An L-C circuit containing an 80.0 ml inductor and a 1.25 nF capacitor oscillates with a maximum

step 1 In the first part of this problem, we are going to calculate the charge on the capacitor. But th

An L-C circuit containing an 80.0 ml inductor and a 1.25 nF...

$\operatorname{An} L-C$ circuit containing an $80.0 \mathrm{ml}$ inductor and a $1.25 \mathrm{nF}$ capacitor oscillates with a maximum current of 0.750 A. Calculate: (a) the maximum charge on the capacitor and (b) the oscillation frequency of the circuit. (c) Assuming the capacitor had its maximum charge at time $t=0,$ calculate the energy stored in the inductor after $2.50 \mathrm{~ms}$ of oscillation.

$\operatorname{An} L-C$ circuit containing an $80.0 \mathrm{ml}$ inductor and a $1.25 \mathrm{nF}$ capacitor oscillates with a maximum current of 0.750 A. Calculate:
(a) the maximum charge on the capacitor and (b) the oscillation frequency of the circuit. (c) Assuming the capacitor had its maximum charge at time $t=0,$ calculate the energy stored in the inductor after $2.50 \mathrm{~ms}$ of oscillation.

Key Concepts

LC Circuit Oscillations

An LC circuit is composed of an inductor and a capacitor connected together, where energy is continuously exchanged between the electric field of the capacitor and the magnetic field of the inductor. The circuit oscillates like a harmonic oscillator, with the capacitor and inductor acting similarly to a spring and mass system, respectively.

Maximum Charge in a Capacitor

In the context of an oscillating LC circuit, the maximum charge on the capacitor is the highest charge it holds when the energy stored is completely electric. This value is determined by the capacitor’s characteristics and the amplitude of the voltage, reflecting the initial energy state of the system.

Oscillation Frequency in LC Circuits

The natural oscillation frequency of an LC circuit is dictated by its inductance and capacitance and is given by the formula f = 1/(2??(LC)). This frequency is crucial as it determines how fast the energy oscillates between the capacitor and the inductor.

Energy Storage in an Inductor

The energy stored in an inductor is expressed as U = 1/2 L I², where I is the current through the inductor at any given time. In an LC circuit, this current varies sinusoidally with time, meaning that the energy stored in the inductor also changes periodically as the energy is transferred between the inductor and capacitor.

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