Solved: An RLC circuit is driven at its resonance

An ac generator produces a peak voltage of 55 V. What is the rms voltage of this generator?

European Electricity In many European homes the rms voltage available from a wall socket is 240 V. What is the maximum voltage in this case?

An rms voltage of 120 V produces a maximum current of 2.1 A in a certain resistor. Find the resistance of this resistor.

The rms current in an ac circuit with a resistance of is 0.85 A. What are (a) the average and (b) the maximum power consumed by this circuit?

A resistor is connected to a generator with a maximum voltage of 141 V. Find (a) the average and (b) the maximum power delivered to this circuit.

A75-watt lightbulb uses an average power of 75 W when connected to an rms voltage of 120 V. (a) What is the resistance of the lightbulb? (b) What is the maximum current in the bulb? (c) What is the maximum power used by the bulb at any given instant of time?

Square-Wave Voltage IThe relationship is valid only for voltages that vary sinusoidally. Find the relationship between and for the square-wave voltage shown in Figure 2426.

The reactance of a capacitor is at a frequency of 57 Hz. What is its capacitance?

The capacitive reactance of a capacitor at 60.0 Hz is . At what frequency is its capacitive reactance ?

A capacitor is connected to an ac generator with an rms voltage of 20.0 V and a frequency of 100.0 Hz. What is the rms current in this circuit?

The rms voltage across a capacitor is 1.8 V at a frequency of 52 Hz. What are (a) the rms and (b) the maximum current through the capacitor?

An ac generator with a frequency of 30.0 Hz and an rms voltage of 12.0 V is connected to a capacitor. (a)What is the maximum current in this circuit? (b) What is the current in the circuit when the voltage across the capacitor is 5.25 V and increasing? (c) What is the current in the circuit when the voltage across the capacitor is 5.25 V and decreasing?

The maximum current in a capacitor connected to an ac generator with a frequency of 120 Hz is 0.15 A. (a) What is the maximum voltage of the generator? (b) What is the voltage across the capacitor when the current in the circuit is 0.10 Aand increasing? (c) What is the voltage across the capacitor when the current in the circuit is 0.10 Aand decreasing?

An rms voltage of 20.5 V with a frequency of 1.00 kHz is applied to a capacitor. (a) What is the rms current in this circuit? (b) By what factor does the current change if the frequency of the voltage is doubled? (c) Calculate the current for a frequency of 2.00 kHz.

A circuit consists of a 1.00-kHz generator and a capacitor. When the rms voltage of the generator is 0.500 V, the rms current in the circuit is 0.430 mA. (a) What is the reactance of the capacitor at 1.00 kHz? (b) What is the capacitance of the capacitor? (c) If the rms voltage is maintained at 0.500 V, what is the rms current at 2.00 kHz? At 10.0 kHz?

Acapacitor has an rms current of 21 mAat a frequency of 60.0 Hz when the rms voltage across it is 14 V. (a)What is the capacitance of this capacitor? (b)If the frequency is increased, will the current in the capacitor increase, decrease, or stay the same? Explain.(c)Find the rms current in this capacitor at a frequency of 410 Hz.

A capacitor is connected to an ac generator with an rms voltage of 12 V. For what range of frequencies will the rms current in the circuit be less than 1.0 mA?

At what frequency will a generator with an rms voltage of 504 V produce an rms current of 7.50 mAin a capacitor?

Find the impedance of a 60.0-Hz circuit with a resistor connected in series with a capacitor

An ac generator with a frequency of 105 Hz and an rms voltage of 22.5 V is connected in series with a resistor and a capacitor. What is the rms current in this circuit?

The rms current in an RCcircuit is 0.72 A. The capacitor in this circuit has a capacitance of and the ac generator has a frequency of 150 Hz and an rms voltage of 95 V. What is the resistance in this circuit?

A 65.0-Hz generator with an rms voltage of 135 V is connected in series to a resistor and a capacitor. Find (a) the rms current in the circuit and (b) the phase angle, , between the current and the voltage.

(a)At what frequency must the circuit in Problem 22 be operated for the current to lead the voltage by 23.0? (b)Using the frequency found in part (a), nd the average power consumed by this circuit.

(a) Sketch the phasor diagram for an ac circuit with a resistor in series with a capacitor. The frequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?

Find the power factor for an RCcircuit connected to a 70.0-Hz generator with an rms voltage of 155 V. The values of R and C in this circuit are and , respectively.

(a) Determine the power factor for an RC circuit with and that is connected to an ac generator with an rms voltage of 24 V and a frequency of 150 Hz. (b) Will the power factor for this circuit increase, decrease, or stay the same if the frequency of the generator is increased? Explain.

Square-Wave Voltage II The square-wave voltage shown in Figure 2427 is applied to an RC circuit. Sketch the shape of the instantaneous voltage across the capacitor, assuming the time constant of the circuit is equal to the period of the applied voltage.

Predict/Explain When a long copper wire of nite resistance is connected to an ac generator, as shown in Figure 2428(a), a certain amount of current ows through the wire. The wire is now wound into a coil of many loops and reconnected to the generator, as indicated in Figure 2428(b). (a) Is the current supplied to the coil greater than, less than, or the same as the current supplied to the uncoiled wire? (b) Choose the best explanation from among the following: I. More current ows in the circuit because the coiled wire is an inductor, and inductors tend to keep the current owing in an ac circuit. II. The current supplied to the circuit is the same because the wire is the same. Simply wrapping the wire in a coil changes nothing. III. Less current is supplied to the circuit because the coiled wire acts as an inductor, which increases the impedance of the circuit.

An inductor has a reactance of at 75.0 Hz. What is its reactance at 60.0 Hz?

What is the rms current in a 77.5-mH inductor when it is connected to a 60.0-Hz generator with an rms voltage of 115 V?

What rms voltage is required to produce an rms current of 2.1 Ain a 66-mH inductor at a frequency of 25 Hz?

A resistor and a 295-mH inductor are connected in series with an ac generator with an rms voltage of 20.0 V and a frequency of 60.0 Hz. What is the rms current in this circuit?

The rms current in an RL circuit is 0.26 A when it is connected to an ac generator with a frequency of 60.0 Hz and an rms voltage of 25 V. (a) Given that the inductor has an inductance of 145 mH, what is the resistance of the resistor? (b) Find the rms voltage across the resistor. (c) Find the rms voltage across the inductor. (d)Use your results from parts (b) and (c) to show that is equal to 25 V.

An ac generator with a frequency of 1.34 kHz and an rms voltage of 24.2 V is connected in series with a resistor and a 315-mH inductor. (a)What is the power factor for this circuit? (b) What is the average power consumed by this circuit?

An rms voltage of 22.2 V with a frequency of 1.00 kHz is applied to a 0.290-mH inductor. (a) What is the rms current in this circuit? (b) By what factor does the current change if the frequency of the voltage is doubled? (c) Calculate the current for a frequency of 2.00 kHz.

A inductor is connected to an ac generator with an rms voltage of 12 V. For what range of frequencies will the rms current in the circuit be less than 1.0 mA?

The phase angle in a certain RL circuit is 76 at a frequency of 60.0 Hz. If for this circuit, what is the value of the inductance, L?

An RL circuit consists of a resistor , an inductor, , and an ac generator with an rms voltage of 120 V. (a)At what frequency will the rms current in this circuit be 1.5 A? For this frequency, what are (b)the rms voltage across the resistor, , and (c) the rms voltage across the inductor, ? (d) Show that , but that 2V2rms,R + V2rms,L = 120 V.

(a) Sketch the phasor diagram for an ac circuit with a resistor in series with a 22.5-mH inductor. The frequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?

In Problem 37, does the phase angle increase, decrease, or stay the same when the frequency is increased? Verify your answer by calculating the phase angle at 70.0 Hz.

A large air conditioner has a resistance of and an inductive reactance of . If the air conditioner is powered by a 60.0-Hz generator with an rms voltage of 240 V, nd (a) the impedance of the air conditioner, (b) its rms current, and (c) the average power consumed by the air conditioner.

Square-Wave Voltage III The square-wave voltage shown in Figure 2427 is applied to an RL circuit. Sketch the shape of the instantaneous voltage across the inductor, assuming the time constant of the circuit is much less than the period of the applied voltage.

An inductor and a capacitor are to be connected to a generator. Will the generator supply more current at highfrequency if the inductor and capacitor are connected in series or in parallel? Explain.

An inductor and a capacitor are to be connected to a generator. Will the generator supply more current at low frequency if the inductor and capacitor are connected in series or in parallel? Explain.

