Solve GRE Problem: LC Circuit Maximum Power Output

In summary, the question is asking when the energy dissipation in an LRC circuit is at its maximum rate. The answer is when the current through the resistor is at its maximum, which occurs when the energy is equally divided between electric and magnetic fields in the inductor and capacitor. Matching impedance between the inductor and capacitor is not necessary for determining the amount of energy stored in each device. This is a conceptual problem and the key is understanding the behavior of current in an LRC circuit and the distribution of charge carriers in the inductor and capacitor.
  • #1
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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  • #2
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:

1. What is an LC circuit?

An LC circuit is a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected in series. It has the ability to store energy in the electric and magnetic fields between the inductor and the capacitor.

2. How do you calculate the maximum power output of an LC circuit?

The maximum power output of an LC circuit can be calculated using the formula Pmax = Vrms^2/R, where Vrms is the root mean square voltage and R is the resistance of the circuit. This formula assumes that the inductor and capacitor are ideal and there are no losses in the circuit.

3. What is the significance of the maximum power output in an LC circuit?

The maximum power output in an LC circuit represents the point at which the circuit is most efficient in converting electrical energy into other forms. It is also the point at which the inductor and capacitor are exchanging energy most rapidly.

4. How does the frequency affect the maximum power output in an LC circuit?

The frequency of the power source affects the maximum power output in an LC circuit as it determines the rate at which the inductor and capacitor exchange energy. At the resonant frequency, the maximum power output is achieved because the inductor and capacitor are in phase and the exchange of energy is most efficient.

5. What factors can affect the maximum power output in an LC circuit?

The maximum power output in an LC circuit can be affected by factors such as the quality of the components, the resistance in the circuit, and the frequency of the power source. Real-world factors such as losses in the circuit and imperfections in the components can also impact the maximum power output.

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