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)
Answer to Problem 49CP
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)
Answer to Problem 49CP
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)
Answer to Problem 49CP
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)
Answer to Problem 49CP
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)
Answer to Problem 49CP
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)
Answer to Problem 49CP
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)
Answer to Problem 49CP
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
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