Predict/Explain(a)When the ac generator in Figure 2429 operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following: I. The current is the same because at high frequency the inductor is like an open circuit, and at low frequency the capacitor is like an open circuit. In either case the resistance of the circuit is R. II. Less current ows at high frequency because in that limit the inductor acts like an open circuit, allowing no current to ow. III. More current ows at high frequency because in that limit the capacitor acts like an ideal wire of zero resistance.

Predict/Explain(a)When the ac generator in Figure 2430 operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following: I. The current at high frequency is greater because the higher the frequency the more charge that ows through a circuit. II. Less current ows at high frequency because in that limit the inductor is like an open circuit and current has only one path to ow through. III. The inductor has zero resistance, and therefore the resistance of the circuit is the same at all frequencies. As a result the current is the same at all frequencies.

Predict/Explain (a) When the ac generator in Figure 2431 operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following: I. The capacitor has no resistance, and therefore the resistance of the circuit is the same at all frequencies. As a result the current is the same at all frequencies. II. Less current ows at high frequency because in that limit the capacitor is like an open circuit and current has only one path to ow through. III. More current ows at high frequency because in that limit the capacitor is like a short circuit and current has two parallel paths to ow through.

Find the rms voltage across each element in an RLC circuit with , and . The generator supplies an rms voltage of 115 V at a frequency of 60.0 Hz.

What is the impedance of a resistor, a 105-mH inductor, and a capacitor connected in series with a 60.0-Hz ac generator?

Consider the circuit shown in Figure 2430. The ac generator in this circuit has an rms voltage of 65 V. Given that and , nd the rms current in this circuit in the limit of (a) high frequency and (b) low frequency.

Consider the circuit shown in Figure 2431. The ac generator in this circuit has an rms voltage of 75 V. Given that and , nd the rms current in this circuit in the limit of (a) high frequency and (b) low frequency.

What is the phase angle in an RLC circuit with , , and ? The generator supplies an rms voltage of 115 V at a frequency of 60.0 Hz.

AnRLCcircuit has a resistance of , an inductance of 85.0 mH, and a capacitance of . (a) What is the power factor for this circuit when it is connected to a 125-Hz ac generator? (b) Will the power factor increase, decrease, or stay the same if the resistance is increased? Explain. (c) Calculate the power factor for a resistance of

An ac voltmeter, which displays the rms voltage between the two points touched by its leads, is used to measure voltages in the circuit shown in Figure 2432. In this circuit, the ac generator has an rms voltage of 6.00 V and a frequency of 30.0 kHz. The inductance in the circuit is 0.300 mH, the capacitance is , and the resistance is . What is the reading on a voltmeter when it is connected to points (a)Aand B, (b) B and C, (c)Aand C, and (d)Aand D?

Consider the ac circuit shown in Figure 2432, where we assume that the values of R, L, and Care the same as in the previous problem, and that the rms voltage of the generator is still 6.00 V. The frequency of the generator, however, is doubled to 60.0 kHz. Calculate the rms voltage across (a) the resistor, R, (b) the inductor, L, and (c) the capacitor, C. (d) Do you expect the sum of the rms voltages in parts (a), (b), and (c) to be greater than, less than, or equal to 6.00 V? Explain.

(a) Sketch the phasor diagram for an ac circuit with a resistor in series with a 22.5-mH inductor and a capacitor. The frequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?

Agenerator connected to an RLC circuit has an rms voltage of 120 V and an rms current of 34 mA. If the resistance in the circuit is and the capacitive reactance is , what is the inductive reactance of the circuit?

Manufacturing Plant Power A manufacturing plant uses 2.22 kW of electric power provided by a 60.0-Hz ac generator with an rms voltage of 485 V. The plant uses this power to run a number of high-inductance electric motors. The plants total resistance is and its inductive reactance is . (a) What is the total impedance of the plant? (b) What is the plants power factor? (c) What is the rms current used by the plant? (d) What capacitance, connected in series with the power line, will increase the plants power factor to unity? (e) If the power factor is unity, how much current is needed to provide the 2.22 kW of power needed by the plant? Compare your answer with the current found in part (c). (Because power-line losses are proportional to the square of the current, a utility company will charge an industrial user with a low power factor a higher rate per kWh than a company with a power factor close to unity.)

