Tiêu đề 2.CAPACITOR(89-107).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 89 JEE - ADVANCED VOL - VI CAPACITORS CAPACITORS LEVEL-V 1. n conducting plates are placed face to face. Distance between two consecutive plates is d. Area of plates is 1 1 , , , ..... 2 4 8 2n A A A A A        A dielectric slab of dielectric constant k is inserted between the first and second plates and the assembly is charged by a battery of emf . Find the charge stored in the assembly. A) 0 1 1 2 2 2          n A d k   B) 0 1 1 2 2 1          n A d k   C) 0 1 1 2 2          n A d k   D) 0 1 1 3 2 2          n A d k   2. A capacitor of capacitance 10mF is charged up to a potential difference of 2 V and then the cell is removed . Now it is connected to a cell of emf 4 V and is charged fully. In both cases the polarities of the two cells are in the same directions. Total heat produced in the complete charging process is : (A) 10mJ (B) 20 mJ (C) 40mJ (D) 80mJ 3. For the circuit shown ,which of the following statements is true ? (1999) S1 S2 S2 V1=30V V2=20V C1=2pF C2=3pF (a) With S closed V 15V,V 20V 1 1 2   (b) With S closed V V 25V 3 1 2   (c) With S andS closed V V 0 1 2 1 2   (d) With S closed V 30V, V 20V 3 1 2   4. A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dieletric constant K 2  .The level of liquid is d 3 initially.Suppose the liquid level decreases at a constant speed v, the time constant as a function of time t is (2008) R C d d/3 (a) 0 6 R 5d 3vt   (b)   0 2 2 2 15d 9vt R 2d 3dvi 9v t     (c) 0 6 R 5d 3vt   (d)   0 2 2 2 15d 9vt R 2d 3dvt 9v t     5. A 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. As one goes from 0 to 3d (1998) (a) the magnitude of the dlectric field remains the same (b) the direction of the electric field remains of the same (c) the electric potential increases continuously (d) the electric potential increases at first, then decreases and again increases 6. What amount of heat will be generated in the circuit shown after the switch w S is shifted from position 1 to position 2.
Jr Chemistry E/M CAPACITORS 90 NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED VOL - VI (A)   2 0 0 2 CC C C   (B)   2 0 0 CC C C   (C)   2 0 0 2 CC C C   (D)   2 0 0 2 2 CC C C   7. A parallel plate capacitor was lowered into water in a horizontal position, with water filling up the gap between the plates. The distance between the plates is d . Then a constant voltage V was applied to the capacitor. Find the water pressure increment in the gap. Dielectric constant of water is k. (A)   2 0 2 1 2 k V p d     (B)   2 0 2 1 2 k k V p d     (C)   2 0 2 1 4 k V p d     (D)   2 0 2 2 1 k V p d     8. The gap between the plates of a parallel plate capacitor is filled with glass of dielectric constant k = 6 and of specific resistivity 100 G m . The capacitance of the capacitor is 4.0nF . When a voltage of 2.0kV is applied to the capacitor, the leakage current of the capacitor will be (A) 6 2.0 10 A   (B) 6 3.0 10 A   (C) 6 1.5 10 A   (D) zero 9. Two parallel plate capacitors with area a are connected through a conducting spring of natural length l in series as shown. Plates P and S have fixed positions at separation d. Now the plates are connected by a battery of emf  as shown. If the extension in the spring in equilibrium is equal to the separation between the plates, find the spring constant k. A)   2 0 3 27 8   A k d l   B)   0 3 27 8   A k d l   C)   0 3 28 8   A k d l   D)   0 2 27 8   A k d l   10. Find the potential difference between the points A and b and that between E and F of the circuit shown in figure. A) 5V, 5V B) 10 V, 5V C) 15 V, 5V D) 0V, 0V 11. In the circuit shown in the diagram, E is the e.m.f of the cell, connected to two resistances, each of magnitude R and a capacitor of capacitance C as shown in the diagram. If the switch key K is connected at time t = 0, the growth of potential V across the capacitor will be correctly given by (A)   1 exp t V t E RC                (B)   2 1 exp 2 E t V t RC               
