Capacitors Questions and Answers

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K K K K arranged as shown in the figure The effective dielectric constant K will be 1 K 3 K A 2 K VZ K K K 1 2 KL 2 K K K3 K 2 K K K3 K d 2d 2 K K K3 K K K K3 K K K K K3 2 K K K3 K K K K K

xiii Figure 5 150 shows LC circuit with initial charge on capacitor 200 C If at t 0 switch is closed find the first instant when energy stored in inductor becomes one third that of capacitor 0 2mH oooooo 2 Q 2 F Figure 5 150

0 A long cylindrical capacitor of inner radius x variable and outer radius b is charged to potential Vo If dielectric strength of medium between plates is Eo and capacitor is chargec to maximum potential difference possible then 13 b 010 11

9 Three capacitors connected in series have an effective capacitance of 2 2 poin uF If one of the capacitors is removed the effective capacitance becomes 3 F The capacitance of the capacitor that is removed is a 3 2 F O b 2 3 F c 6 F

The space between two concentric conducting spherical shells of radii b 2 20 cm and a 1 10 cm is filled with a substance of dielectric constant K 14 3 A potential difference V 23 0 V is applied across the inner and outer shells Determine a the capacitance of the device b the free charge q on the inner shell and c the charge q induced along the surface of the inner shell a Number b Number Units Units

A capacitor of capacitance C is charged to a potential difference V from a cell and then disconnected from it A charge Q is now given to its positive plate The potential difference across the capacitor is now A V B C D v 2 if Q CV V

SolveLancer Test In the given figure all the metal plates are identical and are at distance d from each other The area of all plates is A P The charge stored on the upper side of plate 4 is SolveLancer Test a V EA 2d b V c 0 1 V EA

Effective capacitance of parallel combinatio of two capacitors C and C is 10 uF Whe these capacitors are individually connected a voltage source of IV the energy stored in t capacitor C is 4 times that of C If the capacitors are connected in series the effective capacitance will be 1 3 2 F 3 1 6 F 2 8 4 F 4 4 2 F

Q 32 Two concentric spherical shells have radii a and b a Write the capacitance of the system in following cases a Positive terminal of the battery is connected to the outer shell and its other terminal and the inner shell are grounded b Positive terminal of the battery is connected to the inner shell and its negative terminal is grounded

6 If the two springs with spring constants k and k are 2 arranged as shown in figure then the effective spring constant of two spring system will be a k k k fmoo o o o o o o o k2 ooooooo t b k k BCECE 2012 bed

Question 12 Conducting sphere of radius a is surrounded by another spherical conducting shell of radius b The space between them is filled with dielectric material of conductivity o and dielectric constant K The charge Q and Q are given to the inner and outer shell at time t 0 Charge on outer shell at time t is Options a 2 1 exp x Q Q

5 In the circuit shown when the switch is closed the capacitor is charged with time constant and when switch is open then capacitor discharge with time constant to then T T is A 1 2 E R R www S B 1 2 D 1 4

xi A circuit consists of a source of a constant EMFE and a resistance R and a capacitor with capacitance C connected in series The internal resistance of the source is negligible At a moment 0 the capacitance of the capacitor is abruptly decreased n fold Find the current flowing through the circuit as a function of time t n 1 m RC Ee 1

Use the imaging method to find the capacitance per unit length starting from the page of the plane cylinder system in figure 1 Also calculate the force exerted by the plane on the cylinder I Figura 1 V 0

Q49 A capacitor of Capacitance 1uF is filled with two dielectric of dielectric constant 4 and 6 in equal amount as shown in the diagram The new capacitance would be 1 K 4 6 K2 6 A 10 uF B 7 uF C 5 uF D 4 uF 1 d

The potential in given circuit is M C 1 F P C 2 F q R 3S2 R 652 www www Q 12 V HT 1 zero 3 3 6 Volt 122 wwww N 2 4Volt 4 None of these

1 Plates of a parallel plate capacitor have area A and distance between them is d A potential difference Vis maintained across the capacitor by a battery Two identical dielectric slabs D and a metal slab M each of thickness d 3 are inserted in the capacitor as shown in the figure Relative permittivity of each of the dielectric slab is Find expression for modulus of the force of electrostatic interaction on either of the plates DMD

The reading of the A C voltmeter in the network shown in figure is where Vis in volt NCERT Pg 245 112 1 400 V 3 200 V 11 Q2 www m HH Xc 20 2 X 20 2 V 220 2 sin wt 2 220 V