Acapacitor and an inductor connected in series have a period of oscillation given by T. At the time the capacitor has its maximum charge. In terms of T, what is the rst time after that (a) the current in the circuit has its maximum value and (b) the energy stored in the electric eld is a maximum?

Predict/Explain In an RLC circuit a second capacitor is added in seriesto the capacitor already present. (a)Does the resonance frequency increase, decrease, or stay the same? (b) Choose thebestexplanationfrom among the following: I. The resonance frequency stays the same because it depends only on the resistance in the circuit. II. Adding a capacitor in series increases the equivalent capacitance, and this decreases the resonance frequency. III. Adding a capacitor in series decreases the equivalent capacitance, and this increases the resonance frequency.

In an RLC circuit a second capacitor is added in parallel to the capacitor already present. Does the resonance frequency increase, decrease, or stay the same? Explain.

AnRLCcircuit has a resonance frequency of 2.4 kHz. If the capacitance is , what is the inductance?

At resonance, the rms current in an RLC circuit is 2.8 A. If the rms voltage of the generator is 120 V, what is the resistance, R?

The resistance in an RLCcircuit is doubled. (a)Does the resonance frequency increase, decrease, or stay the same? Explain. (b) Does the maximum current in the circuit increase, decrease, or stay the same? Explain.

The voltage in a sinusoidally driven RLCcircuit leads the current. (a) If we want to bring this circuit into resonance by changing the frequency of the generator, should the frequency be increased or decreased? Explain. (b) If we want to bring this circuit into resonance by changing the inductance instead, should the inductance be increased or decreased? Explain.

A resistor, a 67.6-mH inductor, and a capacitor are connected in series to an ac generator. (a)At what frequency will the current in the circuit be a maximum? (b) At what frequency will the impedance of the circuit be a minimum?

An ac generator of variable frequency is connected to an RLC circuit with , and . At a frequency of 1.0 kHz, the rms current in the circuit is larger than desired. Should the frequency of the generator be increased or decreased to reduce the current? Explain.

(a) Find the frequency at which a capacitor has the same reactance as a 33-mH inductor. (b) What is the resonance frequency of an LC circuit made with this inductor and capacitor?

Consider an RLC circuit with , and .(a)At what frequency is this circuit in resonance? (b) Find the impedance of this circuit if the frequency has the value found in part (a), but the capacitance is increased to . (c) What is the power factor for the situation described in part (b)?

An RLC circuit has a resonance frequency of 155 Hz. (a) If bothLandCare doubled, does the resonance frequency increase, decrease, or stay the same? Explain. (b) Find the resonance frequency when L and C are doubled.

An RLC circuit has a capacitance of . (a) What inductance will produce a resonance frequency of 95 MHz? (b) It is desired that the impedance at resonance be one-fth the impedance at 11 kHz. What value of R should be used to obtain this result?

Persistence of Vision Although an incandescent lightbulb appears to shine with constant intensity, this is an artifact of the eyes persistence of vision. In fact, the intensity of a bulbs light rises and falls with time due to the alternating current used in household circuits. If you could perceive these oscillations, would you see the light attain maximum brightness 60 or 120 times per second? Explain.

An inductor in an LC circuit has a maximum current of 2.4 Aand a maximum energy of 36 mJ. When the current in the inductor is 1.2 A, what is the energy stored in the capacitor?

An RLC circuit is driven at its resonance frequency. Is its impedance greater than, less than, or equal to R? Explain.

Predict/Explain Suppose the circuits shown in Figures 2429and 2431are connected to identical batteries, rather than to ac generators. (a)Assuming the value of R is the same in the two circuits, is the current in Figure 2429 greater than, less than, or the same as the current in Figure 2431? (b)Choose the best explanation from among the following: I. The circuits have the same current because the capacitor acts like an open circuit and the inductor acts like a short circuit. II. The current in Figure 2429 is larger because it has more circuit elements, each of which can carry current. III. The current in Figure 2431 is larger because it has fewer circuit elements, meaning less resistance to current ow.

Suppose the circuits shown in Figures 2430and 2431are connected to identical batteries, rather than to ac generators. Assuming the value of R is the same in the two circuits, is the current in Figure 2430 greater than, less than, or the same as the current in Figure 2431? Explain.

