Review. The voltage phasor diagram for a certain series RLC circuit is shown in Figure P33.59. The resistance of the circuit is 75.0 Ω, and the frequency is 60.0 Hz. Find (a) the maximum voltage ΔVmax, (b) the phase angle ϕ, (c) the maximum current, (d) the impedance, (e) the capacitance and (f) the inductance of the circuit, and (g) the average power delivered to the circuit.
(a)
The maximum voltage.
Answer to Problem 33.59AP
The maximum voltage is
Explanation of Solution
Given info: The resistance of the circuit is
The expression for maximum value of the voltage is,
Here,
Substitute
Conclusion:
Therefore, the maximum voltage is
(b)
The phase angle.
Answer to Problem 33.59AP
The phase angle is
Explanation of Solution
Given info: The resistance of the circuit is
The expression for the phase angle is,
Substitute
Conclusion:
Therefore, the phase angle is
(c)
The maximum current.
Answer to Problem 33.59AP
The maximum current is
Explanation of Solution
Given info: The resistance of the circuit is
The expression for maximum current is,
Here,
Substitute
Conclusion:
Therefore, the maximum current is
(d)
The impedance.
Answer to Problem 33.59AP
The impedance is
Explanation of Solution
Given info: The resistance of the circuit is
The expression for the impedance is,
Substitute
Conclusion:
Therefore, the impedance is
(e)
The capacitance.
Answer to Problem 33.59AP
The capacitance is
Explanation of Solution
Given info: The resistance of the circuit is
The circuit is series
The expression capacitive reactance is,
Substitute
The expression capacitive reactance in terms of the capacitance is,
Here,
Rearrange the above equation for the value of capacitance.
Substitute
Conclusion:
Therefore, the capacitance is
(f)
The inductance of the circuit.
Answer to Problem 33.59AP
The inductance of the circuit
Explanation of Solution
Given info: The resistance of the circuit is
The circuit is series
The expression inductive reactance is,
Substitute
Thus the value of inductive reactance is
The expression inductive reactance in terms of the inductance is,
Here,
Rearrange the above equation for the value of inductance.
Substitute
Conclusion:
Therefore, the inductance is
(g)
The average power delivered to circuit.
Answer to Problem 33.59AP
The average power delivered to circuit is
Explanation of Solution
Given info: The resistance of the circuit is
The expression for R.M.S value of the current is,
The expression for the average power delivered is,
Substitute
Substitute
Conclusion:
Therefore, the average power delivered to circuit is
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Chapter 33 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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