3) Below is a picture of a 12.000 Volt battery connected to a capacitor that originally has a capacitance of 0.66666 Farad (before any dielectric is added). A) What is the magnitude of the charge stored on the capacitor plates before any changes are made to the capacitor? B) What is the energy stored in the capacitor before the dielectric is added? A slab of dielectric the same thickness as the spacing between the plates and a width equal to half the width of the plates is added. The dielectric constant is K= 5.0000
3) Below is a picture of a 12.000 Volt battery connected to a capacitor that originally has a capacitance of 0.66666 Farad (before any dielectric is added). A) What is the magnitude of the charge stored on the capacitor plates before any changes are made to the capacitor? B) What is the energy stored in the capacitor before the dielectric is added? A slab of dielectric the same thickness as the spacing between the plates and a width equal to half the width of the plates is added. The dielectric constant is K= 5.0000
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)...
Related questions
Question
Can you please answer this
![### Analyzing a Capacitor in Various Conditions
This educational resource explores a scenario involving a 12 Volt battery connected to a capacitor, initially having a capacitance of 0.66666 Farads before any dielectric is added. We examine the effects of adding a specific dielectric to this setup through various questions.
#### A) Charge Stored Before Adding Dielectric
Calculate the charge stored on the capacitor plates using the initial conditions provided.
The magnitude of the charge \( Q \) is given by:
\[ Q = C \cdot V \]
where \( C \) is the capacitance (0.66666 Farads) and \( V \) is the voltage (12.000 Volts).
#### B) Energy Stored Before Adding Dielectric
Determine the energy stored in the capacitor before any dielectric is added.
The energy \( E \) stored in a capacitor is given by:
\[ E = \frac{1}{2} C V^2 \]
Using the capacitance and the voltage, compute the initial energy stored.
#### Dielectric Introduction
A dielectric slab, having the same thickness as the spacing between the plates and a width equal to half the width of the plates, is introduced. The dielectric constant \( \kappa \) is given as 5.0000.
#### C) New Capacitance with Dielectric
Calculate the new capacitance when the dielectric is inserted.
For a dielectric partially filling the capacitor (half-filled):
\[ C_{\text{new}} = \left(C_0 \cdot \kappa \cdot \frac{A_{\text{dielectric}}}{A_{\text{total}}}\right) + \left(C_0 \cdot \frac{A_{\text{empty}}}{A_{\text{total}}}\right) \]
where \( A_{\text{dielectric}} \) is the area of the dielectric, \( A_{\text{total}} \) is the total area of the plates, and \( A_{\text{empty}} \) is the area without dielectric.
#### D) Total Charge with Battery Attached
If the dielectric is added while the battery is still attached, find the total charge on the top plate.
Since the battery remains connected, the voltage across the capacitor remains unchanged. Therefore, use the new capacitance to find the new charge:
\[ Q_{\text{new}} = C_{\text{new}} \cdot V \]
#### E) Energy Stored](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cd02e14-2925-4f0b-b5d5-f979054af505%2F0cfa9bd1-1d2d-4b70-a045-7bf7e77b3f00%2F0cry3ep_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing a Capacitor in Various Conditions
This educational resource explores a scenario involving a 12 Volt battery connected to a capacitor, initially having a capacitance of 0.66666 Farads before any dielectric is added. We examine the effects of adding a specific dielectric to this setup through various questions.
#### A) Charge Stored Before Adding Dielectric
Calculate the charge stored on the capacitor plates using the initial conditions provided.
The magnitude of the charge \( Q \) is given by:
\[ Q = C \cdot V \]
where \( C \) is the capacitance (0.66666 Farads) and \( V \) is the voltage (12.000 Volts).
#### B) Energy Stored Before Adding Dielectric
Determine the energy stored in the capacitor before any dielectric is added.
The energy \( E \) stored in a capacitor is given by:
\[ E = \frac{1}{2} C V^2 \]
Using the capacitance and the voltage, compute the initial energy stored.
#### Dielectric Introduction
A dielectric slab, having the same thickness as the spacing between the plates and a width equal to half the width of the plates, is introduced. The dielectric constant \( \kappa \) is given as 5.0000.
#### C) New Capacitance with Dielectric
Calculate the new capacitance when the dielectric is inserted.
For a dielectric partially filling the capacitor (half-filled):
\[ C_{\text{new}} = \left(C_0 \cdot \kappa \cdot \frac{A_{\text{dielectric}}}{A_{\text{total}}}\right) + \left(C_0 \cdot \frac{A_{\text{empty}}}{A_{\text{total}}}\right) \]
where \( A_{\text{dielectric}} \) is the area of the dielectric, \( A_{\text{total}} \) is the total area of the plates, and \( A_{\text{empty}} \) is the area without dielectric.
#### D) Total Charge with Battery Attached
If the dielectric is added while the battery is still attached, find the total charge on the top plate.
Since the battery remains connected, the voltage across the capacitor remains unchanged. Therefore, use the new capacitance to find the new charge:
\[ Q_{\text{new}} = C_{\text{new}} \cdot V \]
#### E) Energy Stored
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON