An LC circuit consists of a 20.0 -mH inductor and a 0.500-μF capacitor. If the maximum instantan

step 1 In this problem we have to find the greatest potential difference across capacitor and this is t

An LC circuit consists of a 20.0 -mH inductor and a 0.500-μF...

An LC circuit consists of a 20.0 -mH inductor and a $0.500-\mu \mathrm{F}$ capacitor. If the maximum instantaneous current is $0.100 \mathrm{A},$ what is the greatest potential difference across the capacitor?

Key Concepts

LC Circuit Oscillations

An LC circuit is a fundamental electrical circuit that consists of an inductor (L) and a capacitor (C) connected together. The circuit exhibits oscillatory behavior where energy continuously exchanges between the magnetic field of the inductor and the electric field of the capacitor. This oscillation is characterized by a natural resonant frequency that depends on the values of L and C.

Energy Storage in Inductors

In an inductor, energy is stored in the magnetic field when current flows through it. The energy stored can be expressed as (1/2) L I², where L is the inductance and I is the current. This relation is crucial when analyzing energy transfer in an LC circuit, particularly at the point where the inductor’s stored energy is at its maximum.

Energy Storage in Capacitors

A capacitor stores energy in the electric field between its plates. The energy stored in a capacitor is given by the formula (1/2) C V², where C is the capacitance and V is the voltage across the capacitor. This relationship is essential for determining the potential difference across the capacitor at any point during the oscillations in an LC circuit.

Energy Conservation in LC Circuits

In an ideal LC circuit, the total energy remains constant as it oscillates between the inductor and the capacitor. At the moment of maximum current, the energy is completely stored in the inductor, and when the current is zero, all the energy is stored in the capacitor. By equating the kinetic energy in the inductor to the potential energy in the capacitor, one can determine the maximum voltage across the capacitor.

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