Electrostatic Potential Test

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Electrostatic Potential Test - 6

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Question 1
1 / -0.25

64 water drops having equal charges combine to form one bigger drop. The capacitance of the bigger drop, as compared to that of smaller drop will be:

A
64 times

B
8 times

C
16 times

D
4 times

Solution

Capacitance of the small drop of radius r C₈ = 4 πε₀ r and that of the big drop of radius R is C_B = 4 πε₀ R .
The volume of 64 small drops,
The ratio
Question 2
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An electrolytic capacitor is marked 8 μF, 220 V. It can be used in a circuit where the p.d. across the capacitor may be:

A
300 V

B
500 V

C
200 V

D
1000 V

Solution

The breakdown of the potential of the capacitor is 220 V.

In order to prevent damage to a capacitor, it should be always used in a circuit where the p.d is less than its breakdown potential . The p.d difference can only be 200 V.
Question 3
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The capacitance of a parallel plate capacitor is 5 μF. When a glass slab of thickness equal to the separation between the plates is introduced between the plates, the potential difference reduces to 1/8 of the original value. The dielectric constant of glass is

A
40

B
8

C
5

D
1.6

Solution

When a dielectric of constant K is introduced between the plates of a capacitor, the potential V reduces to V/K. Therefore K=8
Question 4
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For a parallel plate capacitor ______________ possible potential difference between the capacitor plates.

A
dielectric decreases the maximum

B
dielectric decreases the minimum

C
dielectric increases the maximum

D
dielectric increases the minimum

Solution

When a dielectric is introduced between two charged plates of a capacitor having a charge Q and maintained at a potential difference of V, a reverse electric field is set up inside the dielectric due to dielectric polarization. This reduces the electric field in between the plates. The potential is also reduced.

Maximum potential is dependent on the charge on the plates. As the charge remains constant, the presence of the dielectric decreases the maximum potential between the plates .
Question 5
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Which of the following is true about equipotential lines?

A
Electric field lines are tangential to equipotential lines.

B
Electric field lines are parallel to equipotential lines.

C
Electric field lines are perpendicular to equipotential lines.

D
Electric field lines are opposite to equipotential lines.

Solution

Electric field lines show the direction of the electric field at the point. If the electric field lines were tangential, parallel, or opposite to the equipotential surface, a tangential field will exist on the surface and work done in moving a charge on the surface is not zero.

Therefore electric field lines are always perpendicular to the equipotential surface.
Question 6
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In electrolytic capacitors positive terminal is ________

A
one on which aluminium oxide film is formed.

B
one on which aluminium oxide film is not formed.

C
either of the two terminals.

D
none of the above.

Solution

Aluminium electrolytic capacitors have the Aluminium foil anode (positive terminal) which is attached and covered with a layer of Aluminium Oxide which acts as a dielectric. The whole assembly is covered using a paper separator soaked in electrolyte such as, Borax or Glycol and covered by Aluminium foil which acts as cathode ( negative electrode)
Question 7
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If a positive charge moves opposite to the direction of the electric field :

A
Field does positive work on charge,potential energy decreases.

B
Field does negative work on charge,potential energy increases.

C
Field does negative work on charge,potential energy decreases.

D
Field does positive work on charge,potential energy increases.

Solution

A positive charge experiences a force in the direction of the field.
If it moves opposite to the direction of the field, negative work is done by the electric field on the charge.
Potential energy of the charge increases since an external source is required to do work on the charge against the direction of the field, and the work done is stored in the charge as its potential energy.
Question 8
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Submarine cables act as __________

A
cylindrical capacitor with outer cylinder earthed.

B
parallel plate capacitor.

C
cylindrical capacitor with inner cylinder earthed.

D
spherical capacitor.

Solution

A submarine cable consists of an inner conductor which carries power. This conductor is covered by an insulator, which acts as a dielectric. The dielectric material is covered by a metal coating called shield, which is connected to ground.
Thecable acts as a cylindrical capacito r, with the conductor acting as the inner cylinder, and the metal shield as the outer cylinder which is connected to earth.
Question 9
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When 2 charged conductors are connected by a wire,

A
there is loss or gain of energy depending upon the potentials of the

B
there is always loss of energy

C
there will not be any change in energy

D
there is always gain of energy

Solution

Let the two conductors have capacitances C₁ and C₂ and let their potentials be V₁ and V₂ .
Total initial energy of the conductors, U_i = (1/2)C₁ V₁₂ + (1/2)C₂ V₂₂
When two charged conductors are connected by a wire, the flow of charge stops when the potentials are equalized.
Let V be the common potential and Q₁ and Q₂ be the charges on the conductors after the common potential is attained.

The final energy

Therefore ,
Question 10
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Electrostatic shielding is based on the _______

A
electric field inside the cavity of a conductor is zero.

B
electric field inside the cavity of a conductor is less than zero.

C
electric field inside the cavity of a conductor is greater than zero.

D
electric field inside the cavity of a plastic is zero.

Solution

The electric field inside a cavity is always zero. The potential inside a cavity of a conductor is constant.
The potential difference between any two points inside a charged conductor is zero. This phenomenon is called electrostatic shielding .
Question 11
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Two metallic spheres of radii 1 cm and 3 cm are given charges of (-1 x 10^-2 C) and 5 x 10^-2 C , respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

A
2 x 10^-2 C

B
3 x 10^-2 C

C
4 x 10^-2 C

D
1 x 10^-2 C

Solution

Q_total = 4 ×10⁻² C

Charge distribution α capacitance α radius

Q_small :Q_big =1:3

Q_big = 3/4 ×4 ×10⁻² = 3 ×10⁻² C
Question 12
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Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is:

A
zero

B
q/2

C
q

D
2q

Solution

Since there is an equal number of positive and negative charges on capacitor A, the charges won 't flow to capacitor B as the charge are held by strong electrostatic force.
Thecapacitor B will acquire a charge only if a battery (driving force) is put in the circuit.
Question 13
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Three capacitors, each of capacitance C = 3 mF, are connected as shown in the figure. The equivalent capacitance between points P and S is ?

A
9 μF

B
6 μF

C
3 μF

D
1 μF

Solution

If P is at positive potential, then Q is at negative potential and R is at positive potential. The system therefore reduces to 3 capacitors in parallel. C= 9 μF
Question 14
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When two capacitors are put in series, the equivalent capacitance is ________

A
the reciprocal of the capacitances.

B
smaller than both capacitances.

C
the sum of the capacitances.

D
the product of the capacitances.

Solution

When two capacitors C1 and C2 are connected in series, the reciprocal of the equivalent capacitance in series is equal to the sum of the reciprocals of the two individual capacitances.

It has value lesser than the least value of capacitance.
Question 15
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When a capacitor is connected to a battery:

A
no current flows in the circuit at all.

B
the current keeps on increasing.

C
an alternating current flows in the circuit.

D
a current flows in the circuit for sometime and then decreases to zero.

Solution

When an uncharged capacitor is connected to a battery, charges flow from the poles of the battery to the plates of the capacitor and this process continues till the potential across the capacitor attains the potential difference of the battery. The current flow in the circuit till the time the capacitor is charged and then it ceases.