is always equal to zero 4. point charge q is placed at origin. Let E r, E r and E r C be the electric field at three points (1,, 3) (1, 1, 1) and C(,, ) due to charge q then r r r r E E (b) E EC r r E = 4 E C 5. Which of the following is/are incorrect statement? electric field is always conservative r r (d) E = 8 E C (b) electric field due to a varying magnetic field is non-conservative electric field due to a stationary charge is conservative (d) electric field lines are always closed loops 1

2 6. parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with the capacitor are given by Q 0, V 0, E 0 and U 0 respectively. dielectric slab is now introduced to fill the space between the plates with the battery still in connection. The corresponding quantities now given by Q, V, E and U are related to previous ones by Q > Q 0 (b) V > V 0 E > E 0 (d) U > U 0 7. The positive charge +Q is located at centre O of a thin metallic spherical shell. Select the correct statement(s) from the following the electric field at any point outside the shell is zero (b) the electric potential at any point outside the shell is point from O 1 Q, where r is the distance of 4πε r 0 the outer surface of the spherical shell is an equipotential surface (d) the electric field at any point inside the shell other than O is zero 8. Two large, parallel conducting plates are placed close to each other. The inner surfaces of the two plates have surface charge densities +σ and σ. The outer surfaces are with out charge. The electric field has a magnitude of (b) σ ε 0 σ ε 0 σ ε 0 in the region between the plates in the region between the plates in the region outside the plates (d) zero in the region out side the plates 9. In an isolated parallel plate capacitor of capacitance c, the four surfaces have charges Q 1, Q, Q 3 and Q 4 as shown, the potential difference between the plates is Q1 + Q C Q (b) C Q 1 Q 3 Q3 C 1 (Q Q ) (Q Q ) C (d) [ + ] Q Q 4

3 10. non-conducting solid sphere of radius R is uniformally charged. The magnitude of electric field due to the sphere at a distance r from its centre increases as r increases for r < R (b) decreases as r increases for 0 < r < decreases as r increases for R < r < (d) is discontinuous at r = R 11. circular ring of radius R with uniformly distributed charge q is placed in the yz-plane with its centre at the origin as shown in figure, then the electric intensity is maximum at x = ± R (b) the electric intensity is maximum at x = ± R x the maximum intensity is (d) the maximum intensity is q 6 3 πε R q πε R 0 z y 1. Three concentric conducting spherical shells have radii r, r and 3r and charges q 1, q and q 3 respectively innermost and outer most shells are earthed as shown in figure. Select the correct alternative(s) q1 + q = q q (b) q1 = 4 q3 3 q = 1 q3 1 (d) = q 3 3r q 1 r r q q The electric field intensity at a point between the plates of a charged isolated capacitor is proportional to the square of the charge on the plates (b) proportional to the charge on the plates inversely proportional to the distance between the plates (d) independent of the distance between the plates 14. conductor is given a charge of amount +Q and then placed inside, a deep metal ca, with out touching it 3

4 the potential of a does not charges when it is placed inside (b) if is earthed, +Q amount of charge flows from it into the earth if is earthed, the potential of is reduced +Q (d) none of these 15. The electric potential in a region along the x-axis varies with x according to the relation V = 4 + 5x, then (x) potential difference between the points x = 1 and x = is 15 volt (b) force experienced by one coulomb charge at x = 1 will be 10N force experienced by the above charge will be towards +X-axis (d) a uniform electric field exists in this region along the X-axis 16. circular ring carries a uniformly distributed positive charge. The electric field (E) and potential (V) varies with distance (r) from the centre of the ring along its axis as E E (b) r r V V (d) r r 17. capacitor C is charged to a potential V by a battery. The e.m.f. of the battery is V. It is then disconnected from the battery and again connected with its polarity reversed to the battery the work done by the battery is CV (b) the total charge that passes through battery is CV the initial and final energy of the capacitor is same (d) the work done by the battery is CV 18. If at a distance r from a positively charged particle, electric field strength and potential are E and V respectively, which of the following graph(s) is/are 4

5 V V O E (b) O E V V (d) O E O E 19. n elliptical cavity is carved within a perfect conductor. positive charged q is placed at the centre of cavity. The point and are on the cavity surface as shown in figure. Then electric field near in the cavity is equal to electric field war in cavity (b) charge density at is equal to charge density at potential at is equal to potential at (d) total electric flux through the surface of cavity is equal to q ε 0 q 0. In the circuit shown c 1 + q 1 c + + 4µ F =10µF q 3 + 6µF q + 4µ F 100V q = 80 µ C (b) q 3 = 160 µ C q = 10 µ C, q3 = 0 (d) it is impossible to find q and q 3 unless c 1 and c are known 1. Two identical parallel plate capacitors of same dimensions joined in series are connected to a D.C. source. When one of the plates of one capacitor is brought closer to the other plate 5

