(a)
The resonant frequency of the circuit.
(a)
Answer to Problem 86P
The resonant frequency of the circuit is
Explanation of Solution
Write the expression for the resonant frequency of the circuit.
Here,
Conclusion:
Substitute
Therefore, the resonant frequency of the circuit is
(b)
Whether the current or voltage will lead.
(b)
Answer to Problem 86P
The current leads the voltage.
Explanation of Solution
The frequency applied is less than the resonant frequency. At the resonance, the capacitive reactance is equal to the inductive reactance. The applied frequency is small, so the capacitive reactance will be greater due to the relation,
The inductive reactance is small using the relation
(c)
The phase angle of this circuit.
(c)
Answer to Problem 86P
The phase angle of this circuit is
Explanation of Solution
Write the expression of phase angle of the circuit.
Substitute
Substitute
Conclusion:
Substitute
Therefore, the phase angle of this circuit is
(d)
The rms current in this circuit.
(d)
Answer to Problem 86P
The rms current in this circuit is
Explanation of Solution
Write the expression for rms current.
Here,
Conclusion:
Substitute
Therefore, the rms current in this circuit is
(e)
The average power dissipated in the circuit.
(e)
Answer to Problem 86P
The average power dissipated in the circuit is
Explanation of Solution
Write the expression for average power.
Here,
Conclusion:
Substitute
Therefore, the average power dissipated in the circuit is
(f)
The maximum voltage across the resistor, inductor and capacitor.
(f)
Answer to Problem 86P
The maximum voltage across the resistor, inductor and capacitor are
Explanation of Solution
Write the expression for the maximum voltage across the resistor.
Substitute
Write the expression for the maximum voltage across the inductor.
Here,
Substitute
Write the expression for the maximum voltage across the capacitor.
Here,
Substitute
Conclusion:
Substitute
Substitute
Substitute
Therefore, the maximum voltage across the resistor, inductor and capacitor are
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