High School

Part A An RLC circuit with R=23.4 2. L=352 mH and C 42.3 uF is connected to an ac generator with an rms voltage of 24.0 V Determine the average power delivered to this circuit when the frequency of the generator is equal to the resonance frequency Express your answer using two significant figures. VoAd ? P W Submit Request Answer Part B Determine the average power delivered to this circuit when the frequency of the generator is twice the resonance frequency Express your answer using two significant figures. VO | ΑΣΦ ? P = w Submit Request Answer Part C Determine the average power delivered to this circuit when the frequency of the generator is half the resonance frequency Express your answer using two significant figures. IVO AO ? P= w Submit Request Answer

Answer :

Part A: The average power delivered to the circuit when the frequency of the generator is equal to the resonance frequency is 24.7 W.

Part B: The average power delivered to the circuit when the frequency of the generator is twice the resonance frequency is 6.03 W.

Part C: The average power delivered to the circuit when the frequency of the generator is half the resonance frequency is 0.38 W.

Part A:

The average power delivered to an RLC circuit is given by the following formula:

P = I^2 R

The current in an RLC circuit can be calculated using the following formula:

I = V / Z

The impedance of an RLC circuit can be calculated using the following formula:

Z = R^2 + (2πf L)^2

The resonance frequency of an RLC circuit is given by the following formula:

f_r = 1 / (2π√LC)

Plugging in the values for R, L, and C, we get:

f_r = 1 / (2π√(352 mH)(42.3 uF)) = 3.64 kHz

When the frequency of the generator is equal to the resonance frequency, the impedance of the circuit is equal to the resistance. This means that the current in the circuit is equal to the rms voltage divided by the resistance.

Plugging in the values, we get:

I = V / R = 24.0 V / 23.4 Ω = 1.03 A

The average power delivered to the circuit is then:

P = I^2 R = (1.03 A)^2 (23.4 Ω) = 24.7 W

Part B

When the frequency of the generator is twice the resonance frequency, the impedance of the circuit is equal to 2R. This means that the current in the circuit is equal to half the rms voltage divided by the resistance.

I = V / 2R = 24.0 V / (2)(23.4 Ω) = 0.515 A

The average power delivered to the circuit is then:

P = I^2 R = (0.515 A)^2 (23.4 Ω) = 6.03 W

Part C

When the frequency of the generator is half the resonance frequency, the impedance of the circuit is equal to 4R. This means that the current in the circuit is equal to one-fourth the rms voltage divided by the resistance.

I = V / 4R = 24.0 V / (4)(23.4 Ω) = 0.129 A

The average power delivered to the circuit is then:

P = I^2 R = (0.129 A)^2 (23.4 Ω) = 0.38 W

To learn more about resonance frequency: https://brainly.com/question/28168823

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