6 the voltage on the capacitor whose plates come closer is greater than the voltage on the capacitor whose plates are not moved (b) the voltage on the capacitor whose plate comes closer is smaller than the voltage on the capacitor whose plates are not moved the voltage on the two capacitor remain equal (d) the applied voltage is divided among the two inversely as the capacitance. parallel plate capacitor is first connected to D.C. source. It is then disconnected and then immersed in a liquid dielectric, then the capacity increases (b) the liquid level between the plates increases the liquid level will remain same as that outside the plates (d) the potential on the plates will decreases 3. Identity the correct statement(s) about electric intensity (E) and electric potential (V). E and V may be zero simultaneously (b) E = 0 but V 0 E = 0 but V = 0 (d) E 0 and V 0 4. The electric potential at a certain distance from a point charge is 600 Volts and the electric field is 00 N/C. Which of the following statement(s) will be true the magnitude of charge is C (b) the distance of the given point from the charge is 3m the potential at a distance of 9m will be 00 Volt (d) the work done in moving a point charge of 1 µc from the given point to a point at a distance of 9 m will be J. 5. positively charged thin metal ring of radius R is fixed in the xy-plane with its centre at the origin O. negatively charged particle P is released from rest at the point (0,0, Z 0 ) where Z 0 > O. Then motion of P is periodic for all values of z 0 satisfying 0 < z0 < (b) simple harmonic, for all values of z0 satisfying 0 < z0 R approximately simple harmonic, provided z 0 < < R (d) such that P crosses O and continues to move along the negative z-axis towards z = 6. In a parallel plate capacitor of plate area, plate separation d and charge Q, the force of attraction between the plate is F, then 6

7 F Q F d (b) (d) 1 F 1 F d 7. The capacitor C is initially without charge. X is now joining to Y for a long time, during which H 1 heat is produced in the resistance R. X is now joined to Z for a long time, during which H heat is produced in R, then H 1 = H 1 (b) H1 = H c R H 1 = H (d) the maximum energy stored in C at any time is H 1 Z X 8. In the given circuit, in steady state R = 0Ω 14V c 1 = 10µ F c = 4µ F the potential difference across c 1 is 4 volt (b) the potential difference across c is 4 volt the charge on each of c 1 and c is 40 µc (d) the charges on c 1 and c are in the ratio : 7 9. Two identical charge +Q are kept fixed some distance apart. small particle P with charge q is placed midway between them. If P is given a small displacement, it will undergo simple harmonic motion, if q is positive and is along line joining the charges (b) q is positive and is perpendicular to the line joining the charges q is negative and is perpendicular to line joining the charges (d) q is negative and is along the line joining the charges 30. parallel plate capacitor is charged with a battery and the battery remains connected. Then, all the charge drawn from the battery is stored in the capacitor (b) all the energy drawn from the battery is stored in the capacitor one half the energy drawn from the battery is stored in the capacitor 7

8 (d) the potential difference across capacitor increases exponentially and then attains a constant value 31. Capacitor c 1 of capacitance 1 µf and capacitor c of capacitance µf are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time t = 0, the current in each of the two discharging circuits is zero at t = 0 (b) the current in the two discharging circuits at t = 0 are equal but not zero the current in the two discharging circuits at t = 0 are unequal (d) c 1 loses 50% of its initial charge sooner than c loses 50% of its initial charge 3. block of mass m is attached to a spring of force constant k charge on the block is q. horizontal electric field E is acting in the direction as show block is released with the spring in unstretched position block will execute SHM (b) Terne period of oscillation is π m k k E q,m mpti tude of oscillation is qe k smooth (d) block will oscillate but not simple harmonically 33. deuteron and an α-particle are placed in an electric field. The forces acting on them are F 1 and F and their acceleration are a 1 and a respectively. Then F 1 = F (b) F 1 F a 1 = a (d) a 1 a 34. parallel plate capacitor of plate area and plate separation d is charged to potential V and then battery is disconnected. slab of dielectric constant k is then inserted between the plates of the capacitor so as the 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 work done on the system in question in the process of inserting the slab, then ε V 0 ε0 Q = (b) Q = kv d d V E = (d) kd ε V 1 0 W = 1 d k 35. In this circuit shown in figure, 8

9 1V 1 c 1 µ FE c 8µ F E 6V the charge on c is greater than on c 1 (b) the charge on c 1 and c are the same the p.d. across c 1 and c are same (d) the p.d. across c 1 is greater than that across c 36. Two point charges q each are fixed at (a, 0) and ( a, 0). third charge Q is placed at origin. Electrostatic potential energy of the system will increases if Q is slightly displaced along x-axis Y (b) decreases if Q is slightly displaced along x-axis increases if Q is slightly displaced along y-axis (d) decreases if Q is slightly displaced along y-axis q ( a,0) O Q q (a,0) X 37. In the circuit shown in figure c 1 = c = µf, then charge stored in 1Ω Ω 3Ω c 1 c Ω 1Ω 3Ω 10V capacitor c 1 is zero (b) capacitor c is zero both capacitors is zero (d) capacitor c 1 is 40µC 38. n electric dipole of dipole moment 10 6 cm is released from rest in uniform electric field 10 V/m at an angle θ = 60 o. Maximum rotational kinetic energy of the dipole is say k and maximum torque during the motion is I, then k = J I = Nm (b) k = J (d) I = Nm 39. wire having a uniform linear charge density λ, is bent in the form of a ring of radius R. Point as shown in the figure, is in the plane of the ring but not at the centre. Two elements 9

10 of the ring of lengths a 1 and a substend very small same angle at the point. They are at distances r 1 and r from the point respectively r1 the ratio of charge of element a 1 and a is r (b) the elements a, produced greater magnitude of electric field at than element a the element a 1 and a produce same potential at r r 1 a 1 (d) the direction of net electric field at is towards element a a 40. The figure shows, a graph of the current in a discharging circuit of a capacitor through a resistor of resistance 10Ω the initial potential difference across the capacitor is 100V 1 (b) the capacitance of the capacitor is F 10ln the total heat produced in the circuit will be 500 J ln i 10.5 (d) the thermal power in the resistor will decrease with a 1 time constant s ln s t Magnetic Field 1. If a long copper rod carries a direct current, the magnetic field associated with the current will be only inside the rod both inside and outside the rod (b) only outside the rod (d) neither inside nor outside the rod. charge particle moves with velocity v r in a uniform magnetic field r. The magnetic force experienced by the particle is always zero (b) never zero zero if r and v r are perpendicular 3. n electric charge in uniform motion produces (d) zero if r and v r are parallel 10

