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A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be?
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A parallel plate air capacitor has a capacitance C. When it is half fi...
Explanation:
- Capacitance of the capacitor:
The capacitance of a parallel plate capacitor can be calculated using the formula:
\[ C = \frac{\varepsilon A}{d} \]
where C is the capacitance, \(\varepsilon\) is the permittivity of the dielectric material between the plates, A is the area of the plates, and d is the distance between the plates.
- Effect of dielectric:
When a dielectric material is inserted between the plates of a capacitor, the capacitance increases. The amount of increase is dependent on the dielectric constant (\(\kappa\)) of the material.
- Percentage increase in capacitance:
When the capacitor is half-filled with a dielectric of dielectric constant 5, the new capacitance can be calculated using the formula:
\[ C' = \kappa \times C \]
The percentage increase in capacitance can be calculated using the formula:
\[ \text{Percentage increase} = \left( \frac{C' - C}{C} \right) \times 100 \]
- Calculation:
Given that the dielectric constant is 5, the new capacitance (\(C'\)) will be 5 times the original capacitance (C). Therefore, the percentage increase in capacitance will be:
\[ \text{Percentage increase} = \left( \frac{5C - C}{C} \right) \times 100 = 400\% \]
Therefore, when the parallel plate air capacitor is half-filled with a dielectric of dielectric constant 5, the capacitance will increase by 400%.
- Capacitance of the capacitor:
The capacitance of a parallel plate capacitor can be calculated using the formula:
\[ C = \frac{\varepsilon A}{d} \]
where C is the capacitance, \(\varepsilon\) is the permittivity of the dielectric material between the plates, A is the area of the plates, and d is the distance between the plates.
- Effect of dielectric:
When a dielectric material is inserted between the plates of a capacitor, the capacitance increases. The amount of increase is dependent on the dielectric constant (\(\kappa\)) of the material.
- Percentage increase in capacitance:
When the capacitor is half-filled with a dielectric of dielectric constant 5, the new capacitance can be calculated using the formula:
\[ C' = \kappa \times C \]
The percentage increase in capacitance can be calculated using the formula:
\[ \text{Percentage increase} = \left( \frac{C' - C}{C} \right) \times 100 \]
- Calculation:
Given that the dielectric constant is 5, the new capacitance (\(C'\)) will be 5 times the original capacitance (C). Therefore, the percentage increase in capacitance will be:
\[ \text{Percentage increase} = \left( \frac{5C - C}{C} \right) \times 100 = 400\% \]
Therefore, when the parallel plate air capacitor is half-filled with a dielectric of dielectric constant 5, the capacitance will increase by 400%.
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A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be?
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A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be?.
A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be?.
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