NISHITH Multimedia India (Pvt.) Ltd., 91 JEE - ADVANCED VOL - VI CAPACITORS (C)   2 1 exp t V t E RC                (D)   1 exp 2 E t V t RC                12. A capacitors of capacitance C is given a charge Q. At t=0, it is connected to an uncharged capacitor of equal capacirance through a resistance R. Find the charge on the second capacitor as a function of time. 1) 2 1 t Q e RC         2) 2 1 2 t Q RC e         3) 1 2 t Q RC e         4) 1 t Q e RC         13. A capacitor of capacirtance C is given a charge Q. At t=0, it is connceted to an ideal battery of emf E through a resistance R.Find the charge on the capacitor at time t. A) t CR t CR / / CEe Qe    B)   / / 1 t CR t CR CE e Qe     C)   / / 1 t CR t CR CE e Qe     D)   / 1 t CR CE e  14. A circuit consists of a source of a constant emf E, a resistance R and a capacitor with capacitance C connected in series. The internal resistance of the source is negligible. At a moment t= 0, the capacitance of the capacitor is abruptly decreased to  -fold. Find the current flowing through the circuit as a function of time t. 1)  1 t CR E e R     2)  1 t CR E e R    3)  1 1  t CR E e R            4)  1 1  t CR E e R           MORE THAN ONE ANSWERS 15. A parallel plate capacitor of plate area A plate separation 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 denotes 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 (1991) (a) 0AF Q d   (b) 0KAV Q d   (c) V E Kd  (d) 2 0AV 1 W 1 2d K          16. A parallel plate capacitor has smooth square plates of side “a”. It is charged by a battery so that, the charge density becomes  . After charging, the battery is disconnected. Now a smooth dielectric slab of length a which can fill the space between the plates is introduced between the plates from one side between the plates.   K (A) The slab can execute SHM between the plates. (B) The plate can execute oscillatory motion which is not SHM (C) The magnitude of the force experienced by the slab is constant. (D) The magnitude value of the force experienced by the slab is not constant. 17. The plates of a capacitor are connected to a source of e.m.f 320V. Between the plates, there are two dielectric slabs each of uniform thickness filling the whole space. One slab A is of thickness 4mm and dielectric constant 8. The other slab B is of thickness 3mm and dielectric constant 10.
Jr Chemistry E/M CAPACITORS 92 NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED VOL - VI (A) The electric field intensity in A is 4 5 10 /  N C (B) The electric field intensity in B is 4 4 10 /  N C (C) The energy stored per unit area of the capacitor is 4 5.7 10  J . (D) The (induced) bound charge on B is more than in A. 18. The plates of a capacitor are connected to a source of emf and the energy stored is U0 . When dielectric material of dielectric constant K is introduced between the plates filling the whole space, the energy stored becomes U. Now (A) U U 0 (B) U U 0 (C) U U 0 (D) The electric field intensity between the plates is less after the dielectric material is introduced. 19. Four capacitors and two batteries are connected as shown in the diagram. If Va and Vb denote the potentials of the points ‘a’ and ‘b’ then (A) 15 V V V a b   (B) 4 V V V b a   (C) 4 V V V a b   (D) 10 V V V a b   20. There are 10 identical capacitors each of ca pacitance C. (A) If all of them are connected in series, their equivalent capacitance is 10 C (B) If all of them are connected in parallel, their equivalent capacitance is 10C. (C) If two series combinations each having 5 capacitors are connected in parallel, their equivalent capacitance is 2 5 C (D) If they are connected as five parallel combinations each one having two capacitors in series, their equivalent capaitance is 5 2 C . 21. The plates of a parallel plate capacitor are charged by a battery and the battery is disconnected after the charging. Now, the plates are non - parallel as shown in the figure     A B (A) the surface charge density is greater at point A (B) the surface charge density is greater at point B (C) the potential at points A and B is same. (D) the potential at point A is greater 22. Select the correct statement(s) (A) Capacitance of a capacitor depends on the charge on it (B) Capacitance of a capacitor does not depend on the charge on it (C) Capacitance of a capacitor does not depend on the potential difference (D) Capacitance of a capacitor does not depend on the material with which the capacitor is prepared. 23. In the given circuit, find the charge on 1 2 3 4 C C C C , , , and C5 . A battery is connected as shown in the figure. A C D B H I J V v 10 E 1 C f  2 2 C f  4 3 C f 10 2 f 4 f 2 f C6 C5 C4 Select the correct options (A) The charge on C C 1 10 (B) The charge on C C 2  20 (C) The charge on C zero 3  (D) The charge on C C 4 10