Concise Physics Handbook

q — instantaneous charge on the capacitor; qₘ — amplitude; ω — angular frequency; φ₀ — initial phase. Charge changes harmonically over time and determines the oscillation phase.

I — current in the circuit, which is a quarter period out of phase with respect to charge. The maximum current value corresponds to the moment when the charge is zero.

Capacitor energy is maximum when charge is maximum. In the absence of losses, it fully converts to inductor energy.

Inductor energy is proportional to the square of the current. In free oscillations, it periodically converts to electrical energy.

In an ideal LC circuit, total energy is conserved. Reflects the exchange between electrical and magnetic forms without losses.

Angular frequency — how many radians oscillations perform per second. The larger the capacitance or inductance, the lower ω.

T — time for one complete cycle. The formula follows from the relationship between period and angular frequency.

ε — instantaneous EMF value, εₘ — its amplitude. Oscillations occur at a given frequency ω from an external source. These are forced oscillations, maintained by a generator.

I — instantaneous current value in the circuit; Iₘ — current amplitude. In a purely resistive circuit, current is in phase with EMF.

In a resistor, voltage and current are in phase. Here, electrical energy is converted into heat.

Voltage across inductance leads current by 90° in phase. Depends on inductance L and frequency ω. Expresses resistance to current change — inertia of the magnetic field.

X_L — reactive resistance of the coil. The higher the frequency or inductance, the greater the opposition to current.

Voltage across the capacitor lags current by 90° in phase. At high frequencies, U_C decreases — the capacitor "passes" current.

Capacitor reactive resistance is inversely proportional to frequency. As ω increases, resistance decreases, current increases.

Charge q changes with time with a phase shift relative to current. Reflects energy accumulation in the capacitor's electric field.

W — sum of electrical and magnetic energy in the system. Under ideal conditions, conserved, reflects exchange between q and I. Basis for analyzing free oscillations without losses.

Resonance occurs when inductive and capacitive reactances are equal. Total impedance is minimal, current is maximal. Resonant frequency depends only on L and C — as in free oscillations.

This is the average power dissipated in a resistor with sinusoidal current. Only the active component transfers energy — reactive elements do not consume it.