Physics for IIT-JEE 2012-2013: Electricity & Magnetism

B.M. Sharma

Chapter 4

Capacitor and Capacitance - all with Video Answers

Educators

Chapter Questions

Problem 1

Two copper spheres of same radii, one hollow and the other solid, are charged to same potential. Then, which, if any, of the two will have more charge?
a. Hollow.
b. Solid
c. Both will have the same charge
d. Nothing can be predicted

Saman Zulfiqar

Saman Zulfiqar

Numerade Educator

Problem 2

The distance between the plates of a parallel plate capacitor is $d$. A metal plate of thickness $d / 2$ is placed between the plates. What will be its effect on the capacitance?
a. Capacitance will be halved
b. Capacitance will be doubled
c. Capacitance will not change
d. Capacitance will become $1.5$ times original

Saman Zulfiqar

Numerade Educator

Problem 3

Two metallic charged spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$, respectively, are connected to each other. There is.
a. no ch?nge in the energy of the system
b. an increase in the energy of the system
c. always a decrease in the energy of the system
d. a decrease in energy of the system unless $Q_{1} R_{2}=Q_{2} R_{1}$

Hunza Gilgit

Numerade Educator

Problem 4

In the circuit of Fig. $4.89$, find the charge of the condenser having capacity $5 \mu \mathrm{F}$.
a. $4.5 \mu \mathrm{C}$
b. $9 \mu \mathrm{C}$
c. $7 \mu \mathrm{C}$
d. $30 \mu \mathrm{C}$

Saman Zulfiqar

Numerade Educator

Problem 5

In the acconpanying diagram, if $C_{1}=3 \mu \mathrm{F}, C_{2}=6 \mu \mathrm{F}, C_{3}$ $=9 \mu \mathrm{F}, C_{4}=12 \mu \mathrm{F}_{1} C_{5}=15 \mu \mathrm{F}$ and $C_{6}=18 \mu \mathrm{F}$, then the
equivalent capacitance between the ends $A$ and $B$ is
a. $1.22 \mu \mathrm{F}$
b. $5.16 \mu \mathrm{F}$
c. $2.25 \mu \mathrm{F}$
d. $2.51 \mu \mathrm{F}$

Hunza Gilgit

Numerade Educator

Problem 6

Three capacitors of capacitances 2,3 and $4 \mathrm{pF}$ are connected in parallel. What is the charge (in $\mathrm{pC}$ ) on each capacitor if the combination is connected to a $100 \mathrm{~V}$ sup. ply?
a. $200,300,400$
b. $300,200,400$
c. $400,300,200$
d. $400,200,300$

Saman Zulfiqar

Numerade Educator

Problem 7

In the above question, if the capacitors were connected in series, find the potential difference (in V) across each capacitor.
a. $\frac{300}{13}, \frac{600}{13}, \frac{400}{13}$
b. $\frac{600}{13}, \frac{300}{13}, \frac{400}{13}$
c. $\frac{300}{13}, \frac{400}{13}, \frac{600}{13}$
d. $\frac{600}{13}, \frac{400}{13}, \frac{300}{13}$

Hunza Gilgit

Numerade Educator

Problem 8

Four identical metal plates, each with a surface area $A$ (on one side), are placed a distance $d$ from each other as shown in Fig. 4.91. 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. $8_{0} A / d$
b. $2 \varepsilon_{0} A / d$
c. $3 \varepsilon_{0} A / d$
d. $2 \varepsilon_{0} A / 3 d$

Hunza Gilgit

Numerade Educator

Problem 9

We wish to obtain a capacitance of $5 \mu \mathrm{F}$, by using some capacitors, each of $2 \mu \mathrm{F}$. Then, the minimum number of capacitors required is
a. 3
b. 4
c. 5
d. not possible

Saman Zulfiqar

Numerade Educator

Problem 10

A number of capacitors, each of equal capacitance $C_{i}$ are arranged as shown in Fig. 4.92. Equivalent capacitance between $A$ and $B$ is
a. $n^{2} C$
b. $(2 n+1) C$
c. $\frac{(n-1) n}{2} C$
d. $\frac{(n+1) n}{2} C$

