Solve GRE Problem: LC Circuit Maximum Power Output

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SUMMARY

The discussion focuses on determining the conditions under which energy is dissipated at the maximum rate in an LRC circuit connected to an AC source. The key conclusion is that maximum power output occurs when the current through the resistor is at its peak, which correlates with the energy being equally divided between electric and magnetic fields. The participants emphasize the importance of understanding the behavior of current in relation to energy storage in capacitors and inductors.

PREREQUISITES
  • Understanding of LRC circuit dynamics
  • Knowledge of AC circuit theory
  • Familiarity with energy storage in capacitors and inductors
  • Concept of impedance matching in electrical circuits
NEXT STEPS
  • Study the behavior of current in LRC circuits over time
  • Learn about energy transfer between electric and magnetic fields in AC circuits
  • Explore the concept of resonance in LRC circuits
  • Investigate the mathematical modeling of power output in AC circuits
USEFUL FOR

Students studying electrical engineering, physics enthusiasts, and anyone looking to deepen their understanding of AC circuits and energy dissipation in LRC configurations.

HungryChemist
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Homework Statement


An AC source is connected to an LRC circuit (Inductor is connected to Capacitor in series, and then it is connected to register in series). Energy is stored in the capacitor and inductor and is dissipated in the resistor. At what time is the energy dissipated at the maximum rate?

A. When the stored energy is all in electric fields
B. When the stored energy is all in magnetic fields
C When the stored energy is equally divided b/t electric fields magnetic fields
D When no energy is stored
E Under none of the conditions above

Homework Equations


Okay, frankly I have no idea. I tried thinking in terms of matching the impedance b/t capacitor and inductor. However, it doesn't really relate to the amount of energy stored in each devices.


The Attempt at a Solution



Maximum power output through the register means the maximum current through the registor. So the questions is, when will the current through the registor be maximum?

Please, help!
 
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HungryChemist said:

Homework Statement


An AC source is connected to an LRC circuit (Inductor is connected to Capacitor in series, and then it is connected to register in series). Energy is stored in the capacitor and inductor and is dissipated in the resistor. At what time is the energy dissipated at the maximum rate?

A. When the stored energy is all in electric fields
B. When the stored energy is all in magnetic fields
C When the stored energy is equally divided b/t electric fields magnetic fields
D When no energy is stored
E Under none of the conditions above

Homework Equations


Okay, frankly I have no idea. I tried thinking in terms of matching the impedance b/t capacitor and inductor. However, it doesn't really relate to the amount of energy stored in each devices.

You won't need to get that fancy: this is a conceptual problem.

The Attempt at a Solution



Maximum power output through the register means the maximum current through the registor. So the questions is, when will the current through the resistor be maximum?

Maybe this will help as a way to think about it. How does the current through the resistor behave as a function of time? (What does an LRC circuit do?) At the part of the process when the current through the resistor is greatest, what is going on at the inductor and capacitor? (Think about where the charge carriers, say, the excess electrons, are at that moment.)
 
Last edited:

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