Capacitors Questions and Answers

A parallel plate capacitor has a charge magnitude of 80 nC on either plate a plate separation of 0 50 mm and a uniform electric field of magnitude 3000 volts m What is the potential energy stored in the capacitor O a 40 n Ob 30 nj O 60 nj Od 70 nj 0 50 nj

2 Let C be the capacitance of a capacitor discharging through a resistor R Suppose t is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge to reduce to one fourth its initial value Then the ratio will be

30 The switch S shown in figure 32 E35 is kept closed for a long time and is then opened at t 0 Find the current in the middle 10 Q2 resistor at t 1 0 ms 12 VI 25 25 F www 10 Q 10 22 Figure 22 1725

Two identical metal plates are given positive charges and 92 9 respectively If they are now brought close together to form a parallel plate capacitor with capacitance C the potential difference between them is A 91 92 2C B 91 92 C C 91 92 G 00 D 91 92 20 One plate of a capacitor of capacitance 2uF has total charge 10 Cand its other plate has t charge 40 C The potential difference between the plates is in Volt A 7 5 B 15 C 25 D 50

1 K K t ngure 31 12 Figure 31 E30 plates of the capacitor have plate area A and are clamped in the laboratory The dielectric slab is released from rest with a length a inside the capacitor Neglecting any effect of friction or gravity show that the slab will execute periodic motion and find its time period K I 1 1 The 1

Three large conducting plates are placed a distance d apart in air The space between the first two plates is completely filled with a dielectric slab of dielec tric constant K 2 as shown in Figure The plates are given charges Q 7Q Q2 3Q and Q3 2Q respectively The outer two plates are now connected with a conducting wire Find the charges on all the six surfaces d d

The potential at point P is k V V d A C kV 2V k 2 B D kV V K 1 kV 2V k 2 V 2d K P

In the given arrangement the charge on the 3 F capacitor is 2 F HE T 10V 3 F the fur HH 1 F

Find the equivalent capacitance of the combination shown in Fig 2 85 between the points A and B 10 5 9 Cs HH SI C Ans C B 2G G G G

A conducting sphere of radius R carrying charge Q lies inside an uncharged conducting shell of radius 2R If they are joined by a metal wire A Q 3 amount of charge will flow from the sphere to the shell B 2Q 3 amount of charge will flow from the sphere to the shell C Q amount of charge will flow from the sphere to the shell kQ D amount of heat will be produced 4R

In the circuit shown the cells A and B have negligible resistances For V 12 V R 500 S and R 100 2 the galvanometer G shows no deflection The value of V is a 4V c 12 V VA R VB T b 2V d 6V

In the given circuit a charge of 80 C is given to the upper plate of the 4 F capacitor Then in the steady state the charge on the upper plate of the 3 uF capacitor is A 32 C C 48 C B 40 C D 80 C 80 C 2 F HF I 4 F

HH www H 1uf 42 3uf 10V www 422 www 10 11

5 A variable capacitor has n plates and the distance between two successive plates is d Determine its capacitance n 1 A d Ans C

12 Two conducting spheres of radii R and R are kept widely separated from each other What are their individual capacitances If the spheres are connected by a metal wire what will be the capacitance of the combination Think in terms of series parallel connections

c A voltmeter should have small resistance d A voltmeter should have large resistance 8 A capacitor of capacitance 500 uF is connected to a battery through a 10 k2 resistor The charge stored on the capacitor in the first 5 s is larger than the charge stored in the next a 5 s b 50 s c 500 s d 500 s 9 A capacitor C of capacitance 1 F and a capacitor C of capacitance 2 F are separately charged by a common battery for a long time The two capacitors are then H separately discharged through equal resistors Both the discharge circuits are connected at t 0 a The current in each of the two discharging circuits is zero at t 0 b The currents in the two discharging circuits at t 0 are equal but not zero c The currents in the two discharging circuits at t 0 are unequal d C loses 50 of its initial charge sooner than C loses 50 of its initial charge

The equivalent capacity of the infinite net work shown in the figure across AB is Capacity of each capacitor is 1 F D AH BH HE E H 1 2 1uF 3 HH HH 3 2 1 F 4 2 1 3 1 UF

