#LC Circuits: Your Ultimate Guide ⚡

Hey there, future AP Physics C: E&M master! Let's dive into LC circuits – those awesome oscillating systems that play a huge role in electromagnetism. This guide is designed to be your go-to resource the night before the exam, so let's make every minute count!

#Overview of LC Circuits

LC circuits are all about the interplay between capacitors (which store energy in electric fields) and inductors (which store energy in magnetic fields). They're like a playground for energy, constantly swapping back and forth. Understanding these circuits is key to grasping more complex electrical systems.

#

• Energy Transfer: Energy oscillates between the capacitor and the inductor.
• Simple Harmonic Motion: The charge and current in the circuit vary sinusoidally.
• Angular Frequency: The frequency of oscillation depends on the inductance and capacitance.

#Properties of LC Circuits

# Conservation of Energy in LC Circuits

Imagine a swing set – energy goes back and forth between potential and kinetic. In an LC circuit, it's the same, but with electric and magnetic fields! 🔋

• Total Energy is Constant: The total energy in the circuit remains constant, transferring between the capacitor and the inductor.
• Capacitor Fully Charged: All energy is stored as electric potential energy: $$U_C = \frac{1}{2}CV_{max}^2$$
• Energy Transfer: As the capacitor discharges, energy moves to the inductor, becoming magnetic potential energy.
• Inductor Fully Energized: All energy is stored in the inductor's magnetic field: $$U_L = \frac{1}{2}LI_{max}^2$$
• Reversal: The process reverses, energy goes back to the capacitor.