Capacitors Questions and Answers

Two identical capacitors C and C of capacitance 10 F are connected in series to a cell of emf 12 V Capacitor C is filled with dielectric of dielectric constant 4 The energy stored in capacitor C is 110 J 112 J 114 5 J

If the dielectric constant and dielectric strength of a material denoted by K and k respectively then a material suitable for use as a dielectric in a capacitor must have Low Kand low k Low Kand high k High K and low k

18 A parallel plate capacitor is connected across a battery Now keeping the battery connected a dielectric slab is inserted between the plates In this process a no work is done b work is done by the battery and the stored energy increases c work is done by the external agent and the stored energy decreases d work is done by the battery as well as external agent but the stored energy does not change 19 When a dielectric slab is introduced between the plates of

Two capacitors of 25 F and 100 F are connected in series to a source of 120 V Keeping their charges unchanged they are separated and connected in parallel to each other Find out i pot diff between the plates of each capacitor ii energy loss in the process

Two spherical conductor A and B of radii a and b b a are placed concentrically in air The two are connected by a copper wire as shown in figure The equivalent capacitance of the system is X A a UVO 4 ab b a 4 a b 4 ob B

50 In the following circuit a capacitor is charged from q 0 to q 2 C after switching on the circuit find energy delivered by the cell R 1000 2 ww C 1 F V 20 V K 51 In the above question i e Q 50 when will this capacitor get maximum charge and what will be values of maximum charge and current at that state of the circuit

b a 100 V 114 The charge on 4 F capacitor in the given circuit is in C 1 F 5 4 F 3 F 10 V b 24 5 F c 36 ulu d 32 Eet d a

In the network of capacitor and resistances as shown in the figure steady current I enters at junction a and same current leaves junction b Charge on capacitor C3 with KIRC shown polarity is Find K 4 C C I a R C 2C C C3 C 2R

2 conducting spheres each of radius R are placed at a large distance from each other They are connected by coil of inductance L as shown in figure Neglect the resistance of coil The sphere A is given a charge Q and switch S is closed at t 0 Then time at which Charge on B is T LR E y X O Fill in OMR sheet y mm

The circuit shown in the figure consists of a charged capacitor of capacity 3 F and a charge of 304C At time t 0 when the key is closed the value of current flowing through the 5M2 resistor is x p A The value mothongo ngo of x to the nearest integer is C 3 F SMQ HH www thongo q 30 C mathonge mathongo mathongo mathango mathongo mathongo mathongo mathongomathonge mathango

Find the approximate dielectric constant for the material paper in the literature and cite your source using AIP reference style Note that the value may depend on the type of paper moisture and more so this is an approximate value only and your measurement will be the actual constant

7 A parallel plate capacitor is filled by a di electric whose relative permittivity varies with the applied voltage according to the law aV where a 1 per volt The same but containing no di electric capacitor charged to a voltage V 156 volt is connected in parallel to the first non linear uncharged capacitor Determine the final voltage V across the capacitors

5 charge on capacitor C3 C C HE HHH CA 4 C3 V Given that C C C and C3 C4 3C 1 CV 2 2 CV 2

57 If initial charge on all the capacitors were zero work done by the battery in the circuit shown is 1 0 2 mJ 3 0 4 mJ 4 F 4 uF H 2 F 10 V 2 200 mJ 4 400 mJ

5480 33 Four very large metal plates are given charges as shown in Fig 2 107 The middle two are then connected through a wire Find the charge that will flow through the wire a 50 from A to B b 50 2 from A to B c 50 from B to A d no charge will flow d 2 680 right 20 30 A B Fig 2 107 A 40

A capacitor of capacitance C is charged with V volt battery as shown in figure When the switch S is turned to position 2 the energy stored on the capacitor of capacitance 4 C will be V A B CV 25 12 2CV 25 CV C 4 C

55 As in the figure if a capacitor of capacitance C is charged by connecting it with resistance R then energy given by the battery will be 1 1 CV C 11 V R www Less than cV

56 There are two identical capacitors the first one is uncharged and filled with a dielectric of constant K while the other one is charged to potential V having air between its plates If two capacitors are joined end to end the common potential will be 1 2 3 V K 1 KV K 1 4 KV K 1 V K 1