Saman Zulfiqar

Numerade Educator

Problem 11

The plates of a parallel plate capacitor are charged up to $100 \mathrm{~V}$. Now, after removing the battery, a $2 \mathrm{~mm}$ thick plate is inserted between the plates. Then, to maintain the seme potential difference, the distance between the capacitor plates is increased by $1.6 \mathrm{~mm}$. Dielectric constant of the plate is
a. 5
b. $1.25$
c. 4
d. $2.5$

Saman Zulfiqar

Numerade Educator

Problem 12

Three plates $A, B, C$ each of area $50 \mathrm{~cm}^{2}$ have separation $3 \mathrm{~mm}$ between $A$ and $B$ and $3 \mathrm{~mm}$ between $B$ and $C$. The energy stored when the plates are fully charged is
a. $6 \times 10^{-9} \mathrm{~J}$
b. $3.12 \times 10^{-9} \mathrm{~J}$
c. $2.12 \times 10^{-9} \mathrm{~J}$
d. none of these

Saman Zulfiqar

Numerade Educator

Problem 13

Four metallic plates, each with a surface area of one side $A$, are placed at a distance $d$ from each other. The alternate plates are connected to points $A$ and $B$ as shown in Fig. 4.94. Then the capacitance of the system is:
a. $\frac{6_{0} A}{d}$
b. $\frac{2 \varepsilon_{0} A}{d}$
c. $\frac{3 \varepsilon_{0} A}{d}$
d. $\frac{4 \varepsilon_{0} A}{d}$

Saman Zulfiqar

Numerade Educator

Problem 14

The capacitance of an infinite circuit formed by the repetition of the same link consisting of two identical capacitors, each with capacitance $C$ (Fig, $4.95)$, is
a. Zero
b. $0.618 \mathrm{C}$
c. $2.62 \mathrm{C}$
d. infinite

Saman Zulfiqar

Numerade Educator

Problem 15

Two parellel plate capacitors, each of capacitance $40 \mu \mathrm{F}$, are connected in series. The space between the plates of one capacitor is filled with a dielectric of dielectric constant $K=3$, then the equivalent cepacitance of the combination is
a. $30 \mu \mathrm{F}$
b. $120 \mu \mathrm{F}$
c. $40 \mu \mathrm{F}$
d. $160 \mu \mathrm{F}$

Saman Zulfiqar

Numerade Educator

Problem 16

For making a parallel plate capacitor you have two plates of copper, a sheet of mica (thickness $=0.10 \mathrm{~mm}, K=5.4)$, a sheet of glass (thickness $=0.20 \mathrm{~mm}, K=7$ ) and a slab of paraffin (thickness $=1.0 \mathrm{~cm}, K=2$ ). To obtain the largest capacitance, which sheet should you place between the copper plates?
a. Mica
b. Copper
c. Glass
d. Information is insufficient

Saman Zulfiqar

Numerade Educator

Problem 17

For configuration of media of permittivity $\varepsilon_{0}, \varepsilon, e_{0}$ between parallel plates each of area $A$, as shown in Fig. $4.96$. the equivalent capacitance is
a. $80 A / d$
b. $\varepsilon \varepsilon_{0} A / d$
c. $\frac{\varepsilon e_{0} A}{d\left(8+\varepsilon_{0}\right)}$
d. $\frac{880 A}{\left(2 \varepsilon+\varepsilon_{0}\right) d}$

Saman Zulfiqar

Numerade Educator

Problem 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

Saman Zulfiqar

Numerade Educator

Problem 19

When a dielectric slab is introduced between the plates of an isolated charged capacitor, it
a. increases the capacitance of the capacitor
b. decreases the electric field between the plates
c. decreases the amount of energy stored in the capacitor
d. all of the above

Saman Zulfiqar

Numerade Educator

Problem 20

Seven capacitors, each of capacitance $2 \mu \mathrm{F}$, are to be combined to obtain a capacitance of $10 / 11 \mu \mathrm{F}$. Which of the following combination is possible?
a. 2 in parallel, 5 in series
b. 3 in parallel, 4 in series.
c. 4 in parallel, 3 in series
d. 5 in parallel, 2 in series

