A 1.00-μF capacitor is charged by a 40.0 -V power supply....

A $1.00-\mu \mathrm{F}$ capacitor is charged by a $40.0$ -V power supply. The fully-charged capacitor is then discharged through a $10.0$ -mH inductor. Find the maximum current in the resulting oscillations.

Key Concepts

Inductor Energy Storage

An inductor stores energy in its magnetic field when there is current flow through it. The magnetic energy stored is proportional to the inductance and the square of the current. In LC circuits, this stored energy becomes significant when the system converts the electric energy from the capacitor, thereby determining the peak current of the oscillations.

Energy Conservation in Oscillatory Systems

The principle of energy conservation is central to analyzing LC circuits. Initially, energy is stored in the capacitor when charged. As the circuit oscillates, this energy is completely converted into magnetic energy in the inductor at the point of maximum current. By equating the energy expressions for the capacitor and the inductor, one can determine the maximum current and other dynamic parameters of the oscillation.

LC Circuit Oscillations

An LC circuit involves a capacitor and an inductor connected together such that energy oscillates between the electric field of the capacitor and the magnetic field of the inductor. This type of circuit exhibits simple harmonic motion, and the study of its behavior provides insight into resonant systems in both physics and electrical engineering.

Capacitor Energy Storage

A capacitor stores energy in its electric field when a voltage is applied across its plates. The stored energy is given by a function of its capacitance and the square of the voltage. This concept is fundamental in understanding how energy is initially accumulated and later released in circuit oscillations.

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