11 an electric field only both electric and magnetic fields (b) a magnetic field only (d) no such field at all 4. Two parallel wires carrying currents in the same direction attract each other because of potential difference between them electric force between them (b) mutual induction between them (d) magnetic force between them 5. conducting circular loop of radius r carries a constant current i. It is placed in uniform magnetic field such that is perpendicular to the plane of loop. The magnetic force acting on the loop is i r (b) π i r zero (d) π i r 6. straight steel wire of length l has a magnetic moment M. When it is bent in the form of a semi circle, its magnetic moment will be M (b) M π M π (d) Mπ 7. current I flows in an infinitely long straight conductor along the positive X-axis, as shown in the figure. t the point a the direction of magnetic field is along the positive Y-axis (b) along the negative Y-axis along the positive Z-axis (d) along the negative X-axis 8. The magnitude of magnetic induction produced by an infinite sheet of current with linear current density j at a distance r is given by Y I a X µ 0 j (b) µ 0 j µ 0 j µ 0 (d) j r r r r 9. mpere s law states Ñ dl = m0 I Choose the correct statement ò I is the current enclosed at the centre of the loop (b) r is the magnetic field produced by the enclosed current only. 11

12 It is not valid for a straight wire of finite length (d) ll the above 10. stream of electron is flowing in a solenoid conductor as indicated below 1 The entire solenoide behaves like the south pole of magnet (b) The entire solenoide behaves like north pole of magnet Face -1 behaves like north pole and Face- like south pole (d) Face -1 behaves like south pole and Face- like north pole 11. X, Y and Z are three mutually perpendicular axes. proton moving with a constant velocity along the X-axis, the magnetic field along the X-axis. Indicate whether the force on the proton acts along. Z-axis X-axis (b) Y-axis (d) bisector of Z and Y-axes 1. The north pole of a magnet is brought near a stationary positively charged conductor. the north pole will exert a force which will attract the conductor not affect the conductor at all (b) try to repel the conductor (d) repel the north pole itself 13. Two protons move parallel to each other with equal speed m/s. The ratio of magnetic force and electric force between them is (b) (d) Two long parallel wires separated by a distance r have equal current I flowing, each. wire experiences a magnetic force F N/m. If the distance r is increased to 3r and current in each wire is reduced to I. The force between them will be 3 3F N / m (b) 9 F N/m F N / m 9 (d) F 7 N / m 1

13 15. circular loop has radius R and current I flows through it, another circular loop is of radius R and a current of I flows through it. Ratio of magnetic fields at their centres is 1 4 (b) 1 (d) circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be 1 th to its value at the centre of the 8 coil is R 3 (b) R 3 R 3 (d) 3 R 17. person is facing magnetic north pole, an electron infront of him flies horizontally towards north and then deflects towards east. He is in/at northern hemisphere equator (b) southern hemisphere (d) can not be predicated by this data 18. magnetic needle is kept in a non uniform magnetic field, it experiences a force and a torque a torque but not a force (b) a force but not a torque (d) neither a force nor a torque 19. charge particle entering magnetic field from outside in a direction perpendicular to the field. can never complete one rotation inside the field (b) may or may not complete one rotation in the field depending on its angle of entry into the field will always complete exactly half the rotation before leaving the field (d) may follow a helical path depending on its angle of entry into the field 0. moving charge will gain energy due to the application of electric field (b) magnetic field both of these (d) none of these 1. Power associated with the force exerted by a magnetic field on a moving charged particle is always equal to zero (b) is equal to zero only when direction of motion is perpendicular to the magnetic field. 13

14 is equal to zero only when direction of motion is parallel to the magnetic field. (d) is never equal to zero. Choose the incorrect statement about the magnetic force It is does not act on stationary charge (b) It is always perpendicular to the velocity vector It can not accelerate a moving charge (d) none of these 3. r The expression F = r r I dl denotes the force experienced by a small current element Id r l in a magnetic field r (b) it is aplicable only when field is uniform r r is equal to I( l ) if the magnitude and direction of r over the conductor r l is constant (d) all the above 4. The magnetic moment of the loop as shown in the figure is given by Y π (a + b )I kˆ (b) π (a b )I kˆ (d) π (a + b )I kˆ π (a b )I kˆ I a O b X 5. If magnetic dipole p r m is placed parallel to an infinitely long straight wire as shown in the figure the potential energy of the dipole is minimum (b) the torque acting on the dipole is zero the force acting on the dipole is zero (d) none of these I p m 6. Two concentric coplanar circular loops of radii r 1 and r carry currents of i 1 and i in opposite directions (one clock and other anticlock wise) The magnetic induction at the centre of the loops is half of that due to i 1 along the centre. If r = r 1, the value of i /i 1 is 14

15 1 (b) 3 (d) 4 7. Two infinitely long parallel wires having linear charge densities λ 1 and λ respectively are placed at a distance of R metre. The force per unit length on either 1 wire will be k = 4πε0 λ1λ k R λ1λ k R λ1λ (b) k R λ1λ (d) k R 8. In a certain region of space, electric field E r and magnetic field r are perpendicular to each other and an electron enters in region perpendicular to the direction of r and E r both and moves undeflected, then velocity of electron is E r r r r (b) E r r E r r (d) E 9. n ionised gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along +X-axis and magnetic field along +Z axis. then positive ions are deflected towards +Y-axis and negative ions towards Y axis (b) all ions are deflected towards +Y axis all ions are deflected towards Y axis (d) positive ions are deflected towards Y axis and negative ions towards +Y axis 30. particle of charge q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on ω and q q and m (b) ω, q and m (d) ω and m SECTION 15