Saman Zulfiqar

Numerade Educator

Problem 21

A spherical capacitor has an inner sphere of radius $12 \mathrm{~cm}$ and an outer sphere of radius $13 \mathrm{~cm}$. The outer sphere is earthed and the inner sphere is given a charge of $2.5 \mu \mathrm{C}$. The space between the concentric spheres is filled with a liquid of dielectric constant 32. Determine potential of the inner sphere.
a. $400 \mathrm{~V}$
b. $450 \mathrm{~V}$
c. $500 \mathrm{~V}$
d. $300 \mathrm{~V}$

Saman Zulfiqar

Numerade Educator

Problem 22

A parallel plate capacitor has plates of area $A$ and separation $d$ and is charged to a potential difference $V .$ The charging battery is then disconnected and the plates are pulled apart until their separation is $2 d$. What is the work required to separate the plates?
a. $2 \varepsilon_{0} A V^{2} / d$
b. $\varepsilon_{0} A V^{2} / d$
c. $3 \varepsilon_{0} A V^{2} / 2 d$
d. $8_{0} A V^{2} / 2 d$

Saman Zulfiqar

Numerade Educator

Problem 23

A parallel plate capacitor is charged and then disconnected from the source of potential difference. If the plates of the condenser are then moved farther apart by the use of insulated handle, which one of the following is true?
A. The charge on the capacitor increases
b. The charge on the capacitor decreases
c. The capacitance of the capacitor increases
d. The potential difference across the plates increases

Saman Zulfiqar

Numerade Educator

Problem 24

For the section $A B$ of a circuit shown in Fig. $4.97$, $C_{1}=1 \mu \mathrm{F}, C_{2}=2 \mu \mathrm{F}_{1} E=10 \mathrm{~V}$ and the potential difference
$V_{A}-V_{B}=-10 \mathrm{~V}$, Charge on capacitor $C_{1}$ is
a. $0 \mu \mathrm{C}$
b. $20 / 3 \mu \mathrm{C}$
c. $40 / 3 \mu \mathrm{C}$
d. none of these

Saman Zulfiqar

Numerade Educator

Problem 25

A $600 \mathrm{pF}$ capacitor is charged by a $200 \mathrm{~V}$ supply. It is then disconnected from the supply and is connected to another uncharged $600 \mathrm{pF}$ capacitor. What is the common potential (in $\mathrm{V}$ ) and energy lost (in J) after reconnection?
a. $100,6 \times 10^{-6}$
b. $200,6 \times 10^{-5}$
c. $200,5 \times 10^{-6}$
d. $100,6 \times 10^{-5}$

Saman Zulfiqar

Numerade Educator

Problem 26

Two parallel plate capacitors of capacitances $C$ and $2 C$ are connected in parallel and charged to potential difference $V$, The battery is then disconnected and the region between the plates of $C$ is filled completely with a material of dielectric constant $K$. The common potential difference across the combination becomes
a. $\frac{2 V}{K+2}$
b. $\frac{V}{K+2}$
c. $\frac{3 V}{K+3}$
d. $\frac{3 V}{K+2}$

Saman Zulfiqar

Numerade Educator

Problem 27

Three capacitors $A, B$ and $C$ are connected in a circuit as shown in the Fig. 4.98. What is the charge in $\mu \mathrm{C}$ on the Capacitor $B$ ?
8. $1 / 3$
b. $2 / 3$
c. 1
d. $4 / 3$

Saman Zulfiqar

Numerade Educator

Problem 28

A parallel plate capacitor is made by stacking $n$ equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is $C$, then the resultant capacitance is
a. $n C$
b. $C$
c. $(n+1) C$
d. $(n-1) C$

Saman Zulfiqar

Numerade Educator

Problem 29

Three capacitors are connected as shown in Fig. $4.99 .$ Then, the charge on capacitor $C_{1}$ is
a. $6 \mu \mathrm{C}$
b. $12 \mu \mathrm{C}$
c. $18 \mu \mathrm{C}$
d. $24 \mu \mathrm{C}$

Saman Zulfiqar

Numerade Educator

Problem 30

In the above question, the potential of point $A$ is
a. $3 \mathrm{~V}$
b. $6 \mathrm{~V}$
c. $9 \mathrm{~V}$
d. zero