A 4 F capacitor is connected to another 8 F capacitor The combination charged to 300 V calculate 1 Total charge on the combination Total energy stored in the combination

F a 1 F c 3 F d 4 F 93 Four capacitors are connected in a circuit as shown in the figure The effective capacitance in F between points A and B will be a 28 9 A b 4 2 F 2 F 12 F 11 2 F B c 5 V 01 d 18 98 There a capacit The e in pa 99 The W pc V

Consider the circuit shown in the figure Capacitors A and B each have capacitance C 2 F The plates of capacitor A are shorted using a wire of resistance R 1 2 while the left plate of capacitor B is given an initial charge Q 4 C The switch is closed at a time t 0 What will be the initial current in ampere drawn from the battery immediately after the switch is closed Ans 7 A C www R H www R E 4Q C

An air core parallel plate capacitor has capacitance Co and separation between its plates is do It is given a charge Qo and connected to a bulb of resistance R through a switch S The switch is closed at time t 0 and the separation between the capacitor plate is changed as d for 0 t 1 second For t 1 do 1 t do second the plate separation is held fixed at d 2 Find charge on the capacitor at t 1 second is Find charge on the capacitor as a time t 1 second is HH J www R S

36 a What is the potential of point a with respect to point b in figure when switch S is open V 18 0 V 6 00 S 3 00 www a www S b 6 00 uF 3 00 uF fo Which point a or b is at the higher potential c What is the final potential of point b with respect to ground when switch S is closed d How much charge flows through switch S when it is closed

A 4 00 uF capacitor and a 6 00 uF capacitor are connected in parallel across a 660 V supply line a Find the charge on each capacitor and the voltage across each b The charged capacitors are disconnected from the line and from each other and then reconnected to each other with terminals of unlike sign together Find the final charge on each and the voltage across each

Out of the three conducting identical plates middle flat is given charge 3 C and other two plates are not having any charge If switch S is closed Find the charge passing through switch S in C 0 3

25 A circuit has a section AB as shown in the figure If the potential differnce between two points AB is 10V A at higher potential then potential difference across 2 uF capacitor is a 9V AHHHHB SV b 7V 2 F 3 F c 12V d None

The capacitance C of a capacitor is Question Type Single Correct Type 1 Independent of the charge and potential of the capacitor 2 Dependent on the charge and independent of potential 3 Independent of the geometrical configuration of the capacitor 4 Independent of the dielectric medium between the two conducting surfaces of t capacitor

Answer questions 11 12 and 13 by appropriately matching the information given in the three columns of the following table Three parallel plates A B C of large area carry charge Q Q and Q respectively Values of Q Q and Q are listed in Column 1 Column 2 and Column 3 respectively The separation between A and B is d whereas between B and C is 2d 11 Column 0 0 1H iv Column 2 0 2Q P Q R S Column 3 0 2Q d B II iii R D IV iv S B If plate A and C are connected by conducting wire then in which of the following case the charge flowing through conducting wire is Q 3 A 1 1 P C III ii Q

12 In the given circuit charge Q on the 2uF capacitor changes as C is varied from 1pF to 3pF Q as a function of C is given properly by figures are drawn schematically and are not to scale a c Q Q Charge 1 F Charge LE C E 3 F b d luF 2 F Q Q Charge 1 F Charge 5 3 F C C

Two capacitors are connected of capacitance 2 F and 3 F in series The outer plate of the 2 F capacitor is connected to 1000 V source and outer plate of 3 uF is earthed The potential of inner plate of each capacitor is 300 V 500 V 600 V

the capacitor at steady state is R 1 2 3 R CE 9 2CE 9 CE 3 network shown the energy stored in OCE R wwww C HHH E R www R www of n n n x ve l an n 1 n

Find the energy stored in the capacitor in J in steady state in the given circuit shown A 7 C 9 B 8 D 6 AD 2 F RC CA A 192 ww 2V 6V 492 292 ww www 312 HH 3V SEV 62 www

The equivalent capacitance of the circuit shown in the figure between terminals A and Bis C C 5 A 05 2C 0 200 5 3C 5 C C B

shown positi in the figure When switch S is turned to 2 the percentage of its stored energy dissipated is V v 1 20 3 40 1 F 26 4 F 2 80 4 60 ES V 110 F

