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Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k is
Correct answer is '2'. Can you explain this answer?
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Understanding Capacitance
The capacitance (C) of a parallel plate capacitor is given by the formula:
C = (ε₀ * A) / d
where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between them.
Given Values
- Initial capacitance (C₀) = 10 pF
- Initial radius (r) of the plates
- Area (A₀) = πr²
- Initial distance (d)
Effects of Changing Dimensions
When the radius is doubled:
- New radius = 2r
- New area (A₁) = π(2r)² = 4πr² = 4A₀
When the distance is halved:
- New distance (d₁) = d/2
New Capacitance without Dielectric
The new capacitance (C₁) without introducing the dielectric is:
C₁ = (ε₀ * A₁) / d₁
= (ε₀ * 4A₀) / (d/2)
= (8ε₀ * A₀) / d
= 8C₀ = 8 * 10 pF = 80 pF
Introducing the Dielectric
When a dielectric medium with a dielectric constant k is introduced, the capacitance becomes:
C₂ = k * C₁
Given that the capacitance increases 16 times:
C₂ = 16C₀
Therefore:
k * C₁ = 16C₀
Substituting C₁:
k * 80 pF = 16 * 10 pF
k * 80 = 160
k = 160 / 80 = 2
Conclusion
Thus, the dielectric constant k is 2.
The capacitance (C) of a parallel plate capacitor is given by the formula:
C = (ε₀ * A) / d
where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between them.
Given Values
- Initial capacitance (C₀) = 10 pF
- Initial radius (r) of the plates
- Area (A₀) = πr²
- Initial distance (d)
Effects of Changing Dimensions
When the radius is doubled:
- New radius = 2r
- New area (A₁) = π(2r)² = 4πr² = 4A₀
When the distance is halved:
- New distance (d₁) = d/2
New Capacitance without Dielectric
The new capacitance (C₁) without introducing the dielectric is:
C₁ = (ε₀ * A₁) / d₁
= (ε₀ * 4A₀) / (d/2)
= (8ε₀ * A₀) / d
= 8C₀ = 8 * 10 pF = 80 pF
Introducing the Dielectric
When a dielectric medium with a dielectric constant k is introduced, the capacitance becomes:
C₂ = k * C₁
Given that the capacitance increases 16 times:
C₂ = 16C₀
Therefore:
k * C₁ = 16C₀
Substituting C₁:
k * 80 pF = 16 * 10 pF
k * 80 = 160
k = 160 / 80 = 2
Conclusion
Thus, the dielectric constant k is 2.
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Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer?
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Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer?.
Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer?.
Solutions for Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k isCorrect answer is '2'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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