Saman Zulfiqar

Numerade Educator

Problem 31

In Fig. 4.100, if the potential at point $B$ is taken as zero, then the potential at point $A$ will be
a. $8 \mathrm{~V}$
b. $16 \mathrm{~V}$
c. $24 \mathrm{~V}$
d. none of the above

Hunza Gilgit

Numerade Educator

Problem 32

A capacitor of capacitance $C_{1}=1 \mu \mathrm{F}$ charged up to a volfage $V=110 \mathrm{~V}$ is connected in parallel to the terminal of a circuit consisting of two uncharged capacitors connected in series and possessing capacitances $C_{2}=2 \mu \mathrm{F}$ and $C_{3}=3 \mu \mathrm{F}$. Then, the amount of charge that will flow through the connecting wires is
a. $40 \mu \mathrm{C}$
b. $50 \mu \mathrm{C}$
c. $60 \mu \mathrm{C}$
d. $110 \mu \mathrm{C}$

Saman Zulfiqar

Numerade Educator

Problem 33

Ten capacitors are joined in parallel and charged with a battery up to a potential $V$. They are then disconnected from battery and joined in series. Then, the potential of this combination will be
a. $1 \mathrm{~V}$
b. $10 \mathrm{~V}$
c. $5 \mathrm{~V}$
d. $2 \mathrm{~V}$

Saman Zulfiqar

Numerade Educator

Problem 34

In Fig. $4.101$, three capacitors $C_{1}, C_{2}$ and $C_{3}$ are joined to a battery. With symbols having their usual meaning, the correct conditions will be
a. $Q_{1}=Q_{2}=Q_{3}$ and $V_{1}=V_{2}=V_{3}+V$
b. $Q_{1}=Q_{2}+Q_{3}$ and $V=V_{1}+V_{2}+V_{3}$
c. $Q_{1}=Q_{2}+Q_{3}$ and $V=V_{1}+V_{2}$
d. $Q_{2}=Q_{3}$ and $V_{2}=V_{3}$

Saman Zulfiqar

Numerade Educator

Problem 35

The cross section of a cable is shown in Fig. 4.102. The inner conductor has a radius of $10 \mathrm{~mm}$ and the dielectric has a thickness of $5 \mathrm{~mm}$. The cable is $8 \mathrm{~km}$ long. Then, the capacitance of the cable is (given log $1.5=0.4$ ).
a. $3.8 \mu \mathrm{F}$
b. $1.1 \mu \mathrm{F}$
c. $4.8 \times 10^{-10} \mathrm{~F}$
d. none of these

Saman Zulfiqar

Numerade Educator

Problem 36

An uncharged parallel plate capacitor having a dielectric of dielectric constant $K$ is connected to a similar air cored parallel plate capacitor charged to a potential $V_{0}$. The two share the charge and the common potential becomes $V$. The dielectric constant $K$ is
a. $\frac{V_{0}}{V}-1$
b. $\frac{V_{0}}{V}+1$
c. $\frac{V}{V_{0}}-1$
d. $\frac{V}{V_{0}}+1$

Saman Zulfiqar

Numerade Educator

Problem 37

Fig. $4.103$ shows two identical parallel plate capacitors connected to a battery. The switch is now opened and the free space between the plates of capacitors is filled with a dielectric of $K=3 .$ The ratio of the total electrostatic energy stored in both the capacitors before and after the introduction of the dielectric is
a. $3 / 4$
b. $4 / 5$
c. $2 / 3$
d. $3 / 5$

Saman Zulfiqar

Numerade Educator

Problem 38

Two identical parallel plate capacitors are connected in series and then joined in series with a battery of $100 \mathrm{~V}$, $\mathrm{A}$ slab of dielectric constant $K=3$ is inserted between the plates of the first capacitor. Then, the potential difference across the capacitors will be, respectively.
a. $25 \mathrm{~V}, 75 \mathrm{~V}$
b. $75 \mathrm{~V}, 25 \mathrm{~V}$
c. $20 \mathrm{~V}, 80 \mathrm{~V}$
d. $50 \mathrm{~V}, 50 \mathrm{~V}$

Saman Zulfiqar

Numerade Educator

Problem 39

A parallel plate air capacitor is charged to $100 \mathrm{~V}$ and is then connected to an identical capacitor in parallel. The second capacitor has some dielectric medium between its plates. If the common potential is $20 \mathrm{~V}$, the dielectric constant of the medium is
a. $2.5$
b. 4
c. 5
d. 8

