### 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.![Need Help? Button](https://i.imgur.com/1zC66Bb.png)**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!

Answered: Find the charge on the capacitor and…

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

Linear Algebra: A Modern Introduction

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ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 16EQ

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Question

### 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.

![Need Help? Button](https://i.imgur.com/1zC66Bb.png)

**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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