16 1. circular coil of wire carries a current. PQ is the part of long wire carrying a current and passing close to the circular coil. If the direction of current in both wires is as shown in the figure, hat is the direction of force acting on PQ? parallel to PQ, towards P (b) parallel to PQ, towards Q at right angles to PQ, to the right (d) at right angles to PQ, to the left P Q. cube made of wires of equal length is connected to a battery as shown in the figure. The side of cube is L. The magnetic field at the centre of the cube is 1 µ 0 I πl (b) 6 µ 0 I πl I µ 6 0I πl (d) zero 3. coaxial cable consists of a thin inner conductor fixed along the axis of a hollow outer conductor. The two conductors carry equal currents in opposite direction. Let 1 and be the magnetic fields in the region between the conductors and outside the conductor respectively then 1 0, 0 (b) 1 = = 0 1 0, = 0 (d) 1 = 0, 0 4. wire is carrying current I as shown in the figure. Section is a quarter circle of radius r. The magnetic field at C is directed along the bisector of the angle C, away from (b) along the bisector of the angle C, towards + - perpendicular to the plane of the paper directed into the paper C (d) at an angle 4 π to the plane of the paper 5. Two particles X and Y having equal charges, after being accelerated through the same potential difference enter a region of uniform magnetic field and described circular paths of radii R 1 and R respectively. The ratio of masses of X to that of Y r R1 R 1/ R1 (b) R 16

17 R1 R R (d) R 1 6. The field normal to the plane of a wire of n turns and radius r which carries a current i is measured on the axis of the coil at a small distance h from the centre of the coil. This is smaller than the field at the centre by the fraction 3 h r (b) h 3 r 3 r h (d) r 3 h 7. The field pattern produced by an infinite sheet of current with linear current density j is given by x x x x x x (b) x x x x x x x x x x x x (d) x x x x x x 8. Consider a thick infinitely long wire of radius R carrying a current I. ssuming that the current is uniformly distributed over the cross-section of wire the magnetic field at the centre of the wire is maximum (b) the magnetic field at any point in the cross-section is zero the magnetic field at the surface of the wire is maximum (d) the magnetic field inside the cross-section is constant everywhere. 9. In the figure shown, the value of at the centre O is I I I R R O 0I 0I µ µ 4πR 8R outwards (b) µ 0I µ 0I 4πR 4R outwards 17

18 0I 0I µ µ + 4πR 8R inwards (d) µ 0I µ 0I 8R 4πR inwards 10. positively charged particle moving with velocity v enters a region of space having a constant magnetic induction. The particle will experience the largest force when the angle between vector v r and r is 0 o 90 o (b) 45 o (d) 180 o 11. Due to magnetic field of earth, charged particles coming from outer space require greater kinetic energy to reach the equator than the poles. (b) require lesser kinetic energy to reach the equator than the poles. can never reach the equator. (d) can never reach the poles. 1. If electron velocity is (i ˆ + 3j) ˆ and it is subjected to a magnetic field 4k ˆ, then speed will change both and (b) (b) path will change (d) none of these 13. Two thick wires and two thin wires, all of the same material and same length form a square in three different ways P, Q and R as shown in the figure. With the current connection shown, the magnetic field at the centre of the square is zero in case of P only I R and Q only P I Q I R (b) P and Q only (d) P and R only 14. steady current I flows in a small square loop of wire of side L in a horizontal plane. The loop is now folded in the middle such that half of it lies in a vertical plane. Let µ r 1 and µ r respectively denote the magnetic moment due to the current before and after folding, then r µ = 0 (b) µ r 1 and µ r are in same direction r r µ 1 µ = 1 1 r (d) r = µ µ 15. When a proton is released from rest in a room, it starts with an initial acceleration a towards west. When it is projected towards north with speed v it moves with an initial acceleration 3a towards west. The magnetic field in the room is 18

19 ma ev upward ma ev upward (d) ma ev ma (b) ev downward downward 16. length of wire carries a steady current. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius as shown in the figure. The magnetic field at the centre caused by the same current is a quarter of its initial value (b) unaltered four times its initial value (d) half of its initial value r o 17. n electron is revolving around a proton in a circular orbit of diameter 1. It produces a magnetic field of 14 Wb/m at the proton, its angular velocity will be rad/s (b) rad/s rad/s (d) rad/s 18. In the given diagram, two long parallel wires carry equal currents in opposite directions. Point O is situated midway between the wires and X Y plane contains the two wires and the positive Z- axis comes normally out of the plane of paper. The magnetic field at O is non-zero along X, Y and Z-axis (b) X-axis Y-axis (d) Z-axis i x= d Y O Z d X i x= + d 19. circular loop of radius a, carrying a current I, is placed in a two dimensional magnetic field. The centre of the loop coincides with the centre of the field. The strength of the magnetic field at the periphery of the loop is. Find magnetic force on the wire π i a (b) 4π i a a i zero (d) π i a 19