Hunza Gilgit

Numerade Educator

Problem 40

In the given network of capacitors as shown in Fig. $4.104$. given $C_{1}=C_{2}=C_{3}=400 \mathrm{pF}$ and $C_{4}=C_{5}=C_{5}=200$
$\mathrm{pF}$. The effective capacitance of the circuit between $X$ and $Y$ is
a. $810 \mathrm{pF}$
b. $205 \mathrm{pF}$
c. $600 \mathrm{pF}$
d. $410 \mathrm{pF}$

Saman Zulfiqar

Numerade Educator

Problem 41

The work done in increasing the potential of a capacitor from $V$ volt to $2 V$ volt is $W$. Then, the work done in increasing the potential of the same capacitor form $2 V$ volt to $4 V$ volt will be
a. $W$
b. $2 W$
c. $4 W$
d. $8 \mathrm{~W}$

Saman Zulfiqar

Numerade Educator

Problem 42

The plates of a parallel plate capacitor have an area of 90 $\mathrm{cm}^{2}$ cach and are separated by $2 \mathrm{~mm}$. The capacitor is charged by connecting it to a $400 \mathrm{~V}$ supply. Then the energy density of the energy stored (in $\mathrm{Jm}^{-3}$ ) in the capacitor is (Take $\varepsilon_{0}=8.8 \times 10^{-12} \mathrm{Fm}^{-1}$ )
a. $0.113$
b. $0.177$
c. $0.152$
d. none of these

Saman Zulfiqar

Numerade Educator

Problem 43

Three identical capacitors, each of capacitance $C$, are connected in series with a battery of e.m.f. $V$ and get fully charged. Now, the battery is removed and the capacitors are connected in paraliel with positive terminals at one point and negative terminals at other point. Then, the common potential will be
a. $V$
b. $3 \mathrm{~V}$
c. $V / 3$
d. Zero

Saman Zulfiqar

Numerade Educator

Problem 44

In Fig. 4. 105, given $C_{1}=3 \mu \mathrm{F}_{1} C_{2}=5 \mu \mathrm{F}, C_{3}=9 \mu \mathrm{F}$ and $C_{4}$
$=13 \mu \mathrm{F}$. What is the potential difference between points $A$ and $B$ ?
a. $13 \mathrm{~V}$
b. $9 \mathrm{~V}$
c. $0 \mathrm{~V}$
d. $11 \mathrm{~V}$

Saman Zulfiqar

Numerade Educator

Problem 45

Two capacitors of 12 and $4 \mu \mathrm{F}$ capacitors are connected in series and charged by using a battery of $12 \mathrm{~V}$ e.m.f.. Now, the battery is disconnected and the charged capacitors are connected in parallel. Then, the redistributed charges on each capacitor after parallel connection will be, respectively,
a. $36 \mu \mathrm{C}, 36 \mu \mathrm{C}$
b. $54 \mu C, 18 \mu C$
c. $18 \mu \mathrm{C}, 54 \mu \mathrm{C}$
d. none of these

Hunza Gilgit

Numerade Educator

Problem 46

In the combination of capacitors shown in Fig. 4.106, the potential difference across the plates of the capacitor $A$ will be
a. $4.8 \mathrm{~V}$
b. $6 \mathrm{~V}$
c. $1.2 \mathrm{~V}$
d. $2.4 \mathrm{~V}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 47

In a circuit shown in Fig. 4.107, the potential difference across the capacitor of $2 \mathrm{~F}$ is
a. $8 \mathrm{~V}$
b. $4 \mathrm{~V}$
c. $12 \mathrm{~V}$
d. $6 \mathrm{~V}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 48

When a metal plate is introduced between fhe two plates of a charged capacitor and insulated from them, then
a. the metal plate divides the capacitor into two capacitors connected in parallcl to each other
b. the metal plate divides the capacitor into two capacitors connected in series with each other
c. the métal plate is equivalent to a dielectric of zero dielectric constant
d. capacitance of the capacitor decreases

Saman Zulfiqar

Numerade Educator

Problem 49

The potential gradient at which dielectric of the condenser just gets punctured, is called
a. dielectric constant
b. dielectric strength
c. dielectric resistance
d. dielectric nuinber