Predict/Explain Consider a circuit consisting of a lightbulb and a capacitor, as shown in circuit 2 of Conceptual Checkpoint 242. (a) If the frequency of the generator is increased, does the intensity of the lightbulb increase, decrease, or stay the same?(b)Choose the bestexplanationfrom among the following: I. As the frequency increases it becomes harder to force current through the capacitor, and therefore the intensity of the lightbulb decreases. II. The intensity of the lightbulb increases because as the frequency becomes higher the capacitor acts more like a short circuit, allowing more current to ow. III. The intensity of the lightbulb is independent of frequency because the circuit contains a capacitor but not an inductor.

Consider a circuit consisting of a lightbulb and an inductor, as shown in Conceptual Checkpoint 243. If the frequency of the generator is increased, does the intensity of the lightbulb increase, decrease, or stay the same? Explain.

A and an capacitor are connected in parallelto a 60.0-Hz generator operating with an rms voltage of 115 V. What is the rms current supplied by the generator?

A and an capacitor are connected in seriesto a 60.0-Hz generator operating with an rms voltage of 115 V. What is the rms current supplied by the generator?

A capacitor and a capacitor are connected in parallel to an ac generator with a frequency of 60.0 Hz. What is the capacitive reactance of this pair of capacitors?

A generator drives an RLC circuit with the voltage V shown in Figure 2433. The corresponding current Iis also shown in the gure. (a) Is the inductive reactance of this circuit greater than, less than, or equal to its capacitive reactance? Explain. (b) Is the frequency of this generator greater than, less than, or equal to the resonance frequency of the circuit? Explain.

Consider the RLCcircuit shown in Example 246, and the corresponding phasor diagram given in the Insight. (a) On the basis of the phasor diagram, can you conclude that the resonance frequency of this circuit is greater than, less than, or equal to 60.0 Hz? Explain. (b) Calculate the resonance frequency for this circuit. (c) The impedance of this circuit at 60.0 Hz is . What is the impedance at resonance?

When a certain resistor is connected to an ac generator with a maximum voltage of 15 V, the average power dissipated in the resistor is 22 W. (a) What is the resistance of the resistor? (b) What is the rms current in the circuit? (c) We know that , and hence it seems that reducing the resistance should reduce the average power. On the other hand, we also know that , which suggests that reducing R increases . Which conclusion is correct? Explain

A9.5-Hz generator is connected to a capacitor. If the current in the generator has its maximum value at , what is the earliest possible time that the voltage across the capacitor is a maximum?

The voltage across an inductor reaches its maximum value 25 ms before the current supplied by the generator reaches its maximum value. What is the lowest possible frequency at which the generator operates?

Find the average power consumed by an RC circuit connected to a 60.0-Hz generator with an rms voltage of 122 V. The values of R and C in this circuit are and , respectively.

A resistor and a 505-mH inductor are connected in series to a 1250-Hz generator with an rms voltage of 14.2 V. (a) What is the rms current in the circuit? (b) What capacitance must be inserted in series with the resistor and inductor to reduce the rms current to half the value found in part (a)?

RLC Phasor The phasor diagram for an RLC circuit is shown in Figure 2434.(a)If the resistance in this circuit is , what is the impedance? (b) If the frequency in this circuit is increased, will the impedance increase, decrease, or stay the same? Explain.

Figure 2434 shows the phasor diagram for an RLC circuit in which the impedance is . (a)What is the resistance, R, in this circuit? (b) Is this circuit driven at a frequency that is greater than, less than, or equal to the resonance frequency of the circuit? Explain.

An RLC circuit has a resistance and an inductance , and is connected to an ac generator with a frequency of 55 Hz. The phasor diagram for this circuit is shown in Figure 2434. Find (a) the impedance, Z, and (b) the capacitance, C, for this circuit. (c) If the value of C is decreased, will the impedance of the circuit increase, decrease, or stay the same? Explain.

Black-Box ExperimentYou are given a sealed box with two electrical terminals. The box contains a resistor in series with either an inductor or a capacitor. When you attach an ac generator with an rms voltage of 0.750 V to the terminals of the box, you nd that the current increases with increasing frequency. (a) Does the box contain an inductor or a capacitor? Explain. (b) When the frequency of the generator is 25.0 kHz, the rms current is 87.2 mA. What is the capacitance or inductance of the unknown component in the box?

