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Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 24 - Capacitance, Dielectrics, Electric Energy, Storage Problema 53
Capitolo 23, Problema 53

What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 2.3 mm of mica?

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1
Start by recalling the formula for the capacitance of a parallel plate capacitor: C=εd⋅A, where ε is the permittivity of the material between the plates, d is the separation between the plates, and A is the area of one plate.
Determine the permittivity of mica. The permittivity ε is given by ε=ε0⋅κ, where ε0 is the permittivity of free space (8.85×10-12 F/m) and κ is the dielectric constant of mica (approximately 7).
Calculate the area of one circular plate using the formula for the area of a circle: A=π⋅r2, where r is the radius of the plate. Convert the radius from centimeters to meters before substituting into the formula.
Convert the separation between the plates from millimeters to meters. This is necessary to ensure all units are consistent in the SI system.
Substitute the values for ε, A, and d into the capacitance formula to calculate the capacitance. Ensure that all calculations are performed with consistent units.

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Capacitance

Capacitance is the ability of a system to store electric charge per unit voltage. It is defined as the ratio of the electric charge (Q) stored on the plates to the potential difference (V) between them, expressed as C = Q/V. The unit of capacitance is the farad (F), and it is influenced by the physical characteristics of the capacitor, including the area of the plates and the distance between them.
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Capacitors & Capacitance (Intro)

Parallel Plate Capacitor

A parallel plate capacitor consists of two conductive plates separated by an insulating material, known as a dielectric. The capacitance of such a capacitor can be calculated using the formula C = (ε₀ * ε_r * A) / d, where ε₀ is the permittivity of free space, ε_r is the relative permittivity of the dielectric, A is the area of one plate, and d is the separation between the plates. This configuration allows for efficient charge storage.
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Parallel Plate Capacitors

Dielectric Material

A dielectric material is an insulating substance that can be polarized by an electric field, which enhances the capacitance of a capacitor. Mica, in this case, is a type of dielectric with a high relative permittivity (ε_r), which increases the capacitor's ability to store charge compared to a vacuum. The presence of a dielectric reduces the electric field strength between the plates, allowing for greater charge accumulation.
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Intro To Dielectrics
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