Saman Zulfiqar

Numerade Educator

Problem 50

A parallel plate capacitor is charged and then isolated. What is the offect of increasirig the plate separation on charge, potential and capacitance, respectively?
a. Constant, decreases, decreases
b. Increases, decreases, decreases
c. Constant, decreases, increases
d. Constant, increases, decreases

Saman Zulfiqar

Numerade Educator

Problem 51

Six identical capacitors are joined in parallel, charged to a potential difference of $10 \mathrm{~V}$, separated and then connected in series, i.e., the positive plate of one is connected to negative plate of other. Then, potential difference between free plates becomes
a. $10 \mathrm{~V}$
b. $30 \mathrm{~V}$
c. $60 \mathrm{~V}$
d. $10 / 6 \mathrm{~V}$

Saman Zulfiqar

Numerade Educator

Problem 52

The effective capacitance between points $X$ and $Y$ in Fig. 4.108, assuming $C_{2}^{\circ}=10 \mu \mathrm{F}$ and that outer capacitors are all $4^{4} \mu \mathrm{F}$ each, is
a. $1 \mu \mathrm{F}$
b. $3 \mu \mathrm{F}$
c. $4 \mu \mathrm{F}$
d. $5 \mu \mathrm{F}$

Saman Zulfiqar

Numerade Educator

Problem 53

The resultant 'capacitance between the points $A$ and $B$ in Fig. $4.109$ is
a. $15 \mu \mathrm{F}$
b. $30 \mu \mathrm{F}$
c. $60 \mu \mathrm{F}$
d. $45 \mu \mathrm{F}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 54

Two condensers $C_{1}$ and $C_{2}$ in a circuit are joined as shown in Fig. 4.110. The potential of point $A$ is $V_{1}$ and that of $B$ is $V_{2}$. The potential of point $D$ will be
a. $\frac{1}{2}\left(V_{1}+V_{2}\right)$
b. $\frac{C_{1} V_{2}+C_{2} V_{1}}{C_{1}+C_{2}}$
c. $\frac{C_{1} V_{1}+C_{2} V_{2}}{C_{1}+C_{2}}$
d. $\frac{C_{2} V_{1}-C_{1} V_{2}}{C_{1}+C_{2}}$

Saman Zulfiqar

Numerade Educator

Problem 55

A capacitor is charged to store an energy $U .$ The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitor is now
a. $3 U / 2$
b. $U$
c. $U / 4$
d. $U / 2$

Saman Zulfiqar

Numerade Educator

Problem 56

Consider a parallel plate capacitor of capacity $10 \mu \mathrm{F}$ with air filled in the gap between the plates. Now, one half of the space between the plates is filed with a dielectric of dielectric constant 4 as shown in Fig. $4.111$. The capacity of the capacitor changes to
a. $25 \mu \mathrm{F}$
b. $20 \mu \mathrm{F}$
c. $40 \mu \mathrm{F}$
d. $5 \mu \mathrm{F}$

Saman Zulfiqar

Numerade Educator

Problem 57

A $2 \mu \mathrm{F}$ capacitor is charged to $100 \mathrm{~V}$ and then its plates are connected by a conducting wire. The heat produced is
a. $0.001 \mathrm{~J}$
b. $0.01 \mathrm{~J}$
c. $0.1 \mathrm{~J}$
d. I J

Saman Zulfiqar

Numerade Educator

Problem 58

In Fig. $4.112$ initial status of capacitance and their connection is shown. Which of the following is incorrect about this circuit
a. Final charge on each capacitor "will be zero
b. Final total electricál energy of the capacitance will be zero
c. Total charge flown from $A$ to $D$ is $30 \mu \mathrm{C}$
d. Total charge flown from $A$ to $D$ is $-30 \mu C$

Saman Zulfiqar

Numerade Educator

Problem 59

A parallel plate capacitor with no dielectric has a capacitance of $0.5 \mu \mathrm{F}$. The space between the plates is filled with equal amounts of two diclectric matcrials of dielectric constants 2 and 3 as shown in Fig. $4.113$. Find the capacitance of the system now.
a. $1.2 \mu \mathrm{F}$
b. $1.8 \mu \mathrm{F}$
c. $1.25 \mu \mathrm{F}$
d. none of these