Distance between plates of a parallel plate charged capacitor disconnected from battery is increased The quantity that remains constant is Potential difference between plates Charge Electric field between plates

A capacitor of capacitance 2 mF is charged to a potential of 10 V The capacitor is now connected to an identical capacitor charged to a voltage 20 V such that the plates of same polarity are connected together The loss of energy in redistribution of the charges is 2 8 J 0 5 J 0 05 J 6 6 J

3 Three long coaxial conducting cylindrical shells have radii R 2R and 2 2 R Inner and outer shells are connected to each other The capacitance across middle and outer shells per unit length is 1 3 1 3 0 In 2 TEO 2n2 2 6 In 2 4 E In2 8

The equivalent capacitance of the combination as shown in the figure between point A and Bis 10 F A 20 uF 30 F O 30 F O 20 F O 10 F 20 F 11 40 F B

View in English A parallel plate air capacitor is charged to a potential difference V After disconnecting from battery the plates of capacitor is pushed gent by an insulating handle to decrease the separation between them As a result the charge on the plate O Decreases O Increases Becomes zero Remains same

In the given circuit the potential difference between point A and B is 18 V and charge on 2 F capacitor is 24 C The energy stored in capacitor Cis 2 F 6 F AH 72 J O 144 J O 36 J Data insufficient B

13 A capacitor of capacity Cis charged to a potential difference V and another capacitor of capacity 2C is charged to a potential difference 4 V The charging batteries are disconnected and the two capacitors are connected with reverse polarity i e positive plate of first capacitor is connected to negative plate of second capacitor The heat produced during the redistribution of charge between the capacitors will be 125 CV2 50 CV 3 3 a b c 2CV d 25 CV2 3

A A dielectric slab of thickness d 2 and dielectric constant 2 is inserted in capacitor as shown in figure If capacitor is connected to 10 V emf battery then find potential difference between the two surface A and B of dielectric slab Question Type Single Correct Type 1 B 4 V 20

Two capacitors of capacitances C and 2C connected in parallel and are charged to a potentia difference of V If now battery is removed and a material of dielectric constant k is placed between plates of capacitance C the potential drop across this capacitor will be 1 3 V 2 K 3 3K V 2 2 4 3V K 2 2V K 3

Two isolated spherical conductors have radii 5 cm and 10 cm respectively They have charges of 12 C and 3 C Find the charge of bigger sphere after they are connected by a conducting wire A 6 C B 3 C D 4 C C 9 C

The time constant for a circuit containing 99 capacitance C and resistance R is t In this time an uncharged capacitor can be charged to about x per cent of the maximum charge 90 or a charged capacitor having charge q can be discharged to about y percent of q Then A x y 100 C x y 63 1 B x y 1 1 D x y 0 100

Cells in Series and Parallel Kirchhoff s 16 The charge in the 2 F capacitor at steady state is 1 Zero 2 2 C 3 4 C 4 6 C 1 V www PA Medal SE www 20 Division Aatucational

Consider the circuit below E 48 0 V internal resistance is negligible R 102 C 5 F and C 10 F After the capacitors reach their final charges charge on C is q 20 C What is R R fe tama E R C C

If an electron enters into space between the plates of parallel plate capacitor a an angle of 30 with the plates and leaves at an angle of 60 to the plates The ratio of its kinetic energy while entering the plates to that while leaving will be 01 3 03 1 02 3

Two identical capacitors 1 and 2 are connected in series to a battery as sho in figure Capacitor 2 contains a dielectric slab of dielectric constant K as shown Q and Q2 are charges stored in capacitors Now dielectric slab is removed and corresponding charges are and then K 1 K Q K 1 2K E

02 A parallel plate capacitor with air between plates has capacity of 1 pF Now plates are moved apart with insulating handle so that separation is twice of original value The space between plates is filled with a medium of dielectric constant 6 The new value of capacity in pF is 03 01 Mark for Review 6 hr

2 A parallel plate capacitor of capacity 5 F and plate separation 6 cm is connected to a 1 V battery and is charged A dielectric of constant 4 and thickness 4 cm is introduced into the capacitor The additional charge that flows into the capacitor from the battery is 1 2 C 2 3 C 3 5 C 4 10 C