A 2.0 µF capacitor and a 4.0 µF capacitor are connected in parallel across a 300 V potential difference. Calculate the total energy stored in the capacitors.
A 2.0 µF capacitor and a 4.0 µF capacitor are connected in parallel across a 300 V potential difference. Calculate the total energy stored in the capacitors.
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
Please explain analysis solution and Numeric solution thanks
![### Capacitors in Parallel and Energy Storage
**Problem Statement:**
A 2.0 µF capacitor and a 4.0 µF capacitor are connected in parallel across a 300 V potential difference. Calculate the total energy stored in the capacitors.
---
**Solution:**
To solve this problem, we need to follow these steps:
1. **Calculate the total capacitance:**
In a parallel connection, the total capacitance \( C_t \) is the sum of the individual capacitances:
\[
C_t = C_1 + C_2
\]
Where:
- \( C_1 = 2.0 \, \mu\text{F} \)
- \( C_2 = 4.0 \, \mu\text{F} \)
So,
\[
C_t = 2.0 \, \mu\text{F} + 4.0 \, \mu\text{F} = 6.0 \, \mu\text{F}
\]
2. **Calculate the energy stored in each capacitor:**
The energy \( U \) stored in a capacitor is given by the formula:
\[
U = \frac{1}{2} C V^2
\]
For \( C_1 \):
\[
U_1 = \frac{1}{2} \times 2.0 \, \mu\text{F} \times (300 \, V)^2 = \frac{1}{2} \times 2.0 \times 10^{-6} \, F \times 90000 \, V^2
\]
\[
U_1 = \frac{1}{2} \times 0.18 \, J = 0.09 \, J
\]
For \( C_2 \):
\[
U_2 = \frac{1}{2} \times 4.0 \, \mu\text{F} \times (300 \, V)^2 = \frac{1}{2} \times 4.0 \times 10^{-6} \, F \times 90000 \, V^2
\]
\[
U_2 = \frac{1}{2} \times 0.36](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba35cc5f-959d-4f80-acdd-e9cc0bd31dfa%2F63569234-f6c8-485e-8a6c-8cdcc22961c2%2F4ljgqo8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Capacitors in Parallel and Energy Storage
**Problem Statement:**
A 2.0 µF capacitor and a 4.0 µF capacitor are connected in parallel across a 300 V potential difference. Calculate the total energy stored in the capacitors.
---
**Solution:**
To solve this problem, we need to follow these steps:
1. **Calculate the total capacitance:**
In a parallel connection, the total capacitance \( C_t \) is the sum of the individual capacitances:
\[
C_t = C_1 + C_2
\]
Where:
- \( C_1 = 2.0 \, \mu\text{F} \)
- \( C_2 = 4.0 \, \mu\text{F} \)
So,
\[
C_t = 2.0 \, \mu\text{F} + 4.0 \, \mu\text{F} = 6.0 \, \mu\text{F}
\]
2. **Calculate the energy stored in each capacitor:**
The energy \( U \) stored in a capacitor is given by the formula:
\[
U = \frac{1}{2} C V^2
\]
For \( C_1 \):
\[
U_1 = \frac{1}{2} \times 2.0 \, \mu\text{F} \times (300 \, V)^2 = \frac{1}{2} \times 2.0 \times 10^{-6} \, F \times 90000 \, V^2
\]
\[
U_1 = \frac{1}{2} \times 0.18 \, J = 0.09 \, J
\]
For \( C_2 \):
\[
U_2 = \frac{1}{2} \times 4.0 \, \mu\text{F} \times (300 \, V)^2 = \frac{1}{2} \times 4.0 \times 10^{-6} \, F \times 90000 \, V^2
\]
\[
U_2 = \frac{1}{2} \times 0.36
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 2 steps with 1 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