(a)
The maximum voltage
(a)
Answer to Problem 59AP
The maximum voltage
Explanation of Solution
Write the expression to calculate the maximum voltage using the given phasor diagram.
Here,
Conclusion:
Substitute
Therefore, the maximum voltage
(b)
The phase angle
(b)
Answer to Problem 59AP
The phase angle
Explanation of Solution
Write the expression to calculate the phase angle using the given phasor diagram.
Here,
Conclusion:
Substitute
Therefore, the phase angle
(c)
The maximum current in the circuit.
(c)
Answer to Problem 59AP
The maximum current in the circuit is
Explanation of Solution
Write the expression to calculate the maximum current in the circuit.
Here,
Conclusion:
Substitute
Therefore, the maximum current in the circuit is
(d)
The impedance of the circuit.
(d)
Answer to Problem 59AP
The impedance of the circuit is
Explanation of Solution
Write the expression to calculate the impedance of the circuit.
Here,
Conclusion:
Substitute
Therefore, the impedance of the circuit is
(e)
The capacitance of the circuit.
(e)
Answer to Problem 59AP
The capacitance of the circuit is
Explanation of Solution
Write the expression to calculate the capacitance.
Here,
Conclusion:
Substitute
Therefore, the capacitance of the circuit is
(f)
The inductance of the circuit.
(f)
Answer to Problem 59AP
The inductance of the circuit is
Explanation of Solution
Write the expression to calculate the capacitance.
Here,
Conclusion:
Substitute
Therefore, the inductance of the circuit is
(g)
The average power delivered to the circuit.
(g)
Answer to Problem 59AP
The average power delivered to the circuit is
Explanation of Solution
Write the expression to calculate the average power.
Here,
Write the expression for rms value of current.
Substitute
Conclusion:
Substitute
Therefore, the average power delivered to the circuit is
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Chapter 33 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- An inductor and a resistor are connected in series across an AC source as in Figure OQ33.1. Immediately after the switch is closed, which of the following statements is true? (a) The current in the circuit is V/R. (b) The voltage across the inductor is zero, (c) The current in the circuit is zero, (d) The voltage across the resistor is V (e) The voltage across the inductor is half its maximum value.arrow_forwardProblems 71 and 72 paired. Figure P33.71 shows a series RLC circuit with a 25.0- resistor, a 430.0-mH inductor, and a 24.0-F capacitor connected to an AC source with Vmax = 60.0 V operating at 60.0 Hz. What is the maximum voltage across the a. resistor, b. inductor, and c. capacitor in the circuit? FIGURE P33.71 Problems 71 and 72.arrow_forwardIn the LC circuit in Figure 33.11, the inductance is L = 19.8 mH and the capacitance is C = 19.6 mF. At some moment, UB = UE= 17.5 mJ. a. What is the maximum charge stored by the capacitor? b. What is the maximum current in the circuit? c. At t = 0, the capacitor is fully charged. Write an expression for the charge stored by the capacitor as a function of lime. d. Write an expression for the current as a function of time.arrow_forward
- 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 , and a capacitance of 45.7 F. 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?arrow_forwardConsider the Filter circuit shown in Figure P33.56. (a) Show that the ratio of the amplitude of the output voltage to that of the input voltage is to that of input voltage is VoutVin=1/CR2+(1C)2 (b) What value does this ratio approach as the frequency decreases toward zero? (c) What value does this ratio approach as the frequency increases without limit? (d) At what frequency is the ratio equal to one-half?arrow_forwardAn RLC series circuit with R = 600 Ω, L = 30 mH,and C = 0.050µF is driven by an ac source whosefrequency 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) Whatis the phase angle between the emf of the source and the current?arrow_forward
- A resistor ( R = 9.00 × 102 Ω), a capacitor (C = 0.250 µF), and an inductor (L = 2.50 H) are connected in series across a 2.40 × 102-Hz AC source for which ΔV max = 1.40 × 102 V. Calculate (a) the impedance of the circuit, (b) the maximum current delivered by the source, and (c) the phase angle between the current and voltage. (d) Is the current leading or lagging the voltage?arrow_forwardAn RLC series circuit is constructed with R = 150.0 Ω, C = 7.50 µF, and L = 0.54 H. The circuit is connected to an AC generator with a frequency of 60.0 Hz that delivers a maximum current of 1.70 A to the circuit. (a) What is the impedance of this circuit? Ω(b) What are the maximum potential differences across each of the three circuit elements (R, L, and C)? VR, max = V VL, max = V VC, max = V (c) What is the phase angle between the source emf and the current? radarrow_forwardIn an oscillating LC circuit, L = 25.0 mH and C = 7.80 mF. At time t 0 the current is 9.20 mA, the charge on the capacitor is 3.80 mC, and the capacitor is charging.What are (a) the total energy in the circuit, (b) the maximum charge on the capacitor, and (c) the maximum current? (d) If the charge on the capacitor is given by q = Q cos(vt + f), what is the phase angle f? (e) Suppose the data are the same, except that the capacitor is discharging at t = 0.What then is f?arrow_forward
- What are (a) the capacitive reactance, (b) the inductive reactance, (c) the impedance, (d) the current amplitude, and (e) the phase difference between the current and the emf of the generator? If known that the output of an ac generator connected to an RLC series combination has a frequency of 200 Hz and an amplitude of 0.100 V. Values for elements in circuit:R = 4.00 Ω, L = 3.00 × 10−3H, and C = 8.00 × 10−4F.arrow_forwardA sinusoidal voltage Δv = 35.0 sin(100t), where Δv is in volts and t is in seconds, is applied to a series RLC circuit with L = 180 mH, C = 99.0 µF, and R = 67.0 Ω. (a)What is the impedance (in Ω) of the circuit? Ω (b)What is the maximum current (in A)? A (c)Determine the numerical value for ? (in rad/s) in the equation i = Imax sin(?t − ?). rad/s (d)Determine the numerical value for ? (in rad) in the equation i = Imax sin(?t − ?). rad (e)What If? For what value of the inductance (in H) in the circuit would the current lag the voltage by the same angle ? as that found in part (d)? H (f)What would be the maximum current (in A) in the circuit in this case? Aarrow_forwardA resistor (R = 9.00 x 102 Ω), a capacitor (C 5 0.250 µF),and an inductor (L = 2.50 H) are connected in series across a2.40 x 102 - Hz AC source for which ΔVmax = 1.40 x 102 V.Calculate (a) the impedance of the circuit, (b) the maximumcurrent delivered by the source, and (c) the phase anglebetween the current and voltage. (d) Is the current leadingor lagging the voltage?arrow_forward
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