A series RLC circuit driven by a source with an amplitude of 120.0 V and a frequency of 50.0 Hz has an inductance of 787 mH, a resistance of 267 Ω, and a capacitance of 45.7 µF. a. What are the maximum current and the phase angle between the current and the source emf in this circuit? b. What are the maximum potential difference across the inductor and the phase angle between this potential difference and the current in the circuit? c. What are the maximum potential difference across the resistor and the phase angle between this potential difference and the current in this circuit? d. What are the maximum potential difference across the capacitor and the phase angle between this potential difference and the current in this circuit?
(a)
The maximum current and the phase angle.
Answer to Problem 63PQ
The maximum current in the circuit is
Explanation of Solution
Write the expression to calculate the inductive reactance.
Here,
Write the expression to calculate the capacitive reactance.
Here, the capacitance of the capacitor is
Write the expression for the impedance.
Here,
Write the expression to calculate the maximum current
Here,
Write the expression to calculate the phase angle.
Here,
Conclusion:
Convert form
Substitute
Convert into Farad.
Substitute
Substitute
Substitute,
Substitute
Therefore, the maximum current in the circuit is
(b)
The maximum potential difference and the phase angle between the potential difference across the inductor and the current.
Answer to Problem 63PQ
The maximum potential difference across inductor is
Explanation of Solution
Write the expression for potential difference across
Conclusion:
Substitute
Since, the potential difference across the inductor and the current in the circuit is perpendicular to each other. Hence the phase angle between the potential difference across the inductor and the current in the circuit is
Thus, the maximum potential difference across inductor is
The phase angle between the potential difference across the inductor and the current in the circuit is
(c)
The maximum potential difference and the phase angle between the potential difference across the resistor and the current.
Answer to Problem 63PQ
The maximum potential difference across resistor is
Explanation of Solution
Write the expression for potential difference across
Conclusion:
Substitute
Since, the potential difference across the resistor and the current in the circuit is in the same phase. Hence the phase angle between the potential difference across the resistor and the current in the circuit is
Therefore, the maximum potential difference across resistor is
(d)
The maximum potential difference and the phase angle between the potential difference across the capacitor and the current.
Answer to Problem 63PQ
The maximum potential difference across capacitor is
Explanation of Solution
Write the expression for potential difference across
Conclusion:
Substitute
The phase angle between the potential difference across the resistor and the current in the circuit is
Therefore, the maximum potential difference across capacitor is
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Chapter 33 Solutions
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