Saman Zulfiqar

Numerade Educator

Problem 60

Solve the above question if the dielectric materials were filled as shown in Fig. $4.114$.
a. $1.2 \mu \mathrm{F}$
b. $1.25 \mu \mathrm{F}$
c. $1.80 \mu \mathrm{F}$
d. None of these

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 61

Two metallic spheres of radii $a$ and $b$ are separated by a distance $d$ as shown in Fig. $4.115$. The capacity of the system is
a. $\frac{4 \pi \varepsilon_{0}}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$
b. $\frac{4 \pi \varepsilon_{0}}{\frac{1}{a}+\frac{1}{b}+\frac{2}{d}}$
c. $\frac{4 \pi \varepsilon_{0}}{\frac{1}{a}-\frac{1}{b}+\frac{2}{d}}$
d. $\frac{4 \pi \varepsilon_{0}}{\frac{1}{a}-\frac{1}{b}-\frac{2}{d}}$

Saman Zulfiqar

Numerade Educator

Problem 62

A capacitor of capacitance $C_{0}$ is charged to a potential $V_{0}$ and then isolated. A small capacitor $C$ is then charged from $C_{0}$, discharged and charged again; the process being repeated $n$ times. Due to this, potential of the larger capacitor is decreased to $V$. Value of $C$ is.
a. $C_{0}\left(\frac{V_{0}}{V}\right)^{1 / n}$
b. $C_{0}\left[\left(\frac{V_{0}}{V}\right)^{1 / n}-1\right]$
c. $C_{0}\left[\left(\frac{V}{V_{0}}\right)-1\right]^{n}$
d. $C_{0}\left[\left(\frac{V}{V_{0}}\right)^{n}+1\right]$

Saman Zulfiqar

Numerade Educator

Problem 63

If the current, charging a capacitor, is kept constant, then the potential difference $V$ across the capacitor varies with time $t$ as
a.
b.
c.
d.

Saman Zulfiqar

Numerade Educator

Problem 64

A conducting sphere of radius $R$, carrying charge $Q$, lies inside an uncharged conducting shell of radius $2 R$. If they are joined by a metal wire:
A. a charge $Q / 3$ will fow from the sphere to the shell
b. a charge $2 Q / 3$ will flow from the sphere to the shell
c. a charge $Q$ will flow from the sphere to the shell
d. $\frac{1}{8 \pi \varepsilon_{0}} \frac{Q^{2}}{R}$ amount of heat will be produced

Saman Zulfiqar

Numerade Educator

Problem 65

The plates of a parallel plate capacitor are charged with surface charge densities $\sigma_{1}$ and $\sigma_{2}$, respectively. The electric field at points:
a. inside the region between the plates will be zero
b. above the upper plate and below the lower plate will be zero
c. everywhere in the space will be zero
d. inside the region between the plates will be uniform and non-zero

Saman Zulfiqar

Numerade Educator

Problem 66

The distance between plates of a parallel plate capacitor is $5 d$. The positively charged plate is at $x=0$ and negatively charged plate is at $x=5 d$.
Two slabs, one of conductor and the other of a dielectric of same thickness $d$, are inserted between the plates as shown in Fig. $4.118$. Potential $V$ versus distance $x$ graph will be
A.
b.
c?
d. None of these

Saman Zulfiqar

Numerade Educator

Problem 67

In the circuit shown in Fig. $4.119 C=6 \mu \mathrm{F}$. The charge stored in capacitor of capacity $C$ is
a. zero
b. $90 \mu \mathrm{C}$
c. $40 \mu \mathrm{C}$
d. $60 \mu \mathrm{C}$

Saman Zulfiqar

Numerade Educator

Problem 68

One plate of a capacitor is fixed and the other is connected to a spring as shown in Fig. $4.120$. Area of both the plates is $A$. In steady state (equilibrium), separation between the plates is $0.8 d$ (spring was unstretched and the distance between the plates was $d$ when the capacitor was uncharged). The force constant of the spring is approximately
a. $\frac{4 \varepsilon_{0} A E^{2}}{d^{3}}$
b. $\frac{2 \varepsilon_{0} A E}{d^{2}}$
c. $\frac{6 \varepsilon_{0} E^{2}}{A d^{3}}$
d. $\frac{\varepsilon_{0} A E^{3}}{2 d^{3}}$

Saman Zulfiqar

Numerade Educator

Problem 69

A dielectric slab of area $A$ and thickness $d$ is inserted between the plates of a capacitor of area $2 A$ with constant speed $v$ as shown in Fig. $4.121$. Distance between the plates is $d$.
The capacitor is connected to a battery of e.m.f. $E$. The current in the circuit varies with time as
a.
b.
c.
d.

