Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 27

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Question 1
1 / -0

When moving electron comes closer to other stationary electron, then its kinetic energy and potential energy respectively _____ and _____.

A
Increases, increases

B
Increases, decreases

C
Decreases, increases

D
Decreases, decreases

Solution

When electron comes closer to the other stationary electron, its kinetic energy decreases because of repulsion between them. As per conservation of energy, the potential energy increases.
Question 2
1 / -0

The equivalent capacitance between the points A and B in the given diagram is:

A
$$

8\mu F

$$

B
$$

6\mu F

$$

C
$$\dfrac{8}{3}\mu F$$

D
$$\dfrac{3}{8}\mu F$$

Solution

$${C_S}$$ Capacitance in series
$$\begin{array}{l} \dfrac { 1 }{ { { C_{ S } } } } =\dfrac { 1 }{ 2 } +\dfrac { 1 }{ 2 } +\dfrac { 1 }{ 2 } \\ =\dfrac { 3 }{ 2 } \\ { C_{ S } }=\dfrac { 2 }{ 3 } \end{array}$$
The equivalent capacitance between A & B is
$$\begin{array}{l} { C_{ P } }=\dfrac { 2 }{ 3 } +2 \\ { C_{ P } }=\dfrac { 8 }{ 3 } \mu F \end{array}$$
Question 3
1 / -0

From a supply of identical capacitors rated $$8\ \mu F, 250\ V$$, the minimum number of capacitors required to form a composite $$16\ \mu F, 1000\ V$$ capacitor is:

A
$$2$$

B
$$4$$

C
$$16$$

D
$$32$$

Solution

The required voltage is 1000v and the capacitors are parallel as 250v.
So number of capacitors required will be 4 i.e$$ 250 \times 4 = 1000$$ in series.
Now example of four capacitor in series will be equal $$2 \mu f$$ (micro farade) but the equivalent capacitance required is given as $$16\mu f$$ so there must be 8 series of parallel arrange capacitors each of capacitor 2 micro farad hence total number of capacitor $$= 4 \times 8 = 32$$

Hence option (D) is corrct
Question 4
1 / -0

The dielectric constant of air is.

A
$$8.85\times 10^{-12}C^2N^{-1}M^{-2}$$

B
$$1$$

C
Infinite

D
Zero

Solution

Dielectric constant of a medium $$K = \dfrac{\epsilon}{\epsilon_o}$$
where $$\epsilon$$ is the permittivity of the medium.
For air, $$\epsilon = \epsilon_o$$
$$\implies$$ $$K = 1$$
Question 5
1 / -0

What is not true of equipotential surface?

A
The PD between any two points on the surface is zero

B
The electric field is always perpendicular to the surface

C
Equipotential surfaces are always spherical

D
No work is done in moving a charge along the surface

Solution

Equipotential surface
$$\rightarrow $$ P.D difference between two points on the surface is zero always since potential is same everywhere in equipotential surface.
$$\rightarrow $$ The EF is always perpendicular to the surface because there is no potential gradient along any direction parallel to the surface P so no EF parallel to the surface
$$\rightarrow $$ Equipotential surface can have any shape not just sphere.
$$\rightarrow $$ No work is done in moving a charge along the surface, because potential difference is zero.
Hence option (C) is correct
Question 6
1 / -0

A parallel plate capacitor is charged. If the plates are pulled apart

A
The capacitance increases

B
The potential difference increases

C
The total charge increases

D
The charge and potential difference remain the same

Solution

Capacitance of a parallel plate capacitor
C=ε0Ad
A parallel plate capacitor is charged (battery is disconnected) then the plates are pulled apart, the capacitance decreases while the charge remains the same
∵Potentialdifference=ChargeCapacitance
∴ potential difference increases
Question 7
1 / -0

What is the unit of electric potential difference?

A
Volt

B
Coulamb

C
Joul

D
Watt

Solution

Unit of electric potential difference is volt(V).
Question 8
1 / -0

Find equivalent capacitance between $$A$$ and $$B$$

A
$$4\mu F$$

B
$$6\mu F$$

C
$$8\mu F$$

D
$$10\mu F$$

Solution

In the given figure,
Equivalent capcitance between $$A$$ and $$B$$.
$${C_{eg}} = {C_1} + {C_2}$$
$$ = 4\mu F + 4\mu F$$
Hence,
The equivalent capcitance between $$A$$ and $$B$$ is$$ = 8\mu F$$
Question 9
1 / -0

The net capacity across AB in _____ $$\mu F$$.

A
$$8\mu F$$

B
$$6\mu F$$

C
$$2\mu F$$

D
$$4\mu F$$
Question 10
1 / -0

The potential of a sphere of radius $$2\ cm$$ when a charge of $$2\ coulomb$$ is given to it, will be

A
$$9\times 10^{3}V$$

B
$$9\times 10^{11}V$$

C
$$9\times 10^{6}V$$

D
$$9\times 10^{16}V$$

Solution