A 2200 -pF capacitor is charged to 120 V and then quickly connected to an inductor. The frequen

step 1 So in this problem we have the LC circuit and we know the value of the capacitance. C is a 2 ,20

A 2200 -pF capacitor is charged to 120 V and then quickly...

A 2200 -pF capacitor is charged to 120$\mathrm { V }$ and then quickly connected to an inductor. The frequency of oscillation is observed to be 17$\mathrm { kHz }$ . Determine $( a )$ the inductance, (b) the peak value of the current, and (c) the maximum energy stored in the magnetic field of the inductor.

Key Concepts

Resonant Frequency in LC Circuits

A fundamental property of LC circuits is that they oscillate at a natural frequency determined by the inductance (L) and capacitance (C) of the circuit. This resonant frequency is given by f = 1/(2??(LC)), which relates the two components. Understanding this relationship is key to calculating any parameter in the circuit when the frequency is known.

Energy Storage in Capacitors

Capacitors store energy in the electric field between their plates. The energy stored is given by U = ½CV², where C is the capacitance and V is the voltage across the capacitor. This stored energy is initially available in the circuit and can be completely transferred to the inductor, initiating oscillations.

Energy Storage in Inductors

Inductors store energy in their magnetic field when current flows through them, and the energy stored is expressed as U = ½LI², with L representing the inductance and I the current through the inductor. Recognizing this energy storage mechanism helps in determining maximum current values when the circuit's energy is fully transferred from the capacitor.

Conservation of Energy in LC Circuits

An ideal LC circuit demonstrates the principle of energy conservation, where the total energy oscillates between the electric field of the capacitor and the magnetic field of the inductor. At any moment, the sum of the energies remains constant, allowing one to use the initial stored energy to compute other parameters such as peak current or maximum magnetic energy.

Transcript

Please give Ace some feedback