Power in a driven RLC Circuit

In summary, the power delivered by the source in a driven RLC circuit is equal to the power dissipated as heat in the resistor. This is because while the inductor and capacitor may trade stored energy, the source must continuously replenish the energy lost due to resistance in the circuit. This results in a balance between the power delivered by the source and the power dissipated as heat in the resistor.
  • #1
thelonious
15
0

Homework Statement



For a driven RLC circuit, compare the power delivered by the source to the power dissipated as heat in the resistor.

Homework Equations



P[itex]_{avg}[/itex] = I[itex]_{rms}[/itex]*V[itex]_{rms}[/itex]*cos([itex]\phi[/itex])

The Attempt at a Solution



My thinking was that the power dissipated in the resistor would be less than the power delivered by the source.

I thought so because in addition to the energy radiated as heat at the resistor, energy is either being stored or being released back into the circuit by the capacitor and inductor.

However, I was told that the power at the source equals the power dissipated as heat in the resistor. If all of the source energy is accounted for by the capacitor, what happened to the energy in the inductor and capacitor?
 
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  • #2
thelonious said:

Homework Statement



For a driven RLC circuit, compare the power delivered by the source to the power dissipated as heat in the resistor.

Homework Equations



P[itex]_{avg}[/itex] = I[itex]_{rms}[/itex]*V[itex]_{rms}[/itex]*cos([itex]\phi[/itex])

The Attempt at a Solution



My thinking was that the power dissipated in the resistor would be less than the power delivered by the source.

I thought so because in addition to the energy radiated as heat at the resistor, energy is either being stored or being released back into the circuit by the capacitor and inductor.

However, I was told that the power at the source equals the power dissipated as heat in the resistor. If all of the source energy is accounted for by the capacitor, what happened to the energy in the inductor and capacitor?

The inductor and capacitor are going to trade stored energy back and forth, true, but that energy is not manufactured by those components. Further, there are losses on every cycle in the resistance. The source has to replenish this energy if the circuit is to operate at a steady state.
 

1. What is a driven RLC circuit?

A driven RLC circuit is an electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) in series, with an external power source connected to it. The external power source, also known as the driving force, provides energy to the circuit to maintain oscillations.

2. How does power behave in a driven RLC circuit?

In a driven RLC circuit, power is continuously transferred between the capacitor and inductor as the circuit oscillates. During the charging phase, power is transferred from the external source to the capacitor, and during the discharging phase, power is transferred from the inductor to the capacitor. The resistor dissipates this energy in the form of heat.

3. What is the relationship between power and frequency in a driven RLC circuit?

The power in a driven RLC circuit is directly proportional to the frequency of the driving force. This means that as the frequency increases, the power also increases. However, there is a resonant frequency at which the power reaches its maximum value, and beyond this frequency, the power decreases.

4. How does the quality factor affect power in a driven RLC circuit?

The quality factor (Q) of a driven RLC circuit is a measure of its efficiency. A higher Q value indicates a more efficient circuit, meaning that less power is lost as heat in the resistor. Therefore, a higher Q value results in a higher power transfer between the capacitor and inductor, leading to a larger amplitude of oscillations.

5. How does the phase difference between voltage and current affect power in a driven RLC circuit?

The phase difference between voltage and current in a driven RLC circuit can affect the power in two ways. If the voltage and current are in phase, the power is at its maximum value. However, if the voltage and current are out of phase, the power decreases. This is because when the voltage and current are out of phase, the power from the external source is partially used to overcome the inductive or capacitive reactance, resulting in a decrease in the power transferred to the circuit.

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