Concept Questions A charged capacitor and an inductor are...

Concept Questions A charged capacitor and an inductor are connected as shown in the drawing (this circuit is the same as that in Figure $23-16 a$ ). There is no resistance in the circuit. As Section 23.4 discusses, the electrical energy initially present in the charged capacitor then oscillates back and forth between the inductor and the capacitor. (a) What is the amount of electrical energy initially stored in the capacitor? Express your answer in terms of its capacitance $C$ and the magnitude $q$ of the charge on each plate. A little later, this energy is transferred completely to the inductor (see Figure $23-16 b$ ). Write down an expression for the energy stored in the inductor. Give your answer in terms of its inductance $L$ and the magnitude $I_{\max }$ of the maximum current in the inductor. (c) If values for $q, C,$ and $L$ are known, how could one obtain a value for the maximum current in the inductor? Remember that energy is conserved. Problem The initial charge on the capacitor has a magnitude of $q=2.90 \mu \mathrm{C} .$ The capacitance is $C=3.60 \mu \mathrm{F},$ and the inductance is $L=75.0 \mathrm{mH} .$ (a) What is the electrical energy stored initially in the charged capacitor? (b) Find the maximum current in the inductor.

Key Concepts

Energy Stored in a Capacitor

This concept involves the formula U = q²/(2C) or equivalently U = (1/2)CV², which quantifies the electrical energy stored in a capacitor due to the electric field created by the separated charges. It is fundamental in analyzing the energy available in a circuit before energy is transferred to other components.

Energy Stored in an Inductor

An inductor stores energy in its magnetic field when current flows through it, which is mathematically expressed as U = (1/2)L I². Recognizing this energy storage mechanism is crucial when examining circuits where energy transitions between electric and magnetic forms during oscillatory processes.

LC Oscillatory Behavior

An LC circuit, comprising an inductor (L) and a capacitor (C), exhibits periodic energy transfer between the capacitor and the inductor. This oscillatory behavior results in the conversion of energy back and forth between the electrical and magnetic fields, which is a modeling example of simple harmonic motion in electrical systems.

Conservation of Energy in LC Circuits

This principle states that in an ideal LC circuit without resistive losses, the total energy remains constant over time. Energy conservation allows one to equate the energy stored in the capacitor to that in the inductor at different points in the oscillation cycle, thereby enabling the derivation of parameters like the maximum current in the inductor.

Transcript

Please give Ace some feedback