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The outer sphere of spherical capacitor is earthed. For increasing its capacitance.
- a)the earthing of the outer sphere is removed
- b)vacuum is created between two spheres
- c)the space between two spheres is increased
- d)dielectric material is filled between the two spheres
Correct answer is option 'D'. Can you explain this answer?
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The outer sphere of spherical capacitor is earthed. For increasing its...
The correct answer is: dielectric material is filled between the two spheres
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The outer sphere of spherical capacitor is earthed. For increasing its...
Explanation:
In a spherical capacitor, the capacitance can be increased by filling a dielectric material between the two spheres. Let's understand why this is the case.
Capacitance of a Spherical Capacitor:
The capacitance of a spherical capacitor is given by the formula:
C = 4πε₀r₁r₂ / (r₂ - r₁)
Where:
C is the capacitance,
ε₀ is the permittivity of free space,
r₁ is the radius of the inner sphere, and
r₂ is the radius of the outer sphere.
Effect of Removing Earthing:
Removing the earthing of the outer sphere does not directly affect the capacitance of the spherical capacitor. Earthing helps in maintaining the potential difference between the two spheres, but it does not play a role in determining the capacitance.
Effect of Creating Vacuum:
Creating a vacuum between the two spheres does not increase the capacitance of the spherical capacitor. The capacitance is determined by the geometry of the capacitor and the dielectric material between the spheres. In a vacuum, the permittivity is equal to ε₀, which is the same as the permittivity of free space. Therefore, the capacitance remains unchanged.
Effect of Increasing the Space:
Increasing the space between the two spheres would actually decrease the capacitance of the spherical capacitor. The capacitance is inversely proportional to the distance between the spheres. So, increasing the space would result in a larger distance, leading to a smaller capacitance.
Effect of Filling Dielectric Material:
Filling a dielectric material between the two spheres increases the capacitance of the spherical capacitor. The dielectric material has a permittivity greater than ε₀, which increases the overall capacitance. The permittivity of the dielectric material can be denoted as ε. So, the new capacitance of the capacitor with the dielectric material becomes:
C' = εC
Where C' is the new capacitance and C is the original capacitance without the dielectric material. Since ε > ε₀, the new capacitance will be greater than the original capacitance.
Therefore, the correct option is D: filling a dielectric material between the two spheres.
In a spherical capacitor, the capacitance can be increased by filling a dielectric material between the two spheres. Let's understand why this is the case.
Capacitance of a Spherical Capacitor:
The capacitance of a spherical capacitor is given by the formula:
C = 4πε₀r₁r₂ / (r₂ - r₁)
Where:
C is the capacitance,
ε₀ is the permittivity of free space,
r₁ is the radius of the inner sphere, and
r₂ is the radius of the outer sphere.
Effect of Removing Earthing:
Removing the earthing of the outer sphere does not directly affect the capacitance of the spherical capacitor. Earthing helps in maintaining the potential difference between the two spheres, but it does not play a role in determining the capacitance.
Effect of Creating Vacuum:
Creating a vacuum between the two spheres does not increase the capacitance of the spherical capacitor. The capacitance is determined by the geometry of the capacitor and the dielectric material between the spheres. In a vacuum, the permittivity is equal to ε₀, which is the same as the permittivity of free space. Therefore, the capacitance remains unchanged.
Effect of Increasing the Space:
Increasing the space between the two spheres would actually decrease the capacitance of the spherical capacitor. The capacitance is inversely proportional to the distance between the spheres. So, increasing the space would result in a larger distance, leading to a smaller capacitance.
Effect of Filling Dielectric Material:
Filling a dielectric material between the two spheres increases the capacitance of the spherical capacitor. The dielectric material has a permittivity greater than ε₀, which increases the overall capacitance. The permittivity of the dielectric material can be denoted as ε. So, the new capacitance of the capacitor with the dielectric material becomes:
C' = εC
Where C' is the new capacitance and C is the original capacitance without the dielectric material. Since ε > ε₀, the new capacitance will be greater than the original capacitance.
Therefore, the correct option is D: filling a dielectric material between the two spheres.
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The outer sphere of spherical capacitor is earthed. For increasing its capacitance.a)the earthing of the outer sphere is removedb)vacuum is created between two spheresc)the space between two spheres is increasedd)dielectric material is filled between the two spheresCorrect answer is option 'D'. Can you explain this answer?
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