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Chapter 28: Problem 8

When the capacitor voltage in an undriven \(L C\) circuit reaches zero, why don't the oscillations stop?

Short Answer

Expert verified
The oscillations in an LC circuit don't stop when the capacitor's voltage reaches zero because that is when the energy in the system is fully stored in the inductor. The system oscillates due to the continuous exchange of energy between the inductive and capacitive parts of the circuit.

Step by step solution

01

Understanding the Behavior of an LC Circuit

An LC circuit oscillates because of the trade-off of energy between the inductor and the capacitor. When the capacitor is fully charged (can also be considered as the 'maximum potential energy'), it will start to discharge and induce a current in the inductor. The current will reach its maximum as the capacitor discharges completely, at which point the voltage across the capacitor is zero.
02

Interpretation of Zero Voltage across the Capacitor

The capacitor voltage reaching zero doesn't represent the system's energy reaching zero, but rather that the energy has transferred from the capacitor (electric field) to the inductor (magnetic field). The inductor now has the maximum current it can achieve as a result of drawing the energy from the capacitor.
03

The Continuation of Oscillations

At zero capacitor voltage, the inductor, which now possesses maximum energy (or 'maximum kinetic energy'), starts to 'discharge'. This means it induces a current in the opposite direction to recharge the capacitor. Thus, the energy swings back to the capacitor, providing the conditions for continuous oscillations in an ideal LC circuit without energy loss.

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Most popular questions from this chapter

An electric drill draws \(4.6 \mathrm{A}\) rms at \(120 \mathrm{V}\) rms. If the current lags the voltage by \(25^{\circ},\) what's the drill's power consumption?

A series \(R L C\) circuit has \(R=75 \mathrm{k} \Omega, L=20 \mathrm{mH},\) and resonates at \(4.0 \mathrm{kHz}\). (a) What's the capacitance? (b) Find the circuit's impedance at resonance and (c) at \(3.0 \mathrm{kHz}\)

Why is Equation 28.5 not a full description of the relation between voltage and current in a capacitor?

Your professor tells you about the days before digital computers when engineers used electric circuits to model mechanical systems. Suppose a 5.0 -kg mass is connected to a spring with \(k=1.44 \mathrm{kN} / \mathrm{m} .\) This is then modeled by an \(L C\) circuit with \(L=2.5 \mathrm{H} .\) What should \(C\) be in order for the \(L C\) circuit to have the same resonant frequency as the mass-spring system?

A damped \(L C\) circuit consists of a 0.15 -uF capacitor and a \(20-\mathrm{mH}\) inductor with resistance \(1.6 \Omega .\) How many oscillation cycles will occur before the peak capacitor voltage drops to half its initial value?
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