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A parallel-plate capacitor is constructed by filling the space between two square plates with a block of three dielectric materials, as shown in the figure below. You may assume that ℓ ≫ d.   (a) Find an expression for the capacitance of the device in terms of the plate area A and d, ?1, ?2, and ?3. (Use the following as necessary: ?1, ?2, ?3, ?0, A and d.) C = (b) Calculate the capacitance using the values A = 1.30 cm2, d = 2.00 mm, ?1 = 4.90, ?2 = 5.60, and ?3 = 2.50.

A parallel-plate capacitor is constructed by filling the space between two square plates with a block of three dielectric materials, as shown in the figure below. You may assume that ℓ ≫ d.   (a) Find an expression for the capacitance of the device in terms of the plate area A and d, ?1, ?2, and ?3. (Use the following as necessary: ?1, ?2, ?3, ?0, A and d.) C = (b) Calculate the capacitance using the values A = 1.30 cm2, d = 2.00 mm, ?1 = 4.90, ?2 = 5.60, and ?3 = 2.50.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A parallel-plate capacitor is constructed by filling the space between two square plates with a block of three dielectric materials, as shown in the figure below. You may assume that ℓ ≫ d.

 
(a) Find an expression for the capacitance of the device in terms of the plate area A and d, ?1, ?2, and ?3. (Use the following as necessary: ?1, ?2, ?3, ?0, A and d.)
C =

(b) Calculate the capacitance using the values A = 1.30 cm2, d = 2.00 mm, ?1 = 4.90, ?2 = 5.60, and ?3 = 2.50.
The image depicts a rectangle divided into three sections, each labeled with a different thermal conductivity, represented as \( \kappa_1 \), \( \kappa_2 \), and \( \kappa_3 \). ### Description of Sections: 1. **Left Section (\( \kappa_1 \)):** - Color: Orange - Dimensions: - Width: \( \ell/2 \) - Height: \( d \) 2. **Upper Right Section (\( \kappa_2 \)):** - Color: Yellow - Dimensions: - Width: \( \ell/2 \) - Height: \( d/2 \) 3. **Lower Right Section (\( \kappa_3 \)):** - Color: Light Blue - Dimensions: - Width: \( \ell/2 \) - Height: \( d/2 \) ### Overall Dimensions: - Total Width: \( \ell \) - Total Height: \( d \) ### Explanation: This diagram could be used in educational contexts to illustrate a composite material or system with different thermal conductivities. The rectangle represents a physical model divided into sections with distinct properties, useful for solving problems related to heat transfer, thermal resistance, or material science. Each section demonstrates how thermal conductivities might be distributed within a given boundary, relevant for studying effective conductivity in systems with multiple materials.
Transcribed Image Text:The image depicts a rectangle divided into three sections, each labeled with a different thermal conductivity, represented as \( \kappa_1 \), \( \kappa_2 \), and \( \kappa_3 \). ### Description of Sections: 1. **Left Section (\( \kappa_1 \)):** - Color: Orange - Dimensions: - Width: \( \ell/2 \) - Height: \( d \) 2. **Upper Right Section (\( \kappa_2 \)):** - Color: Yellow - Dimensions: - Width: \( \ell/2 \) - Height: \( d/2 \) 3. **Lower Right Section (\( \kappa_3 \)):** - Color: Light Blue - Dimensions: - Width: \( \ell/2 \) - Height: \( d/2 \) ### Overall Dimensions: - Total Width: \( \ell \) - Total Height: \( d \) ### Explanation: This diagram could be used in educational contexts to illustrate a composite material or system with different thermal conductivities. The rectangle represents a physical model divided into sections with distinct properties, useful for solving problems related to heat transfer, thermal resistance, or material science. Each section demonstrates how thermal conductivities might be distributed within a given boundary, relevant for studying effective conductivity in systems with multiple materials.
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