The plates of a parallel plate condenser are pulled apart with a velocity v If at any instant mutual distance of separa tion is d then the magnitude of the time of rate of change of electrostatic energy of the capacity depends on d as fol lows 1 1 1 2 17 12 d 3 d 4 d

igure its two ends are connected to two wires and it is hanging by those wires with its plane being vertical The wires are connected to a capacitor with charge Q through a switch The coil is in a horizontal uniform magnetic field B parallel to the plane of the coil When the switch is closed the capacitor gets discharged through the coil in a very short time By the time the capacitor is discharged fully magnitude of the angular momentum gained by the coil will be assume that the discharge time is so short that the coil has hardly rotated during this time A NQB R Ans B ALLEN CAREER INSTITUTE TO CREATIONS B NQB R B Sol Torque experienced by circular loop Mx B whara Mis magnatic moment C 2 NQB R JEE Advanced 2020 Paper 1 Held on Sunday 27 September 2020 D 4 NQB R JEE Advanced 2020 Paper 1 3

The complex power consumed by a constant voltage load is given by P jQ Where 1 kW P 1 5 kW and 0 5 kVAR Q 1 KVAR A compensating shunt capacitor is chosen such that Q 0 25 kVAR where Q is the net reactive power consumed by the capacitor load combination The reactive power in KVAR supplied by the capacitor is

Four identical metal plates each with a surface area on one side are placed at a distance d from each other as shown in Fig 4 84 The two inner plates are connected to point B and the other two plates to another point A Then the capacitance of the system is a A d C 36 Ald Fig 4 84 b 2e A d d 26 1 3

1 A capacitor of capacitance 100 uF is charged by connecting it to a battery of voltage 12 V with internal resistance 2 Q The time after which 99 of the maximum charge is stored on the capacitor is a 0 92 ms b 0 72 ms c 0 34 ms UP CPMT 2015 d 0 54 ms

4 8 If the key k is closed find the charge that will flow in capacitors 1 C C 2 3 C3 V V V3 V V V3 3 C C C E C C C C 11 E A k G 4 11

4 1 33 F In the figure potential of 1200 V is given to point A and point B is earthed What is the potential at point P A 3 F 1 100 V 2 200 V 3 400 V 4 F F HH 2 F B

29 Two condensers one of capacity C and other of capacity C 2 are connected to a V volt battery as shown The work done in charging fully both the non condensers is AIPMT Prelims 2007 V t C C 2

A parallel plate capacitor is connected with a battery whose potential difference remains constant If the plates of the capacitor are shifted apart then the intensity of electric field 1 decreases and charge on plates also decreases 2 remains constant but charge on plates decreases 3 remains constant but charge on the plates increases 4 increases but charge on the plates decreases

48 Three identical charged capacitors each of capacitance 5 F are connected as shown in figure Potential difference across capacitor 3 long time after the switches K and K are closed is 100 C 1 20 V 100 C K 100 C3 K 2 10 V

x d Figure shows a solid conducting sphere of radius 1 m enclosed by a metallic shell of radius 3 m such that their centres coincide If outer shell is given a charge of 6 C and inner sphere is earthed find magnitude charge on the surface of inner shell 3m 1m

Find the effective capacitance between P and Q of the arrangement shown in figure 2 F 11 11 2 F 1 MF 2 1 F 5 F HH T 2 F 2 F F 1 F HH HT 1 F Q

In the adjoining figure three capacitors C C and C3 joined to a battery are shown The correct condition will be symbols have their usual meaning C 1 Q Q V C 2 Q V3 Q3 C3 V Q Q3 and V V V3 V 2 Q Q Q3 and V V V V3 2 3 Q Q Q3 and V V V

A capacitor of 2 F is charged as shown in the diagram When the switch S is turned to position 2 the percentage of its stored energy dissipated is NEET 2016 1 80 2 0 2 F 20s S 8 F

When the key is pressed at time t 0 then which of the following statements about the current i in the resistor AB of the given circuit is true 2 V KA B www 1000 Q 1 F C 1000 Q 1 at t 0 i 2 mA and it reduces to 1 mA at t 2 i oscillates between 1 mA and 2 mA 3 i 2 mA at all time 4 i 1 mA at all time