Related to adjacent circuit after switch S is closed which of the following statements are correct A B A S S A Flux through closed surface S is zero B Energy stored by the capacitor is less than work done by battery in chargin the capacitor C Direction of electric field between the plates of the capacitor is from A to I D Total charge on each plate of capacitor is zero

The capacitance of the capacitor formed by introducing three slabs of three different dielectric material between the plates of ta parallel plate capacitor as shown in the figure is A as area of plates 1 Point d K OA EOA 2 2 2 K 19 1934 K3

14 Suppose you need a capacitor bank with a total capacitance of 0 750 F 1 point withstanding 160 V but you have only 1 50 mF capacitors withstanding 40 V at your disposal What is the smallest number of capacitors you could connect together to achieve your goal O a 8000 b 400 O c 2000 d 40 EN

Find the equivalent capacitance in uF between points P and Q of the combination shown in figure if capacitance of capacitor is C 4 5 F DO Answer 00 10 C 01 DO 02 3 54 05 06 07 00 09

7 In oscillating LC circuit the total stored energy is U and maximum charge upon capacitor is Q the When the charge upon the capacitor is 2 energy stored in the inductor is 1 2 DIN DIT IS 3 U 3U

A B C D E The figure above shows four very thin parallel planes of charge with equal separation between them The charge density on plate 1 is 2 o The charge density on plate 2 is 1 a The charge density on plate 3 is 5 o The charge density on plate 4 is 3 0 Your answers for the electric field must include the correct sign We choose positive electric field along the positive x dire What is the Electric Field at point E in units of a eo

Fill in the blank The energy stored in a capacitor becomes times of its initial value U when the air in charged isolated capacitor is replaced by a medium of dielectric constant k 1 Point

rging and discharging of a capacitor through resistance 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 HP R 1000 22 ww Tv 20 V C 1 F

Four identical conducting plates are placed at separation d from each other Plates are given charges q 2q 3q 4q respectively as shown Switch S is closed Based on this information match the entries in Column l with entries in Column II q2q 3q 4q 3 0000 S Column l Q1 Charge on plate 1 Q2 Charge on plate 4 Q3 Charge on right surface of plate 2 Q4 Charge on right surface of plate 3 Column II A1 A2 A3 A4 03 8q 3 013 7q 3 5g

A 2 F capacitor is charged as shown in figure The percentage of its stored energy dissipated after the switch S is turned in position 2 is 1 2 1 0 2 F 2 F T 8 F 8 F 2 20

A parallel plate capacitor has plate area A the distance between its two plates x and y is d and a dielectric slab of dielectric constant is filled between the regions It is connected to a cell of emf E If the dielectric slab is removed then A a e 1 E charge is absorbed by the cell d A b 1 E charge flows through the circuit d c negative charge flows from plate y to plate x d negative charge flows from plate x to plate y

2 Two dielectric slabs of dielectric constant K and 2K are placed inside a parallel plate capacitor whose initial capacitance with vacuum between the plates was C as shown The separation between the plates is d The thickness of both slabs is The slab of dielectric constant 2K covers half the area of the left plate while the slab of dielectric constant K covers the entire area of the right plate The remaining space is vacuum If x 3 and the capacitance is now c the ratio is 2 K

a parallel plate capacitor the separation between the plates is 3mm 1mm with air between them Now a thick layer of a material of dielectric constant 2 is introduced between the plates due to which the capacity increases In order to bring its capacity to the original value the separation between the plates must be made In

3 Zero 19 In the given network of capacitors the equivalent capacitance between points A and B is A T H B Road New Delhi 110005 Pt 01141

An air filled parallel plate capacitor is connected to a battery and allowed to charge up Now a slab of dielectric material is placed between the plates of the capacitor while the capacitor is still connected to the battery After this is done we find that the charge on the capacitor had not changed O the energy stored in the capacitor had decreased O the voltage across the capacitor had increased O the charge on the capacitor had increased O None of these choices are true

Find the charge on the capacitor C in the following circuit 1 2 3 4 orrect Answer 4 ur Anguer 1 12 C 14 C 20 C 18 c 2 3 00 12V 20 60

Switch S and S2 is closed at t 0 then choose the correct statement s Initial current in each circuit is same 2 F achieves 50 of its steady charge sooner than 1 F Steady state charges in both capacitors are unequal None of these 2 F 10V 1092 www S 1 F 10V 1052 www S

