Max Power Dissipated in RLC circuit

In summary, the conversation discusses a sample exam question on an RLC circuit with an alternative emf of 1 V and various components. The question asks for the maximum power dissipated by the resistance and the frequencies at which the maximum power is half as large. The equations for finding the maximum power are mentioned, but there is uncertainty about whether the question refers to the resistor or the entire circuit. The frequency can be determined by looking at the impedance of the resonant circuit, and the quality factor (Q) is related to the frequencies for the second part of the question.
  • #1
pynergee
7
0

Homework Statement


For this sample exam, we are given an RLC circuit, with an alternative emf of 1 V, connected all in series with a 500 ohm resistor, a .4 mH inductor, and two capacitors in parallel of 50 pF each.
It asks for the "maximum power dissipated by the resistance" and at what frequencies w would the max power be half as large.

Homework Equations


I am not sure if the question is asking for the power dissipated by resistor, or the entire circuit.
If it were just the resistor, Pmax = (Ipeak)squared * R
But if it were the entire circuit, Pmax = (Irms)(Vrms)cos(phi)
where, (Irms) = (Vpeak/Z)/Sqrt(2) and (Vrms) = (Vpeak)/Sqrt(2) and cos(phi) = (R/Z) I believe.
The frequency = 1/Sqrt(LC)

The Attempt at a Solution


I know how to find the Pmax, but I just need to know for that, if it is the resistor or the entire circuit its asking for.
However for the frequency, I am somewhat stuck.
Would I try to use the derivation of <P> = <[(Ipeak)sin(wt-phi)][(Vpeak)sin(wt)]?

Please help, thank you.
 
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  • #2
Don't get hung too up on cosinusoids, but look at the impedance of your resonant circuit. What is it exactly on resonance? This will answer the first question. It should show you the way to the second question, too. As a practical matter, the quality factor or Q of the resonator is related to the frequencies you'll find for part two.
 
  • #3


I would provide the following response to this content:

Based on the given information, the question is asking for the maximum power dissipated by the resistance (500 ohm) in the RLC circuit. This can be calculated using the formula Pmax = (Ipeak)^2 * R, where Ipeak is the peak current in the circuit.

To find the peak current, we can use the equation Irms = Vrms/Z, where Z is the impedance of the circuit. Since the circuit is in series, the impedance can be calculated by adding the individual impedances of the components (resistor, inductor, and capacitors). Once we have the Irms, we can use the equation Ipeak = Irms * sqrt(2) to find the peak current.

To find the frequency at which the maximum power is half as large, we can use the formula f = 1/sqrt(LC), where L is the inductance and C is the total capacitance of the parallel capacitors. We can also use the relationship between frequency and angular frequency (w = 2*pi*f) to find the corresponding value of w.

In summary, the maximum power dissipated by the resistance in the RLC circuit can be calculated using the formula Pmax = (Ipeak)^2 * R, where Ipeak is the peak current, which can be found using the equation Irms = Vrms/Z. The frequency at which the maximum power is half as large can be found using the formula f = 1/sqrt(LC) or w = 2*pi*f.
 

1. What is Max Power Dissipated in RLC circuit?

The maximum power dissipated in an RLC (resistor-inductor-capacitor) circuit is the highest amount of energy that is lost as heat due to the resistance of the components. This occurs when the circuit is in resonance, meaning the inductive and capacitive reactances cancel each other out, resulting in a purely resistive circuit.

2. How is Max Power Dissipated calculated in an RLC circuit?

The formula for calculating the maximum power dissipated in an RLC circuit is P = Vrms^2/R, where Vrms is the root mean square voltage and R is the resistance in the circuit. This formula assumes that the inductance and capacitance have been adjusted to achieve resonance.

3. What factors affect the Max Power Dissipated in an RLC circuit?

The main factors that affect the maximum power dissipated in an RLC circuit are the resistance, inductance, and capacitance values. These components all play a role in determining the resonance of the circuit and therefore the maximum power dissipated. Other factors that can affect power dissipation include the quality factor (Q) of the circuit and the frequency of the input signal.

4. Why is it important to consider Max Power Dissipated in an RLC circuit?

Max Power Dissipated is an important factor to consider in an RLC circuit because it represents the maximum amount of energy that is being lost as heat. This can have implications for the efficiency and performance of the circuit. In some cases, it may be desirable to minimize power dissipation to reduce heat and improve efficiency.

5. How can Max Power Dissipated be reduced in an RLC circuit?

To reduce the maximum power dissipated in an RLC circuit, the resistance can be decreased, the inductance and capacitance can be adjusted to change the resonance of the circuit, or the frequency of the input signal can be altered. Additionally, using higher quality components with lower resistance and adjusting the circuit design can also help to reduce power dissipation.

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