Saman Zulfiqar

Numerade Educator

Problem 70

A photographic flash unit consists of a xenon filled tube. It gives a flash of average power $2000 \mathrm{~W}$ for $0.04 \mathrm{~s}$. The fash is due to discharge of a fully charged capacitor of $40 \mu \mathrm{F}$. The voltage to which it is charged before a flash is given by the unit is
a. $1500 \mathrm{~V}$
b. $2000 \mathrm{~V}$
c. $2500 \mathrm{~V}$
d. $3000 \mathrm{~V}$

Saman Zulfiqar

Numerade Educator

Problem 71

A parallel plate capacitor is constructed using three different dielectric materials as shown in the Fig. 4.123. What is the capacitance across $P$ and $Q$ ?
a. $\left(\frac{K_{1}}{2}+\frac{K_{2} K_{3}}{K_{2}+K_{3}}\right) \frac{\varepsilon_{9} A}{t}$
b. $\left(K_{1}+\frac{K_{2} K_{3}}{K_{2}+K_{3}}\right) \frac{\varepsilon_{0} A}{t}$
c. $\left(K_{1}+\frac{2 K_{2} K_{3}}{K_{2}+K_{3}}\right) \frac{\varepsilon_{0} A}{t}$
d. $\left(K_{1}+\frac{K_{2} K_{3}}{2\left(K_{2}+K_{3}\right)} \frac{\varepsilon_{0} A}{t}\right)$

Saman Zulfiqar

Numerade Educator

Problem 72

Two square plates $(l \times l)$ and dielectric $\left(\frac{l}{2} \times \frac{t}{2} \times l\right)$ are arranged as shown in Fig. 4.124. Find the equivalent capacitance of the structure.
a. $\frac{2 \varepsilon_{n} A}{t}\left(\frac{K+1}{K+3}\right)$
b. $\frac{2 \varepsilon_{0} A}{t}\left(\frac{K+3}{K+1}\right)$
c. $\frac{\varepsilon_{0} A}{t}\left(\frac{K+1}{K+3}\right)$
d. $\frac{\varepsilon_{0} A}{t}\left(\frac{2 K+1}{2 K+3}\right)$

Hunza Gilgit

Numerade Educator

Problem 73

The equivalent capacitance across $A B$ (Fig. $4.125$ ) is
a. $8 \mu \mathrm{F}$
b. $12 \mu \mathrm{F}$
c. $4 \mu \mathrm{F}$
d. $24 \mu \mathrm{F}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 74

The equivalent capacitance between $P$ and $Q$ (Fig. $4.126$ ) is
a. $\frac{C}{3}$
b. $3 C$
c. $2 \mathrm{C}$
d. $C$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 75

The equivalent capacitance between $P$ and $Q$ (Fig. $4.127$ ) is
a. $\frac{C}{3}$
b. $3 C$
c. $2 C$
d. $C$

Hunza Gilgit

Numerade Educator

Problem 76

Find capacitance between $P$ and $O$ (Fig. $4.128$ ) is
a. $2 C$
b. $3 C$
c. $8 C$
d. $6 C$

Hunza Gilgit

Numerade Educator

Problem 77

In the circuit shown in Fig. $4.129 C_{1}=6 \mu \mathrm{F}, C_{2}=3 \mu \mathrm{F}$
and battery $B=20 \mathrm{~V}$. The switch $S_{1}$ is first closed. It is then opened and afterwards $S_{2}$ is closed. What is the final charge on $C_{2} ?$
a. $120 \mu \mathrm{C}$
b. $80 \mu \mathrm{C}$
c. $40 \mu \mathrm{C}$
d. $20 \mu \mathrm{C}$

Saman Zulfiqar

Numerade Educator