Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. L = 1 h, R = 100 , C = 0.0004 f, E(t) = 40 V, q(0) = 0 C, i(0) = 2 A q(t): = i(t): = C C A Find the maximum charge on the capacitor. (Round your answer to four decimal places.)
Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. L = 1 h, R = 100 , C = 0.0004 f, E(t) = 40 V, q(0) = 0 C, i(0) = 2 A q(t): = i(t): = C C A Find the maximum charge on the capacitor. (Round your answer to four decimal places.)
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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![**Problem Statement:**
Find the charge \( q(t) \) on the capacitor and the current \( i(t) \) in the given LRC-series circuit.
**Given Parameters:**
- Inductance \( L = 1 \) h
- Resistance \( R = 100 \, \Omega \)
- Capacitance \( C = 0.0004 \, f \)
- Voltage \( E(t) = 40 \, V \)
- Initial charge \( q(0) = 0 \, C \)
- Initial current \( i(0) = 2 \, A \)
**Tasks:**
Determine:
1. The charge \( q(t) \) on the capacitor, indicated as \([ \, \, \, \, ] \, \text{C}\).
2. The current \( i(t) \), indicated as \([ \, \, \, \, ] \, \text{A}\).
Additionally, find the **maximum charge** on the capacitor and provide your answer rounded to four decimal places, indicated as \([ \, \, \, \, ] \, \text{C}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25fce74d-50ce-4010-8593-c528dce466b9%2F215a2a97-f80e-44b3-aec6-7ff42554657b%2F2ltu1n_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the charge \( q(t) \) on the capacitor and the current \( i(t) \) in the given LRC-series circuit.
**Given Parameters:**
- Inductance \( L = 1 \) h
- Resistance \( R = 100 \, \Omega \)
- Capacitance \( C = 0.0004 \, f \)
- Voltage \( E(t) = 40 \, V \)
- Initial charge \( q(0) = 0 \, C \)
- Initial current \( i(0) = 2 \, A \)
**Tasks:**
Determine:
1. The charge \( q(t) \) on the capacitor, indicated as \([ \, \, \, \, ] \, \text{C}\).
2. The current \( i(t) \), indicated as \([ \, \, \, \, ] \, \text{A}\).
Additionally, find the **maximum charge** on the capacitor and provide your answer rounded to four decimal places, indicated as \([ \, \, \, \, ] \, \text{C}\).
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