Capacitance of a Random Conductor

Q. Smalles unit of charge is -Frankline -Faraday - Coulomb -e.m.u

Q. 35. If charge on a capacitor is increased by 2 C, then energy stored in it increases by 21 %. Then the original charge on the capacitor is. (1) 40 C (2) 30 C (3) 20 C (4) 10 C CE

Q.

A conducting sphere of radius 10 cm is charged to $10\mu C$. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the spheres are separated then surface density of charges, on the spheres will be in the ratio of:

1. 1:3
2. 3:1
3. 2:1
4. 1:1

Q. 33.A parallel plate air capacitor has capacity C, separation between plates is d and potential difference V is applied between the plates . Force of attraction between the plates, is

Q. (a) Derive the expression for the energy stored in a parallel plate capacitor. Hence obtain the expression for the energy density of the electric field.
(b) A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor.

Q.

When a dielectric slab is introduced between the parallel plate capacitor, its capacitance

1. increases

2. decreases

3. remains the same

4. become zero.

Q.

In the figure shown below, the charge on the left plate of the $10uF$ capacitor is $-30uF$. The charge on the right plate of the $6uF$ capacitor is:

1. $-18uF$

2. $-12uF$

3. $+12uF$

4. $+18uF$

Q.

What are high-level and low-level modulators?

Q.

Identify the wrong statement in the following Coulombs law correctly describes the electric force that

1. binds the electrons of an atom to its nucleus

2. binds protons and neutrons in the nucleus of an atom

3. binds atoms together to form molecules

4. binds atoms and molecules to form solids

Q. (i) If two similar large plates, each of area A having surface charge densities$+\sigma \text{and}-\sigma$ are separated by a distance in air, find the expressions for

(a) field at points between the two plates and on outer side of the plates. Specify the direction of the field in each case.

(b) the potential difference between the plates.

(c) the capacitance of the capacitor so formed.

(ii) Two metallic spheres of radii R and 2R are charged so that both of these have same surface charge density $\sigma$. If they are connected to each other with a conducting wire, in which direction will the charge flow and why ?

Q. Uniform electric field of magnitude 100 v/m in space is directed along the line y=3+x. Find the potential difference between point A(3, 1) a nd B(1, 3)

Q. Figure shows five capacitors connected across a $12\text{V}$ power supply. What is the charge on the $2\mu \text{F}$ capacitor ?

1. $6\mu \text{C}$
2. $10\mu \text{C}$
3. $12\mu \text{C}$
4. $8\mu \text{C}$

Q.

The volume $V$ and depth $x$ of water in a vessel are connected by the relation $V=5x-\frac{x^2}{6}$ and the volume of water is increasing at the rate of $5$ $\raisebox{1ex}{$c{m}^3$}\!\left/ \!\raisebox{-1ex}{$sec$}\right.$, when $x=2cm$.

The rate at which the depth of water is increasing is

1. $\frac{5}{18}$ $\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$sec$}\right.$

2. $\frac{1}{4}$$\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$sec$}\right.$

3. $\frac{5}{16}$$\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$sec$}\right.$

4. None of these

Q. Figure shows three circuits, each consisting of a switch and two capacitors, initially charged as indicated. In which circuit the charge on the left hand capacitor will change after the closing of the switch ?

1. 1
2. 2
3. 3
4. All

Q.

Why there is a decrease in resistance when a parallel combination is used?

Q.

If n drops, each of capacitance C, coalesce to form a single big drop, the capacitance of the big drop will be

1. $\frac{V}{n^{1/3}}$
   

2. $\frac{V}{n^{2/3}}$
   

3. $V{n}^{2/3}$

4. $V{n}^{1/3}$
   

Q.

The capacitance of a parallel plate capacitor does not depend upon

1. shape of plates

2. size of plates

3. separation between plates

4. potential difference between the plates.

