Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

The equivalent capacitance of capacitors $$6\mu F$$ and $$3\mu F$$ connected in series is ______.

A
$$3\mu f$$

B
$$2\mu f$$

C
$$4\mu f$$

D
$$6\mu f$$

Solution

We know the equivalent capacitance of capacitors connected in series can be found by using
$$\dfrac{1}{C_{eq}}$$$$=\dfrac{1}{C_{1}}$$$$+\dfrac{1}{C_{2}}$$$$+\dfrac{1}{C_{3}}+...$$

$$\dfrac{1}{C_{eq}}$$$$=\dfrac{1}{6}$$$$+\dfrac{1}{3}$$

$$\Rightarrow C_{eq} = \dfrac{3\times 6}{3+6} = 2\mu F $$
Therefore, B is correct option.
Question 2
1 / -0

The amount of work done in moving a unit positive charge from infinity to a given point is known as:

A
Nuclear potential

B
Potential energy

C
Electric potential

D
Gravitational potential

Solution

Electric potential may be defined as the amount of work done in moving a unit positive charge from infinity to a given point.
$$V = \cfrac{W}{q}$$
Question 3
1 / -0

The two capacitors $$2\mu F$$ and $$6\mu F$$ are put in series, the effective capacity of the system is $$\mu F$$ is:

A
$$8\mu F$$

B
$$2\mu F$$

C
$$3/2\mu F$$

D
$$2/3\mu F$$

Solution

When connected in series
$$\dfrac{1}{C}=\dfrac{1}{C_1}+\dfrac{1}{C_2}$$
$$\dfrac{1}{C}=\dfrac{1}{2}+\dfrac{1}{6}$$
$$C=\dfrac{3}{2}$$
Question 4
1 / -0

When two capacitors of capacities of $$3\mu F$$ and $$6\mu F$$ are connected in series and connected to $$120\ V$$, the potential difference across $$3\mu F$$ is:

A
$$40\ V$$

B
$$60\ V$$

C
$$80\ V$$

D
$$180\ V$$

Solution

Equivalent capacitance is C
$$\dfrac{1}{C}=\dfrac{1}{3}+\dfrac{1}{6}$$, So $$C=2\mu f$$
Now $$Q=VC=120\times 2=240\mu F$$
Now potential across $$3\mu f$$ is $$V=\dfrac{Q}{3}=240/3=80V$$
Question 5
1 / -0

Which of the following is correct statement :

A
Equipotential lines are always perpendicular to the electric field

B
Work done for moving a charge along the conducting surface (closed and containing charge) very close to it may be negative or positive

C
Electric field may cross each other

D
None of the above

Solution

There is no potential gradient along any direction parallel to the surface, and no electric field is parallel with the surface, This means electric field are always at right angle to the equipotential surface.
Question 6
1 / -0

"The work per unit of charge required to move a charge from a reference point to a specified point, measured in joules per coulomb or volts. The static electric field is the negative of the gradient of the electric potential." comments are given below ,select the correct one

A
Statement is correct

B
Statement is incorrect

C
Comment on electric field is not correct

D
Only comment on electric potential is not correct

Solution

The given statement is correct. Volt or Joules per Coulomb are SI unit of Potential (V) i.e, work done per unit charge to move a charge from a reference point to a certain point.
And electric field E is negative of the gradient of electric potential (V) i.e, $$E=\dfrac{-dV}{dr}$$
Question 7
1 / -0

Three capacitor $$C_{1}, C_{2}$$ and $$C_{3}$$ are connected as shown in figure. Find the equivalent capacitance of the combination between points X and Y.

A
$$(C_{1} + C_{2})$$

B
$$(C_{1} + C_{3})$$

C
$$(C_{1} + C_{2} + C_{3})$$

D
$$( C_{2} + C_{3})$$

Solution

After rearraging circuit we can see clearly that $$C_1,C_2,C_3$$ are in parallel(figure-2).
So,the equivalent capacitance is the sum of all the capacitance
$$\Rightarrow C_{eq} = $$$$C_1+C_2+C_3$$
Therefore, C is correct option
Question 8
1 / -0

How many 6mF, 200 V condensers are needed to make a condenser of 18 mF, 600 V?

A
9

B
18

C
3

D
27

Solution

$$6mF,200V$$
To get potential of 600V, 3 capacitors (6mF,200V) must be connected in series
$$C=6mF\\ { \left( { C }_{ eq } \right) }^{ -1 }=\cfrac { 1 }{ 6 } +\cfrac { 1 }{ 6 } +\cfrac { 1 }{ 6 } \Rightarrow { \left( { C }_{ eq } \right) }^{ -1 }={ 2 }^{ -1 }\\ \Rightarrow { C }_{ eq }=2mF$$
To get 18mF, the above must be repeated combination for 9 times which should be connected in parallel, so that we get $$C_{eq\; final}=18mF$$
So, finally we would get 18mF,600V condenser.
So, total number of required condenser = $$9\times 3=27$$
Question 9
1 / -0

An electric dipole is kept in the origin with charges along the x axis, now choose the correct option,

A
equipotential surface is on $$xy$$ plane

B
equipotential surface is on $$xz$$ plane

C
equipotential surface is on $$yz$$ plane

D
none of the above

Solution

Electric potential of every point lying on the $$\mathbf{YZ}$$ plane is zero as every point is at equal distance from negative and positive charge of dipole. So, the plane will be equipotential.
Therefore, (C) is correct option.
Question 10
1 / -0

An electric dipole is placed at the centre of a sphere, choose the correct options :

A
electric field is zero at every point on the surface

B
flux is zero across the surface

C
no circle is present in the sphere which is equipotential

D
none of the above

Solution

A dipole contains two equal and opposite charge. So total charge inside the sphere will be zero.
By Gauss's law, the flux across a surface is depends on the charge inside the surface. As total charge is zero inside the sphere so the flux through the sphere will be zero.
As the electric field is resultant effect due to all charges so there will be field exists on the surface.
As the sphere contains two equal and opposite charges so there may be exists equipotential surface in the sphere.

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Re-Attempt Weekly Quiz Competition

Electrostatic Potential and Capacitance Test - 45

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Electrostatic Potential and Capacitance Test - 45

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Question 1

$$3\mu f$$

$$2\mu f$$

$$4\mu f$$

$$6\mu f$$

Solution

Question 2

Nuclear potential

Potential energy

Electric potential

Gravitational potential

Solution

Question 3

$$8\mu F$$

$$2\mu F$$

$$3/2\mu F$$

$$2/3\mu F$$

Solution

Question 4

$$40\ V$$

$$60\ V$$

$$80\ V$$

$$180\ V$$

Solution

Question 5

Equipotential lines are always perpendicular to the electric field

Work done for moving a charge along the conducting surface (closed and containing charge) very close to it may be negative or positive

Electric field may cross each other

None of the above

Solution

Question 6

Statement is correct

Statement is incorrect

Comment on electric field is not correct

Only comment on electric potential is not correct

Solution

Question 7

$$(C_{1} + C_{2})$$

$$(C_{1} + C_{3})$$

$$(C_{1} + C_{2} + C_{3})$$

$$( C_{2} + C_{3})$$

Solution

Question 8

9

18

3

27

Solution

Question 9

equipotential surface is on $$xy$$ plane

equipotential surface is on $$xz$$ plane

equipotential surface is on $$yz$$ plane

none of the above

Solution

Question 10

electric field is zero at every point on the surface

flux is zero across the surface

no circle is present in the sphere which is equipotential

none of the above

Solution

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