20 0. The square CD, carrying a current I is placed in a uniform magnetic field as shown in the figure. The loop can rotate about the axis XX. The plane of the loop makes an angle θ(θ < 90 o ) with the direction of. Through what angle will the loop rotate by itself before the torque on it becomes zero? θ 90 o + θ (b) 90 o θ (d) 180 o θ Y I θ X' X C D Z 1. charged particle moves undeflected in a region of crossed electric and magnetic fields. If the electric field is switched off, the particle has an initial acceleration a. If the magnetic field is switched off, the particle will have an initial acceleration equal to 0 equal to a (b) > a (d) < a. Three conductors 1, and 3 each carrying the same current I are placed in a uniform magnetic field, as shown in the figure. I I I O l (1) l l () l l (3) l The force experienced by conductor 1, and 3 are F 1, F and F 3 respectively F 3 > F > F 1 (b) F1 0, F 0, F3 = 0 F 1 acts upwards, F acts downwards, F 3 = 0 (d) all experience the same force in the same direction. 3. closed loop is placed in a uniform magnetic field. If the force experienced by the loop is F, then F is always equal to zero. (b) F is equal to zero only if is perpendicular to loop. 0

21 F is equal to zero only if is parallel to loop. (d) F may be equal to zero. 4. Choose the incorrect statement about the magnetic moment Pr m of a loop of area r carrying a current I It is defined as P r m = I r It is defined only for a planer loop (b) It is a vector quantity (d) none of these 5. square loop of side l is placed in the neighbourhood of an infinitely long straight wire carrying a current I 1. The loop carries a current I as shown in the figure r The magnetic moment of the loop is P r (b) The magnetic moment of the loop is P m m = l = l I k ˆ I k ˆ Y I X I 1 The P.E. of the loop is minimum (d) The torque experienced by the loop is maximum a 6. cyclotron is operating with a flux density of 3 Wb/m. The ion which enters the field is a proton having mass kg. If the maximum radius of the orbit of the particle is 0.5 m. Find the period for half cycle s s (b) s (d) s 7. uniform magnetic field with a slit system as shown in the figure is to be used as a momentum filter for high energy charged particles. With a field of tesla it is found that the filter transmits α particle each of energy 5.3 MeV. The magnetic field is increased to.3 tesla and deuterons are passed into the filter. What is the energy of each deuterons transmitted by the filter? 5.3 MeV (b) MeV 14.0 MeV (d) MeV Source Detector 8. particle having charge 100 times that of an electron is revolving in a circular path of radius 0.8 m with one rotation per second. The magnetic field produced at the centre is 1

22 10 7 µ 0 (b) µ µ 0 (d) µ 0 9. n elastic circular wire of length l carries a current i. It is placed in a uniform magnetic field r (out of paper) such that its plane is perpendicular to the direction of r. The wire will experience a torque (b) no force i a compressive force (d) a stretching force 30. wire C, carrying current. is bent as shown in the figure. It is placed in a uniform magnetic field of magnetic induction. (Length = L and C = 45 o.) The ratio of force on and on C is 1 (b) 1 L 45 o i i C (d) /3

23 SECTION C 1. long straight wire of radius R carries a current distributed uniformally over its cross section. The magnitude of magnetic field is maximum at the axis of wire. (b) minimum at the axis of wire. maximum at the surface of the wire. (d) minimum at the surface of the wire.. If a charged particle kept at rest experiences an electromagnetic force the electric field must not be zero. (b) the magnetic field must not be zero. the electric field may or may not be zero. (d) the magnetic field may or may not be zero. 3. The unit of magnetic flux can be written as Vs (b) H Tm (d) N m s-c 1 4. circular loop of radius R carrying current I is placed in the XY-plane. Choose the correct statement(s) about magnetic field produced by this loop the magnetic field on Z-axis is only along the Z-axis. (b) the magnetic field at the points lying in the XY-plane is zero. the magnetic field at all the points lying in the XY-plane is only along the Z-axis. (d) the magnetic field at the origin is zero. 5. charge q is moving along a straight line with a velocity v r. It produces both electric field E r and magnetic field r (b) The magnetic field is perpendicular to the plane of v r and E r The magnitude of r is less than that of E r (d) The magnetic field is only perpendicular to v r 6. constant current is flowing through a long straight wire of circular cross-section. On the axis of the wire strength of electric and magnetic field, both may be equal to zero 3

24 (b) strength of electric field alone may be equal to zero strength of magnetic field is equal to zero (d) strength of electric field cannot be equal to zero 7. charged particle having charge q and mass m enters into a uniform magnetic field of induction at an angle θ with direction of the field. The frequency of revolution of the particle is independent of the angle θ. (b) is proportional to the specific charge q m of the particle. is inversely proportional to the value of. (d) is independent of speed of the particle, at the instant entering into the field. r r 8. The Gauss Law for magnetic field is given by ds = 0. It means that òñ magnetic field lines are always closed. (b) monopoles do not exist. magnetic field is conservative. (d) a bar magnet is enclosed by the surface. 9. If the Lorentz force on a charge particle is zero in a region where E r and r are not zero, then (if v is the velocity of particle) E must be parallel to (b) E must be perpendicular to (d) E v E v 10. In the given diagram, a line of force of a particular force field is shown. Out of the following options, it can never represent an electrostatic field 4

25 (b) a magnetostatic field a gravitational field of a mass at rest (d) an induced electric field 11. thin wire of length l is carrying a constant current. The wire is bent to form a circular coil. If radius of the coil thus formed is equal to R and number of turn in it is equal to n, then which of the following graphs represent(s) variation of magnetic field induction () at the centre of coil? (b) O n O R (d) O n O R 1. The direction of magnetic moment is given by the direction of area vector (b) the direction of external magnetic field vector in which the loop is placed the direction of the magnetic field produced by the loop itself (d) the direction of current 13. Choose the correct statements about the relation between magnetic momentum Pr m and angular momentum L r of a body of mass m and carrying charge q 5