Q. The charge on $3\mu F$ capacitor shown in the figure is:

1. $2\mu F$
2. $10\mu F$
3. $6\mu F$
4. $8\mu F$

Q. Plates of area A are arranged as shown. The distance between each two plates is d, the net capacitance between ‘a’ and ‘b’ is:

1. $\frac{{\in }_{0}A}{d}$
2. $\frac{7{\in }_{0}A}{d}$
3. $\frac{6{\in }_{0}A}{d}$
4. $\frac{5{\in }_{0}A}{d}$

Q. Write Coulombs law in vectorial form

Q. a parallel plate capacitor is to be designed with a voltage rating 1 kV using a material of dielectric constant 10 and dielectric strength 10^6 V/m.what minimum area of the plates is required to have a capacitance of 88.5 pF

Q. A capacitor of capacitance C initial charge q° and connected to an inductor of Inductance L as shown. At t=0 switch S is closed. The current through the inductor when energy in the capacitor is three times the energy of the inductor is:

Q. The diagram shows a part of disc of radius $R$ carrying uniformly distributed charge of density $\sigma$. Electric potential at the centre $O$ of parent disc is

1. $\frac{\sigma R}{32{ϵ}_0}$
2. $\frac{\sigma R}{16{ϵ}_0}$
3. $\frac{\sigma R}{24{ϵ}_0}$
4. $\frac{\sigma R}{2{ϵ}_0}$

Q. Four plates of equal area A are separated by equal distances $d$ and are arranged as shown in the figure. The equivalent capacity is

1. $\frac{2{\epsilon }_{o}A}{d}$
2. $\frac{3{\epsilon }_{o}A}{d}$
3. $\frac{{\epsilon }_{o}A}{2d}$
4. $\frac{{\epsilon }_{o}A}{d}$

Q. A conducting rod is moving with a constant velocity $v$ over the parallel conducting rails, which are connected to the ends through a resistor $R$ and capacitor $C$ as shown in the figure. Magnetic field $B$ exist in the region perpendicular to the plane of paper.


Consider the following statements:

$\left(i\right)$ Current in loop $\text{AEFBA}$ is anticlockwise.

$\left(ii\right)$ Current in loop $\text{AEFBA}$ is clockwise.

$\left(iii\right)$ Current through the capacitor is zero.

$\left(iv\right)$ Energy stored in the capacitor is
$\frac{1}{2}C{B}^2{L}^2{v}^2$.

Which of the following options is correct?

1. Statements $\left(i\right)$ and $\left(iii\right)$ are correct
2. Statements $\left(ii\right)$ and $\left(iv\right)$ are correct
3. Statements $\left(i\right)$, $\left(iii\right)$ and $\left(iv\right)$ are correct
4. None of these statements are correct.

Q. A conducting circular loop made of a thin wire, has area $3.5\times {10}^{-1}{\text{m}}^2$ and resistance $10\Omega$. It is placed perpendicular to a time dependent magnetic field $B\left(t\right)=\left(0.4\text{T}\right)\sin \left(50\pi t\right)$. The net charge flowing through the loop during $t=0\text{s}$ and $t=10\text{ms}$ is close to:

1. $7\text{mC}$
2. $21\text{mC}$
3. $14\text{mC}$
4. $6\text{mC}$

Q. The capacitance of a cylindrical capacitor of length $72\text{mm}$ is $2\text{pF}$. If the ratio of radii of its outer cylindrical conductor to that of its inner cylindrical conductor is $e^x$, then $x$ is

1. $2$
2. $5$
3. $4$
4. $3$

Q. Assertion $\left(A\right)-$ A current flows in a conductor only when there is an electric field within the conductor.
Reason $\left(R\right)-$ The drift velocity of electron in presence of electric field decreases

Of the following mark the correct statement.

1. Both ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{R}^{\prime }$ are true and ${}^{\prime }{R}^{\prime }$ is the correct explanation of ${}^{\prime }{A}^{\prime }$.
2. Both ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{R}^{\prime }$ are true and ${}^{\prime }{R}^{\prime }$ is not the correct explanation of ${}^{\prime }{A}^{\prime }$
3. ${}^{\prime }{A}^{\prime }$ is true and ${}^{\prime }{R}^{\prime }$ is false
4. ${}^{\prime }{A}^{\prime }$ is false and ${}^{\prime }{R}^{\prime }$ is true

Q. A rod of length $10\text{cm}$ made up of conducting and non-conducting material (shaded part is non-conducting). The rod is revolving with constant angular velocity of $10\text{rad/s}$ about point $O$, in a constant magnetic field of $2\text{T}$ perpendicular to the plane of rotation of the rod as shown in the figure. The induced emf between the point $A$ and $B$ is -

1. $0.02\text{V}$
2. $0.05\text{V}$
3. $0.03\text{V}$
4. $0.04\text{V}$

Q.

In SI unit number of electric field line associated with 1 coulomb charge is