The resistor in Figure P32.49 represents the midrange speaker in a three-speaker system. Assume its resistance to be constant at 8.00 Ω. The source represents an audio amplifier producing signals of uniform amplitude ΔVmax = 10.0 V at all audio frequencies. The inductor and capacitor are to function as a band-pass filter with
Figure P32.49
(a)
The required value of inductance
Answer to Problem 49CP
The required value of inductance
Explanation of Solution
Given info: The value of resistance is
Formula to calculate the output potential difference is,
Here,
Formula to calculate the input potential difference is,
Here,
Divide equation (1) and equation (1).
Formula to calculate the inductive reactance of the circuit is,
Here,
Formula to calculate the inductive reactance of the circuit is,
Here,
Formula to calculate the impedance of the circuit is,
Here,
Substitute
At low frequency that is
Substitute
Substitute
Solve the equation further,
Divide the equation by
At high frequency that is
Substitute
Substitute
Solve the equation further,
Subtract the equation (5) and equation (6) to find the value of
Conclusion:
Therefore, the required value of inductance
(b)
The required value of capacitance
Answer to Problem 49CP
The required value of capacitance
Explanation of Solution
Given info: The value of resistance is
The equation (6) is given as,
Substitute
Conclusion:
Therefore, the required value of capacitance
(c)
The maximum value of the ratio
Answer to Problem 49CP
The maximum value of the ratio
Explanation of Solution
Given info: The value of resistance is
The value
At resonance condition,
Substitute
Conclusion:
Therefore, the maximum value of the ratio
(d)
The frequency
Answer to Problem 49CP
The frequency
Explanation of Solution
Given info: The value of resistance is
Since the ratio
Formula to calculate the resonance frequency is,
Substitute
Conclusion:
Therefore, the frequency
(e)
The phase shift between
Answer to Problem 49CP
The phase shift between
Explanation of Solution
Given info: The value of resistance is
Formula to calculate the phase shift between
At
Substitute
At
Substitute
At
Substitute
Conclusion:
Therefore, the phase shift between
(f)
The average power transferred to the speaker at
Answer to Problem 49CP
The average power transferred to the speaker at
Explanation of Solution
Given info: The value of resistance is
Formula to calculate the rms output voltage is,
Formula to calculate the power deliver to the speaker is,
Substitute
For low frequency
Substitute
Substitute
For resonance frequency
Substitute
Substitute
Conclusion:
Therefore, the average power transferred to the speaker at
(g)
The quality factor of the circuit.
Answer to Problem 49CP
The quality factor of the circuit is
Explanation of Solution
Given info: The value of resistance is
Formula to calculate the quality factor is,
Substitute
Conclusion:
Therefore, the quality factor of the circuit is
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Chapter 32 Solutions
Physics for Scientists and Engineers with Modern Physics
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