LC Circuit Equation Derivations (11:22)
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In this morning's lesson on LC circuits, we derive equations for charge, current, and energy as functions of time. Exploring the total potential energy in the circuit, we use the chain rule to find the second derivative of charge with respect to time, revealing that an LC circuit exhibits simple harmonic motion. The angular frequency and period equations are derived, demonstrating that an LC circuit undergoes oscillation. Applying these findings, we derive equations for charge, current, and energy over time. Additionally, we prove that the total energy in an LC circuit remains constant due to ideal, zero-resistance wires. Join us in uncovering the dynamics of LC circuits!
Chapters: 0:00 Introduction 0:27 Deriving Angular Frequency 4:44 Deriving Charge as a function of Time 6:21 Deriving Current as a function of Time 7:40 An alternate Derivation of Current Maximum 8:31 Deriving Capacitor Energy as a function of Time 9:21 Deriving Solenoid Energy as a function of Time 10:14 Deriving Total Energy as a function of Time
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