Find the charge on the capacitor and the current in an LC-series circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin(yt) V, g(0) = 0 C, and i(0) = 0 A. q(t) = i(t) = Need Help? Read It
Find the charge on the capacitor and the current in an LC-series circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin(yt) V, g(0) = 0 C, and i(0) = 0 A. q(t) = i(t) = Need Help? Read It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### LC-Series Circuit Charge and Current Calculation
**Problem Statement:**
Find the charge on the capacitor and the current in an LC-series circuit where:
\[ L = 0.1 \, \text{H}, \]
\[ C = 0.1 \, \text{F}, \]
\[ E(t) = 100 \sin(\gamma t) \, \text{V}, \]
\[ q(0) = 0 \, \text{C}, \]
\[ i(0) = 0 \, \text{A}. \]
**Solution:**
To find the charge \( q(t) \) and the current \( i(t) \) in this LC-series circuit, use the provided equations and the initial conditions.
*Input Fields:*
\[ q(t) = \, (\text{Enter the charge expression here}) \quad \text{(indicated with a red 'X' for incorrect response)} \]
\[ i(t) = \, (\text{Enter the current expression here}) \quad \text{(indicated with a red 'X' for incorrect response)} \]
**Assistance:**
If you need help solving this problem, please click the "Read It" button below.
**Additional Resources:**
---
- To understand the fundamentals of LC circuits, review the theoretical derivation of charge and current functions in inductive and capacitive circuits.
- Study the behavior of sinusoidal functions in AC circuits for better comprehension.
Feel free to reach out to the support team if you encounter any difficulties. Happy learning!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ef76dc7-4187-4f97-9d11-35100314604d%2Fba32b315-b1b7-40d9-a80a-f6f7d5b7b91c%2Fmn91jmf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### LC-Series Circuit Charge and Current Calculation
**Problem Statement:**
Find the charge on the capacitor and the current in an LC-series circuit where:
\[ L = 0.1 \, \text{H}, \]
\[ C = 0.1 \, \text{F}, \]
\[ E(t) = 100 \sin(\gamma t) \, \text{V}, \]
\[ q(0) = 0 \, \text{C}, \]
\[ i(0) = 0 \, \text{A}. \]
**Solution:**
To find the charge \( q(t) \) and the current \( i(t) \) in this LC-series circuit, use the provided equations and the initial conditions.
*Input Fields:*
\[ q(t) = \, (\text{Enter the charge expression here}) \quad \text{(indicated with a red 'X' for incorrect response)} \]
\[ i(t) = \, (\text{Enter the current expression here}) \quad \text{(indicated with a red 'X' for incorrect response)} \]
**Assistance:**
If you need help solving this problem, please click the "Read It" button below.
**Additional Resources:**
---
- To understand the fundamentals of LC circuits, review the theoretical derivation of charge and current functions in inductive and capacitive circuits.
- Study the behavior of sinusoidal functions in AC circuits for better comprehension.
Feel free to reach out to the support team if you encounter any difficulties. Happy learning!
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