Acircuit is constructed by connecting a 1.00-k resistor, a capacitor, and a 515-mH inductor in series. (a) What is the highest frequency at which the impedance of this circuit is equal to ? (b) To reduce the impedance of this circuit, should the frequency be increased or decreased from its value in part (a)? Explain.

An RLC circuit with , and C  is connected to an ac generator with an rms voltage of 24 V. Determine the average power delivered to this circuit when the frequency of the generator is (a) equal to the resonance frequency, (b)twice the resonance frequency, and (c)half the resonance frequency.

A Light-Dimmer Circuit The intensity of a lightbulb with a resistance of is controlled by connecting it in series with an inductor whose inductance can be varied from to . This light dimmer circuit is connected to an ac generator with a frequency of 60.0 Hz and an rms voltage of 110 V. (a)What is the average power dissipated in the lightbulb when ? (b) The inductor is now adjusted so that . In this case, the average power dissipated in the lightbulb is onefourth the value found in part (a). What is the value of ?

An electric motor with a resistance of and an inductance of 53 mH is connected to a 60.0-Hz ac generator. (a)What is the power factor for this circuit? (b) In order to increase the power factor of this circuit to 0.80, a capacitor is connected in series with the motor and inductor. Find the required value of the capacitance.

Tuning a Radio A radio tuning circuit contains an RLC circuit with and . (a) What capacitance is needed to produce a resonance frequency of 85 MHz? (b) If the capacitance is increased above the value found in part (a), will the impedance increase, decrease, or stay the same? Explain. (c) Find the impedance of the circuit at resonance. (d) Find the impedance of the circuit when the capacitance is 1% higher than the value found in part (a).

If the maximum voltage in the square wave shown in Figure 2427is , what are (a)the average voltage, , and (b) the rms voltage, ?

An ac generator supplies an rms voltage of 5.00 V to an RC circuit. At a frequency of 20.0 kHz the rms current in the circuit is 45.0 mA; at a frequency of 25.0 kHz the rms current is 50.0 mA. What are the values of RandCin this circuit?

An ac generator supplies an rms voltage of 5.00 V to an RL circuit. At a frequency of 20.0 kHz the rms current in the circuit is 45.0 mA; at a frequency of 25.0 kHz the rms current is 40.0 mA. What are the values of RandLin this circuit?

AnRCcircuit consists of a resistor , a capacitor , and an ac generator with an rms voltage of 120 V. (a) At what frequency will the rms current in this circuit be 2.9 A? For this frequency, what are (b)the rms voltage across the resistor, , and (c) the rms voltage across the ca- pacitor, ?

Suppose a theremin uses an oscillator with a xed frequency of 90.1 MHz and an RLCcircuit with , , and . What is the beat frequency of these two oscillators? (Audio frequencies range from about 20 Hz to 20,000 Hz.) A. 3740 Hz B. 5100 Hz C. 4760 Hz D. 9000 Hz

If the thereminist moves one of her ngers and increases the capacitance of the system slightly, does the beat frequency increase, decrease, or stay the same?

Find the new beat frequency if the thereminist increases the capacitance by 0.100% over its value in Problem 102. All other quantities stay the same. A. 761 Hz B. 41,300 Hz C. 41,900 Hz D. 86,300 Hz

What is the rms current in the theremins RLC circuit (Problem 102) if it is attached to an ac generator with an rms voltage of 25.0 V and a frequency of 90.0 MHz? A. 2.14 mA B. 3.46 mA C. 8.06 A D. 16.7 A

Referring to Example 246 Suppose we would like to change the phase angle for this circuit to , and that we would like to accomplish this by changing the resistor to a value other than . The inductor is still 90.0 mH, the capacitor is , the rms voltage is 120.0 V, and the ac frequency is 60.0 Hz. (a) Should the resistance be increased or decreased? Explain. (b) Find the resistance that gives the desired phase angle. (c) What is the rms current in the circuit with the resistance found in part (b)?

Referring to Example 246You plan to change the frequency of the generator in this circuit to produce a phase angle of smaller magnitude. The resistor is still , the inductor is 90.0 mH, the capacitor is , and the rms voltage is 120.0 V. (a) Should you increase or decrease the frequency? Explain. (b) Find the frequency that gives a phase angle of . (c) What is the rms current in the circuit at the frequency found in part (b)?