Electrostatic Potential Test

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Electrostatic Potential Test - 5

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Question 1
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For a charged conductor of arbitrary shape, inside the conductor

A
V = 0 and E ≠0.

B
E = 0, but V is same as on the surface and non-zero.

C
E is non-uniform but V is zero everywhere.

D
E and V are zero.

Solution

The potential difference between any two points inside the hollow conductor is zero. This means that the potential at all points inside the hollow charged conductor is the same and it is equal to the value of the potential at its surface .
The electric field on the surface of a hollow conductor is maximum and it drops to zero abruptly inside the conductor .
E = - dV/dr
Question 2
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An equipotential surface is a surface ______.

A
on which the potential has positive value at every point.

B
on which the potential has the same value at every point

C
on which the potential has the zero value at every point.

D
on which the potential has negative value at every point.

Solution

When the potential at all points on the surface is the same, such a surface is called an equipotential surface .
The potential difference between any two points on an equipotential surface is zero.
Question 3
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A variable capacitor and an electroscope are connected in parallel to a battery. The reading of the electroscope would be decreased by_______

A
Decreasing the battery potential.

B
Placing a dielectric between the plates.

C
Increasing the area of overlapping of the plates.

D
Decreasing the distance between the plates.

Solution

An electroscope is a device that measures the potential difference.
If it is connected in parallel to the capacitor, the potential across it will be equal to the potential across the capacitor, which is equal to the potential across the battery.
On decreasing the battery potential , the potential difference across the electroscope reduces, and hence the reading reduces.
Question 4
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A 2 μF capacitor C1 is charged to a voltage 100 V and a 4 μF capacitor C2 is charged to a voltage 50 V. The capacitors are then connected in parallel. What is the loss of energy due to parallel connection?

A
1.7 J

B
1.7 ×10⁻³ J

C
1.7 ×10⁻¹ J

D
1.7 ×10⁻² J

Solution
Question 5
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If the potential difference between the plates of a capacitor is increased by 0.1%, the energy stored in the capacitor increases by nearly:

A
0.1%

B
0.144%

C
0.11%

D
0.2%

Solution

The intial energy stored in the capacitor C of potential difference V is
E = (1/2) CV²
When the p.d increased by ΔV, the energy stored will be ΔE.
Question 6
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If the diameter of earth is 128 x 10² km, then its capacitance will be:

A
111 μF

B
331 μF

C
711 μF

D
211 μF

Solution

The capacitance of a spherical conductor of radius R is
Question 7
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If a charge moves in an electrical field:

A
Energy is lost.

B
Energy is gained.

C
Energy is conserved.

D
Energy is unchanged.

Solution

When a charged particle moves in an electric field, its electric potential energy decreases, its kinetic energy will increase i.e. the total energy is conserved.
Question 8
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If the charge on a capacitor is increased by 2 coulomb, the energy stored in it increases by 21%. The original charge on the capacitor (in coulomb) is:

A
30 C

B
10 C

C
40 C

D
20 C

Solution

The initial energy of the capacitor of capacitance C and charge Q₁ ,
When the charge increases to Q₂ the change in the energy of the capacitor,
Given percentage increase of energy,

Since, Q₂ - Q₁ = 2
⇒Q₁ = 20 C
Question 9
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In series combination of capacitors, potential drops across the individual capacitors are equal to_______

A
inverse ratio of charges stored.

B
direct ratio of capacitors.

C
direct ratio of charges stored.

D
inverse ratio of capacitors.

Solution

When capacitors are connected in series, they have equal charge but the potential difference across them is given by
Question 10
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A capacitor of capacitance C is fully charged by a 200 V supply. It is then discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat 2.5 ×10² Jkg⁻¹ K⁻¹ and of mass 0.1 kg. If the temperature of the block rises by 0.4 K, what is the value of C?

A
300 μF

B
500 μF

C
400 μF

D
200 μF

Solution

Energy stored in the capacitor
This is released as heat when the capacitor discharges through the metal block. The quantity of heat = mass xs p.heatx rise in temperature.
Q = m x s x Δθ = 0.1 x 2.5 x 10² x 0.4 = 10 J
U = Q; 2 x 10⁴ C = 10; C = 5 x 10^-4 F = 500 μF