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(a)
The inductance of the inductor.
(a)
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Answer to Problem 77CP
The inductance of the inductor is
Explanation of Solution
Write the expression to obtain the inductive reactance.
Here,
Write the expression to obtain the capacitive reactance.
Here,
Write the expression to obtain the output voltage across the resistor.
Here,
Re-write the above equation.
Substitute
Further substitute
Substitute
Substitute
On multiplying equation (II) by
Conclusion:
Substitute
Substitute
Therefore, the inductance of the inductor is
(b)
The capacitance of the capacitor.
(b)
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Answer to Problem 77CP
The capacitance of the capacitor is
Explanation of Solution
Conclusion:
As the value of capacitance of the capacitor is already calculated in part (a) that is equal to
Therefore, the capacitance of the capacitor is
(c)
The maximum value of the ratio of
(c)
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Answer to Problem 77CP
The maximum value of the ratio of
Explanation of Solution
The maximum value of the
Write the expression to obtain the ratio of
Here,
Conclusion:
Substitute
Therefore, the maximum value of the ratio of
(d)
The frequency at which it has the maximum value of the ratio of
(d)
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Answer to Problem 77CP
The frequency at which it has the maximum value of the ratio of
Explanation of Solution
The maximum ratio of
Write the expression to obtain the frequency at resonance condition.
Here,
Conclusion:
Substitute
Therefore, the frequency at which it has the maximum value of the ratio of
(e)
The phase shift between
(e)
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Answer to Problem 77CP
The phase shift at
Explanation of Solution
Case (i): At
Write the expression to obtain the phase shift between
Here,
Write the expression to obtain the ratio of output and input voltage.
Here,
Substitute
Case (ii): At
Substitute
Case (iii): At
Write the expression to obtain the phase shift between
Here,
Substitute
Conclusion:
At
Substitute
At
Substitute
At
Substitute
Therefore, the phase shift at
(f)
The average power transferred to the speaker at
(f)
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Answer to Problem 77CP
The average power transferred to the speaker at
Explanation of Solution
Write the expression to obtain the average power in the circuit.
Here,
Conclusion:
Case (i): At frequency
Substitute
Further substitute
Case (ii): At frequency
Substitute
Therefore, the average power transferred to the speaker at
(g)
The quality factor while treating the filter as a resonance circuit.
(g)
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Answer to Problem 77CP
The quality factor while treating the filter as a resonance circuit is
Explanation of Solution
Write the expression to obtain the quality factor while treating the filter as a resonance circuit.
Here,
Conclusion:
Substitute
Therefore, the quality factor while treating the filter as a resonance circuit is
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Chapter 33 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
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