Solved: A series RLC circuit contains the following

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 DV/R. (b) The voltage across the inductor is zero. (c) The current in the circuit is zero. (d) The voltage across the resistor is DV. (e) The voltage across the inductor is half its maximum value.

(i) When a particular inductor is connected to a source of sinusoidally varying emf with constant amplitude and a frequency of 60.0 Hz, the rms current is 3.00 A. What is the rms current if the source frequency is doubled? (a) 12.0 A (b) 6.00 A (c) 4.24 A (d) 3.00 A (e) 1.50 A (ii) Repeat part (i) assuming the load is a capacitor instead of an inductor. (iii) Repeat part (i) assuming the load is a resistor instead of an inductor.

A capacitor and a resistor are connected in series across an AC source as shown in Figure OQ33.3. After the switch is closed, which of the following statements is true? (a) The voltage across the capacitor lags the current by 90. (b) The voltage across the resistor is out of phase with the current. (c) The voltage across the capacitor leads the current by 90. (d) The current decreases as the frequency of the source is increased, but its peak voltage remains the same. (e) None of those statements is correct.

. (i) What is the time average of the square-wave potential shown in Figure OQ33.4? (a) !2 DVmax (b) DVmax (c) DVmax/!2 (d) DVmax/2 (e) DVmax/4 (ii) What is the rms voltage? Choose from the same possibilities as in part (i).

If the voltage across a circuit element has its maximum value when the current in the circuit is zero, which of the following statements must be true? (a) The circuit element is a resistor. (b) The circuit element is a capacitor. (c) The circuit element is an inductor. (d) The current and voltage are 90 out of phase. (e) The current and voltage are 180 out of phase.

A sinusoidally varying potential difference has amplitude 170 V. (i) What is its minimum instantaneous value? (a) 170 V (b) 120 V (c) 0 (d) 2120 V (e) 2170 V (ii) What is its average value? (iii) What is its rms value? Choose from the same possibilities as in part (i) in each case.

A series RLC circuit contains a 20.0-V resistor, a 0.750-mF capacitor, and a 120-mH inductor. (i) If a sinusoidally varying rms voltage of 120 V at f 5 500 Hz is applied across this combination of elements, what is the rms current in the circuit? (a) 2.33 A (b) 6.00 A (c) 10.0 A (d) 17.0 A (e) none of those answers (ii) What If? What is the rms current in the circuit when operating at its resonance frequency? Choose from the same possibilities as in part (i).

A resistor, a capacitor, and an inductor are connected in series across an AC source. Which of the following statements is false? (a) The instantaneous voltage across the capacitor lags the current by 90. (b) The instantaneous voltage across the inductor leads the current by 90. (c) The instantaneous voltage across the resistor is in phase with the current. (d) The voltages across the resistor, capacitor, and inductor are not in phase. (e) The rms voltage across the combination of the three elements equals the algebraic sum of the rms voltages across each element separately

Under what conditions is the impedance of a series RLC circuit equal to the resistance in the circuit? (a) The driving frequency is lower than the resonance frequency. (b) The driving frequency is equal to the resonance frequency. (c) The driving frequency is higher than the resonance frequency. (d) always (e) never

What is the phase angle in a series RLC circuit at resonance? (a) 180 (b) 90 (c) 0 (d) 290 (e) None of those answers is necessarily correct.

A circuit containing an AC source, a capacitor, an inductor, and a resistor has a high-Q resonance at 1 000 Hz. From greatest to least, rank the following contributions to the impedance of the circuit at that frequency and at lower and higher frequencies. Note any cases of equality in your ranking. (a) XC at 500 Hz (b) XC at 1 500 Hz (c) XL at 500 Hz (d) XL at 1 500 Hz (e) R at 1 000 Hz

A 6.00-V battery is connected across the primary coil of a transformer having 50 turns. If the secondary coil of the transformer has 100 turns, what voltage appears across the secondary? (a) 24.0 V (b) 12.0 V (c) 6.00 V (d) 3.00 V (e) none of those answers

Do AC ammeters and voltmeters read (a) peak-to-valley, (b) maximum, (c) rms, or (d) average values?

A 20.0-mH inductor is connected to a North American electrical outlet (DVrms 5 120 V, f 5 60.0 Hz). Assuming the energy stored in the inductor is zero at t 5 0, determine the energy stored at t 5 1 180 s.

Review. Determine the maximum magnetic flux through an inductor connected to a North American electrical outlet (DVrms 5 120 V, f 5 60.0 Hz).

