(a)
The inductance of the inductor.
(a)
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)
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)
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)
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)
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)
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)
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
- An PLC series circuit with R=600 , L = 30 mH. and c=0.050F is driven by an ac source whose frequency and voltage amplitude are 500 Hz and 50 V, respectively, (a) What is the impedance of the circuit? (b) What is the amplitude of the current in the circuit? (c) What is the phase angle between the emf of the source and the current?arrow_forwardThe resistor in Figure P32.49 represents the midrange speaker in a three-speaker system. Assume its resistance to be constant at 8.00 . The source represents an audio amplifier producing signals of uniform amplitude Vmax = 10.0 V at all audio frequencies. The inductor and capacitor are to function as a band-pass filter with Vout/Vin=12 at 200 Hz and at 4.00 103 Hz. Determine the required values of (a) L and (b) C. Find (c) the maximum value of the ratio Vout/Vin; (d) the frequency fo at which the ratio has its maximum value; (e) the phase shift between vin and vout at 200 Hz, at fo, and at 4.00 103 Hz; and (f) the average power transferred to the speaker at 200 Hz, at f0, and at 4.00 103 Hz. (g) Recognizing that the diagram represents an RLC circuit driven by an AC source, find its quality factor. Figure P32.49arrow_forwardIn the AC circuit shown in Figure P32.3, R = 70.0 and the output voltage of the AC source is Vmax sin t. (a) If VR = 0.250 Vmax for the first time at t = 0.0100 s, what is the angular frequency of the source? (b) What is the next value of t for which VR = 0.250 Vmax? Figure P32.6 Problem 3 and 5.arrow_forward
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