26 r q r It is given by Pm = L m (b) It is valid only for regular shaped bodies. It is valid for any finite size body. (d) It is not true for elementary particles. 14. charged particle is fired at an angle of θ in an uniform magnetic field directed along the X-axis. During its motion along a helical path, the particle will, never move parallel to X-axis (b) move parallel to X-axis once during every rotation for all values of θ move parallel to the X-axis at least once during every rotation if θ = 45 o (d) never move perpendicular to the X-direction 15. n electron moving in a circular orbit around the nucleus of an atom exerts an electric force on the nucleus equal to that on it by the nucleus (b) produces a magnetic induction at the nucleus has a magnetic dipole moment (d) has a net energy inversely proportional to its distance from the nucleus. 16. Choose the correct statement(s) about the magnetic force It can accelerate a moving charge (b) It can change the velocity of the charge It is a central force (d) It can do work on a moving charge 17. Choose the correct statement(s) about the magnetic dipole of dipole moment Pr m placed in a uniform magnetic field r It experiences torque τ r, if Pr m and r are neither parallel nor antiparallel to each other 6

27 (b) It posses potential energy, if Pr m is not perpendicular to r It does not experience force F r r (d) If τ 0 r, then F n infinite current carrying wire passes through point O and perpendicular to plane containing a current carrying loop CD as shown in the figure choose the correct option(s) C O Q D net force on the loop is zero (b) net torque on the loop is zero as seen from O, the loop rotates clockwise (d) as seen from O, the loop rotates anticlockwise 19. hollow tube is carrying an electric current along its length distributed uniformly over its surface. Then the magnetic field is zero inside the tube (b) is zero outside the tube increases linearly from the axis upto the surface (d) is proportional to 1 r where r is distance of external point from the axis 0. particle of mass 0.6 gm and charge C is given an initial horizontal velocity of m/s. To keep the particle moving in horizontal direction the magnetic field should be parallel to direction of velocity (b) the magnetic field should be perpendicular to the direction of velocity 7

28 the minimum value of magnetic field must be 0.4T (d) no magnetic field is required 1. H +, He + and O ++ all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity. The masses of H +, He + and O ++ are 1 amu, 4 amu and 16 amu respectively, then H + will be deflected most (b) O ++ will be deflected most He + and O ++ will be deflected equally (d) ll will be deflected equally. small circular flexible loop of wire of radius r carries a current I. It is placed in a uniform magnetic field perpendicular to the plane of the loop. The tension in the loop will be double if I is doubled r is doubled (b) is doubled (d) both and I are doubled 3. n α-particle moving with velocity v enters a region of simultaneous electric and magnetic field, but remains undeflected. Then, E r is parallel to v r and r (b) E r, v r and r are mutually perpendicular The speed of particle is E v = (d) The speed of particle is v = E 4. straight wire carrying current i is parallel to Y-axis, then Y the magnetic field at point P is parallel to X-axis. wire (b) the magnetic field at point P is parallel to Z-axis. i P the magnetic lines are concentric circles having common centre at the wire. X (d) magnetic field at P depends on length of the wire. 8

29 5. proton and an electron both moving with the same velocity enter a region of uniform magnetic field directed perpendicular to the velocity of the particles. They will now move in circular orbits such that their time period will be same (b) the time period of proton will be more the radius of proton s orbit will be more (d) the radius of electron s orbit will be more Z 9

30 Current Electricity SECTION 1. steady current I pass through a linear conductor of uniform cross-section. ny given segment of the conductor has a net positive charge (b) a net negative charge a net charge proportional to volume of the segment (d) a zero net charge of any kind. metallic block has no potential difference applied across it, then the mean velocity of the free electron is proportional to T (b) proportional to T zero (d) finite but independent of temperature 3. current I flows through a uniform wire of diameter d when the mean drift velocity is v d. The same current will flow through a wire of diameter d made of the same material, if the mean drift velocity of the electron is vd 4 4 v d (b) vd (d) v d 4. The momentum acquired by the electron in 10 cm of wire when a current of 1 starts flowing is kg m/s (b) kg m/s kg m/s (d) kg m/s 5. The resistance across two opposite faces of a cube of side cm is 10 6 Ω. The specific resistance of its material in Ω cm is 10 6 (b) (d) wire of length l is drawn such that its diameter is reduced to half of its original diameter. If the initial resistance of the wire was 10Ω, its new resistance would be 40Ω (b) 80 Ω 10 Ω (d) 160 Ω 7. Masses of three wires of same metal are in the ratio 1 : : 3 and their lengths in the ratio 3 : : 1. Electric resistance of these wires will be in the ratio 1 : 1 : 1 (b) 1 : : 3 9 : 4 : 1 (d) 7 : 6 : 1 8. If the resistance of wire at 50 C is 5RΩ and at 100 C is 6RΩ, find resistance at 0 C. 30

31 0RΩ 3RΩ (b) RΩ (d) 4RΩ 9. The temperature coefficient of resistance of a wire is per C. Its resistance is 1Ω at 300 K, its resistance will be Ω at 1154 K (b) 1100 K 117 K (d) 1400 K 10. Potential difference between the points and is 1.00 V (b) 0.50 V 1.50 V (d).50 V 11. Figure shows a circuit with known resistance R 1, and R. Neglecting the resistance of conducting wires and internal resistance of current sources find the magnitude of electromotive force E 1 such that current I through the resistance R is zero. R 1 E R R E R 1 R1 + R (b) E R R 1 (d) E R 1 + R 1. In the given circuit below the current through the conductor ab is 1 3 from a to b (b) 1 from b to a 3 from a to b 3 31