3 1 1 18 Three capacitors are connected as shown in the figure The potential at point O is equal to 1 1 4 volt 10 volt 1 F 7 F 2 F TH 4 volt 2 4 7 volt 4 1 8 volt

Find potential difference in volt between the plates of a parallel plate capacitor if charge on capacitor is 100 C The plate area is x 10 2cm and separation between plates is 1 cm Here Eo is permittivity of free 1 0 space

In the given circuit all three capacitors are initially uncharged If a battery of emf E is connected between the points A and B the potential difference across the capacitor of capacitance 2C at steady state becomes C A O O O O 3E 2C C B

2 3 4 For the given input voltage waveform V t the output voltage waveform V t across the capacitor is correctly depicted by in 1kQ 3V 1 2V www 2V 2V 2V 5V Sus 10nF TUE OV V t M 5 s 10 s 15 s 5 s 10 s 15 s V t V t 5 s V t 10 s 15 s t V t 17

All capacitors in the network shown are initially uncharged If a battery of emf Eis connected between the points M and O and the potential difference between the points N and P at steady state is p the ratio J M P 2C 26 N VNP is P

The separation between the plates of an uncharged capacitor of capacitance Cis d Initially there is air dielectric constant 1 between the plates A slab of a material of dielectric constant 2 and thickness is introduced inside the capacitor as shown Now the capacitor is connected across the 2 terminals of a battery of emf V After the capacitor is completely charged 0 The electric field inside the slab is 47 3d 2V The electric field inside the slab is 3d The potential energy stored in the capacitor is cr The potential energy stored in the capacitor is tor is cv

A capacitor of capacitance Cis charged to a potential difference and then connected to two resistances Rand 4R as shown The total resistance of the branch containing the capacitor is negligible After the switch is closed the total heat energy dissipated in the resistance Runtil the capacitor is completely discharged is X CV The value of Xis www R 11

Q15 54 A capacitor of capacitance Cis charged to a potential difference To and then connected to two resistances R and 4R as shown The total resistance of the branch containing the capacitor is negligible After the switch is closed the total heat energy dissipated in the resistance R until the capacitor is completely discharged is x cv The value of Xis wwwww R

Q 8 54 The separation between the plates of an uncharged capacitor of capacitance Cis d Initially there is air dielectric constant 1 between the plates A slab of a material of dielectric constant 2 and thickness d is introduced inside the capacitor as shown Now the capacitor is connected across the terminals of a battery of emf V After the capacitor is completely charged AV The electric field inside the slab is 3d 21 The electric field inside the slab is 3d The potential energy stored in the

Q14 54 All capacitors in the network shown are initially uncharged If a battery of emf Eis connected between the points M and O and the potential difference between the points N and P at steady state is I NP the ratio E is M 2C N C

Q 2 54 In the circuit shown the battery is ideal and both capacitors are initially uncharged If the switch Sis closed the current through the switch immediately afterwards and the current through it after a long time is respectively R S C HH V 3V 3R R 3V V R 3R 3V R D R Hero V HI C www R

Capacitor C of capacity 1 F and capacitor C of capacity 2 F are separately charged fully by a common battery The two capacitors are then separately allowed to discharge through equal resistors at t 0 At t 0 the value of current in the circuit containing 1 F is more than current in the circuit containing 2 F B At t 0 the current in 2 F capacitor circuit is more than current in 1 F capacitor circuit 1 F capacitor losses 50 charge sooner than 2 F capacitor

Q 4 54 In the given circuit all three capacitors are initially uncharged If a battery of emf Eis connected between the points A and B the potential difference across the capacitor of capacitance 2C at steady state becomes A 2E 5 3E C HH HH 2C HH C B

A capacitor of capacitance 20 F is charged to a potential difference of 50 V with a battery The battery is then disconnected and an additional charge of 200 C is given to the positive plate of the capacitor Then A Potential difference across the capacitor will be 60 V B Potential difference across the capacitor will be 55 V C Energy stored in capacitor will be nearly 30 mJ D Energy stored in capacitor will be nearly 25 mJ A 03 B

Two capacitors of capacitances Cand 20 are connected in parallel and are charged to a potential difference of V If now battery is removed and a material of dielectric constant kis placed between plates of capacitance C the potential drop across this capacitor will be 3 V 2 K 3V K 2 3K V 2 2V K 3