Two spherical conductors A and B of radii a and b b a are placed concentrically in air A is given a charge Q while B is earthed Then the equivalent capacitance of the system is B A 1 4 o 4 4 o a ab b a 2 4 a b 3 4 b b Q

ALL A network of four capacitors of capacity equal to C C C 2C C3 3C and C 4C are connected to a battery as shown in the figure The ratio of the charges on C and C4 is 1 7 4 3 C HH C C HH C F 2 4 22 3 4

3 10 C and separation 41 Area of one side of each plate is A between consecutive plates is d Emf of the battery connected is V The charge on plate 2 is 1 A 2 1 A V d A V Id TH 2 3 4 2A V d 2A V

A capacitor is made with a polymeric dielectric having r of 2 26 and a dielectric breakdown strength of 50 kV cm The permittivity rectangular of free space is 8 85 pF m If the plates of the capacitor have a width of 20 cm and a length of 40 cm the maximum electric charge in the capacitor is

29 Two spherical conductors A and B of radii a and b b a are placed concentrically in air B is given a charge Q and A is earthed The equivalent capacitance of the system is a b A B

22 If for a coil having L 2 mH current flowing through it is fe then the time at which emf becomes zero is 1 2 s 3 4 s 2 1 s 4 3 s

A condenser of capacitance 10 F has been charged to 100 V It is now connected to another uncharged condenser in parallel The common potential becomes 40 V The capacitance of another condenser is 3 10 F 1 15 F 2 5 F If magnetic field is long vic on 4 16 F no in po on ionized gac

ONCERT example 8 1 A parallel plate capacitor with circular plates of radius 1m has a capacitance of 1nF At t 0 it is connected for charging in series with a Resistor R 1M across a 2V battery Calculate the magnetic field at a point P halfway between the center and the periphery of plates after t 10 s the charge on the capacitor at time t is q CV 1 e where time constant T CR

In the circult shown in the figure below C1 21 F C2 40 F C3 21 F and a voltage Vab 38V is applied accross points a and b After C is fully charged the swi thrown to the right What is the final voltage on C Express your answer in units of V Volts using one decimal place S a be C T C C3

89 Four capacitors each of capacity 3 uF are conne as shown in the adjoining figure The ratio of equivalent capacitance between A and B and between A and C will be a 4 3 c 2 3 A HH B C b 3 4 d 3 2 a 9

3 3 A capacitor of capacitance 5 F is connected to a source of constant EMF of 200V for a long time as shown in figure 3 374 then the switch was shifted to contact 1 from contact 2 Calculate the amount of heat generated in the 50092 resistance Sw 2 5 F HH 50052 www 200V Figure 3 374 3000

an refer adva 3 4 The figure 3 375 shows two circuits with a charged capacitor that is to be discharged through a resistor as shown in the figure The ratio of initial charges on capacitors is given as 92 91 2 If both switches are closed at time t 0 the charges become equal at 10 In2 s Find the resistance R 91 91 5 F 552 92 92 al 931 Figure 3 375 10 3 F R

The energy required to charge a parallel plat condenser of plate separation d and plate are of cross section A such that the uniform electric field between the plates is E is 1 E E Ad 2 E E Ad 4 E E Ad 3 E E A d

A time varying voltage is applied to the clamps A and B such that voltage across the capacitor plates is as shown in the figure 3 400 Plot the time dependence of voltage across the terminals of the resistance E and D Vc A Be Ans VRA SR E D Figure 3 400

n 6 Three identical capacitors connected in series have an effective capacitance of 2 F If one of the capacitors is removed the effective capacitance becomes 3 F Find the capacitance of the capacitor that is removed

46 A capacitor consists of two stationary plates shaped as a semi circle of radius R and a movable plate made of dielectric with permittivity and capable of rotating about an axis O between the stationary plates Fig 3 34 The thickness of the movable plate is equal to d which is practically the separation between the stationary plates A potential difference V is applied to the capacitor Find the magnitude of the moment of forces relative to the axis O acting on the movable plate in the position shown in the figure O O R Fig 3 34

64 A solid conducting sphere of radius R is surrounde by another concentric hollow conducting spher of radius R The capacitance of this assembly proportional to 1 3 R R R R R R R R 2 2 R R R R 2 R R 4 R R