32 (d) zero 13. The current in the arm CD of the circuit is I 1 + I (b) I + I 3 I 1 + I 3 (d) I 1 I + I Kirchhoff s law is an application of conservation of charge and energy (b) charge and linear momentum energy and linear momentum (d) none of these 15. In the circuit shown in the figure, every resistance has 4Ω value. The resistance between terminal P and Q is 4 Ω 3 Ω (b) 36 Ω (d) 4.8 Ω 16. Twelve wires of equal length and same crosssection are connected in the form of a cube. If the resistance of each of the wire is R, then effective resistance between each diagonal ends would be R (b) 1 R 5 R 6 (d) 8 R 17. Six equal resistances of 4Ω each are connected as shown in the figure. The resistance between any two corners, is 4 Ω (b) Ω 1 Ω (d) 4 6 Ω 3

33 18. The total electrical resistance between the points and for the circuit as shown in the figure is 0 Ω (b) 15 Ω 30 Ω (d) 100 Ω 19. In the given figure find the resistance between points and. oth the circle and diameter are made of uniform wire of resistance Ω/m. The length is m Ω 4 Ω (b) 0. The ring shown in the figure has zero resistance. The equivalent resistance between points and will be R (b) R 3R (d) 4R π 4 10 Ω 3 (d) Ω 1. In the given circuit, for what value of R, will the ideal battery transfer energy at the rate of 60 W Ω (b) 19.5 Ω 9.6 Ω (d) 6.9 Ω 33

34 . ll bulbs shown in the figure are identical, which of the bulb/bulb s light/lights most brightly? 1 only (b) only 3 and 4 (d) 1 and 5 3. battery of emf 10 V and internal resistance 0.5Ω is connected across a variable resistance R. The value of R for which the power delivered in it is maximum, is given by.0ω (b) 0.5 Ω 1.0 Ω (d) 0.5 Ω 4. Two electric bulbs whose resistance is in the ratio of 1: are connected in parallel to a constant voltage source. The power dissipated in them has the ratio 1 : (b) 1 : 1 : 1 (d) 1 : 4 5. n electric kettle has two coils when one of these is switched on the water in the kettle boils in 6 minutes. When the other coil is switched on, the water boils in 3 minutes. If the two coils are connected in series, the time taken in minutes to boil the water in the kettle, is 3 (b) 6 (d) 9 6. In the circuit shown in figure, the reading of voltmeter is 1.33 V (b) 0.80 V.00 V (d) 1.60 V 7. The potential difference between the points and in the figure will be V 3 (b) 8 V 9 4 V 3 (d) V 34

35 8. In the given circuit R = 8 Ω (b) R = 6 Ω R = 10 Ω (d) Potential difference between point and E is V. 9. Four identical cells each having e.m.f. E and internal resistance zero are shown in the figure. The potential difference between points and is 4 E (b) E zero (d) E 30. In the given circuit an ammeter of negligible resistance and a voltmeter of very high resistance are used. When key K is open, the voltmeter reads 1.53 V. When the key is closed, the ammeter reads 1.0 and the voltmeter reads 1.03 V. The resistance R is 0.5 Ω (b) 1.03 Ω 1.53 Ω (d) 0.53 Ω 35

36 SECTION 1. potential difference is applied across the ends of a metallic wire. If the potential difference is doubled, the drift velocity will be doubled. (b) will be halved. will be quadrupled. (d) will remain unchanged.. n ionization chamber with parallel conducting plates as anode and cathode, has electrons and the same number of singly charged positive ions per cm 3. The electrons are moving towards the anode with velocity 0.4 m/s. The current density from anode to cathode is 4 µ/m. The velocity of positive ions moving towards cathode is 0.4 m/s (b) zero 1.6 m/s (d) 0.1 m/s 3. The electron beam in a television picture tube travels a total distance of 0.50 m in the evacuated space of the tube. If the speed of the electrons is m/s and the beam current is.0 m. Then number of electrons in the beam at any one instant is (b) (d) If E denotes electric field in a uniform conductor and v d corresponding drift velocity of the free electrons in the conductor then which of the following graph is correct? (b) (d) 5. If a source of constant potential difference is connected across a conductor having irregular cross-section as shown in the figure, then electric field intensity at P is greater than that at Q. 36

37 (b) rate of electron crossing per unit area of cross-section at P is less than that at Q rate of generation of heat per unit length at P is greater than that at Q (d) mean kinetic energy of free electron at P is greater than that at Q 6. Variation of current passing through a conductor as the voltage is applied to its ends varies as shown in the figure. If the resistance is determined at points,, C and D we find that resistance at C and D are equal (b) is higher than that at C is higher than that at (d) is lower than that at 7. Figure shows a rectangular block with dimensions x, x and 4x. Electrical contacts can be made to the block between opposite pairs of faces (for example between the faces labeled, and C C). The maximum electrical resistance that can be obtained at which of the two faces- C C (b) (d) same for all the three pairs 8. certain piece of copper is to be shaped into a conductor of a minimum resistance the length and diameter should be l, d (b) l, d l d, d (d) l, 9. V I graph for a conductor (Platinum wire) at temperature T 1 and T as shown, (T T 1 ) is proportional to cos θ (b) sin θ cot θ (d) tan θ 37

38 10. Variation of current and voltage in a conductor has been shown in the figure. The resistance of the conductor is 4 µ (b) Ω 3 Ω (d) 1 Ω 11. Two batteries of e.m.f 4V and 8V with internal resistance 1Ω and Ω are connected in a circuit with a resistance of 9Ω as shown in the figure. The current and potential difference between the points P and Q are 1 3 and 3V (b) 1 6 and 4V 1 and 9V (d) The current in the branch is (as shown in the figure) 1 (b) 1.5 (d) 3 and 1V 13. What is the equivalent resistance across the terminals and? 15 r 7 15 r 14 (b) 7 r 15 (d) 8 r In the given circuit the electrical resistance between points and is 4Ω (b) 1 Ω 18 Ω (d) 9 Ω 38

39 15. The current shown by ammeter in the circuit is.5 (b) (d) The wire used in the arrangement shown in the figure, has a resistance of 1 Ω/m. What is the equivalent resistance between point and 3π Ω (b) 6π π Ω 8π π Ω (d) none. 3π The potential drop between X and Y in the given circuit is 1. V 3.7 V (b) 4.0 V (d) 1.5 V 18. The length of a wire of a potentiometer is 10 cm, and the e.m.f. of its standard cell is E volt. It is employed to measure the e.m.f. of a battery whose internal resistance is 0.5 Ω. If the balance point is obtained at l = 30 cm from the positive end, the e.m.f. of the battery is (If i is current in potentiometer wire) 30E 30E (b) E ( ) 19. In the given circuit, no current is passing through the galvanometer, connected to a meter bridge. C corresponding to null deflection of galvanometer is x. What would be its value if radius of wire is doubled? x (b) x (d) 30(E 0.5i)

40 x (d) none of these 0. Which of the following plots may represent the thermal energy (U) produced in a resistor in a given time as a function of electric current? 1 (b) 3 (d) any one of them 1. Three bulbs 1, and 3 are connected to the mains as shown in the figure. How will the incandescence of bulb. 1 be affected if one of bulbs or 3 is disconnected from the circuit? No change in incandescence (b) ulb 1 will become brighter ulb 1 will become less bright (d) The bulb 1 may become brighter or dimmer depending upon the candle power of the bulb which is disconnected. In the adjoining circuit the battery E 1 has an e.m.f. of 1V and zero internal resistance while the battery E has an e.m.f. of V. If the galvanometer G reads zero, then the value of the resistance X in ohms is 10 (b) (d) In the given circuit, the resistance R = 16Ω (b) current through 0Ω resistance is 1 Potential difference across the middle resistance is 15V 40

41 (d) Potential difference across R is 10V 4. cell of e.m.f. E having an internal resistance r is connected to an external resistance R. The potential drop V across the resistance R as shown in the figure by the curve marked is 4 (b) 1 (d) 3 5. In the given circuit, with steady current, the potential difference across the capacitor will be V (b) V V 3 (d) V 3 SECTION C 1. Choose the correct statement(s) from the following low voltage supply of 6V must have a very low internal resistance (b) high voltage supply of 6000 V must have a very high resistance 41

42 wire carrying current stays electrically neutral (d) high resistance voltmeter is used to measure the e.m.f. of a cell. When a resistance of 9.5 Ω is connected across a battery, the voltage across the resistance is 11.4V. If the resistance connected across the same battery is 11.5 Ω, the voltage across the resistance is 11.5V. The emf of the battery is 1.0 V. (b) The internal resistance of the battery is 0.5 Ω. The e.m.f. of the battery is V. (d) The e.m.f. of the battery is V. 3. The figure shows a potentiometer arrangement. D is the driving cell, C is the cell whose emf is to be determined, is the potentiometer wire, G is a galvanometer and J is a sliding contact which can touch any point on. Which of the following are essential conditions for obtaining balance? The emf of D must be greater than the emf of C (b) Either the positive terminals of both D and C or the negative terminals of both D and C must be joined to The positive terminals of D and C must be joined to (d) The resistance of G must be less than the resistance of 4. Unit of e.m.f. is joule/ampere henry amper sec ond (b) volt/ampere (d) joule/coulomb 5. Constantan wire is used for making standard resistance because it has low specific resistance. neglible temperature coefficient of resistance. (d) high melting point. (b) high specific resistance. 6. In the circuit, the cell has e.m.f. = 10 V, and internal resistance = 1 Ω. Then, 3Ω Ω Ω 4 the current through the 3 Ω resistance is 1 (b) the current through 3 Ω resistance is 0.5 the current through 4 Ω resistance is 0.5 E=10V r = 1Ω 8Ω 8Ω 4Ω Ω Ω Ω

43 (d) the current through the 4 Ω resistance is In a circuit containing two unequal resistors connected in parallel, the current is the same in both the resistors. (b) a large current flows through the large resistance. the voltage drop across both the resistors is the same. (d) the smaller resistance has smaller conductance. 8. If three bulbs of 40W, 60W and 100 W are connected in series with a 00V power supply, then the potential difference will be maximum across 40W bulb. (b) the current will be maximum through 100W bulb. the 40 W bulb has the maximum resistance. (d) the current in the circuit is Choose the correct statement(s) The product of a volt and a coulomb is a joule (b) The product of a volt and an ampere is joule/sec. The product of a volt and a watt is horse power Watt-hour can be measured in terms of electron-volts 10. Two identical fuses are rated at 10. If they are joined in parallel, the combination acts as a fuse of rating 0. (b) in parallel, the combination acts as a fuse of rating 5. in series, the combination acts as a fuse of rating 10. (d) in series, the combination acts as a fuse of rating uniform wire of resistance R is bent in the form of a ring. Four points,, C and D are marked on the ring as shown in the figure. battery of emf E may be connected across the ring in two ways: Case I: attery is connected between and D Case II: attery is connected between and Choose the correct statement(s) In each case same current flows out of the battery (b) In case I, more current comes out of the battery In case II, more current comes out of the battery (d) In case I, minimum current comes out of the battery 43

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