The output voltage of an AC source is given by Dv 5 120 sin 30.0pt, where Dv is in volts and t is in seconds. The source is connected across a 0.500-H inductor. Find (a) the frequency of the source, (b) the rms voltage across the inductor, (c) the inductive reactance of the circuit, (d) the rms current in the inductor, and (e) the maximum current in the inductor.

A 1.00-mF capacitor is connected to a North American electrical outlet (DVrms 5 120 V, f 5 60.0 Hz). Assuming the energy stored in the capacitor is zero at t 5 0, determine the magnitude of the current in the wires at t 5 1 180 s

An AC source with an output rms voltage of 36.0 V at a frequency of 60.0 Hz is connected across a 12.0-mF capacitor. Find (a) the capacitive reactance, (b) the rms current, and (c) the maximum current in the circuit. (d) Does the capacitor have its maximum charge when the current has its maximum value? Explain.

(a) For what frequencies does a 22.0-mF capacitor have a reactance below 175 V? (b) What If? What is the reactance of a 44.0-mF capacitor over this same frequency range?

A source delivers an AC voltage of the form Dv 5 98.0 sin 80pt, where Dv is in volts and t is in seconds, to a capacitor. The maximum current in the circuit is 0.500 A. Find (a) the rms voltage of the source, (b) the frequency of the source, and (c) the value of the capacitance.

What maximum current is delivered by an AC source with DVmax 5 48.0 V and f 5 90.0 Hz when connected across a 3.70-mF capacitor?

A capacitor C is connected to a power supply that operates at a frequency f and produces an rms voltage DV. What is the maximum charge that appears on either capacitor plate?

What is the maximum current in a 2.20-mF capacitor when it is connected across (a) a North American electrical outlet having DVrms 5 120 V and f 5 60.0 Hz and (b) a European electrical outlet having DVrms 5 240 V and f 5 50.0 Hz?

An AC source with DVmax 5 150 V and f 5 50.0 Hz is connected between points a and d in Figure P33.24. Calculate the maximum voltages between (a) points a and b, (b) points b and c, (c) points c and d, and (d) points b and d.

In addition to phasor diagrams showing voltages such as in Figure 33.15, we can draw phasor diagrams with resistance and reactances. The resultant of adding the phasors is the impedance. Draw to scale a phasor diagram showing Z, XL, XC , and f for an AC series circuit for which R 5 300 V, C 5 11.0 mF, L 5 0.200 H, and f 5 500/p Hz.

A sinusoidal voltage Dv 5 40.0 sin 100t, where Dv is in volts and t is in seconds, is applied to a series RLC circuit with L 5 160 mH, C 5 99.0 mF, and R 5 68.0 V. (a) What is the impedance of the circuit? (b) What is the maximum current? Determine the numerical values for (c) v and (d) f in the equation i 5 Imax sin (vt 2 f).

A series AC circuit contains a resistor, an inductor of 150 mH, a capacitor of 5.00 mF , and a source with DVmax 5 240 V operating at 50.0 Hz. The maximum current in the circuit is 100 mA. Calculate (a) the inductive reactance, (b) the capacitive reactance, (c) the impedance, (d) the resistance in the circuit, and (e) the phase angle between the current and the source voltage.

At what frequency does the inductive reactance of a 57.0-mH inductor equal the capacitive reactance of a 57.0-mF capacitor?

An RLC circuit consists of a 150-V resistor, a 21.0-mF capacitor, and a 460-mH inductor connected in series with a 120-V, 60.0-Hz power supply. (a) What is the phase angle between the current and the applied voltage? (b) Which reaches its maximum earlier, the current or the voltage?

Draw phasors to scale for the following voltages in SI units: (a) 25.0 sin vt at vt 5 90.0, (b) 30.0 sin vt at vt 5 60.0, and (c) 18.0 sin vt at vt 5 300.

An inductor (L 5 400 mH), a capacitor (C 5 4.43 mF), and a resistor (R 5 500 V) are connected in series. A 50.0-Hz AC source produces a peak current of 250 mA in the circuit. (a) Calculate the required peak voltage DVmax. (b) Determine the phase angle by which the current leads or lags the applied voltage.

A 60.0-V resistor is connected in series with a 30.0-mF capacitor and a source whose maximum voltage is 120 V, operating at 60.0 Hz. Find (a) the capacitive reactance of the circuit, (b) the impedance of the circuit, and (c) the maximum current in the circuit. (d) Does the voltage lead or lag the current? (e) How will adding an inductor in series with the existing resistor and capacitor affect the current? Explain.

Review. In an RLC series circuit that includes a source of alternating current operating at fixed frequency and voltage, the resistance R is equal to the inductive reactance. If the plate separation of the parallel-plate capacitor is reduced to one-half its original value, the current in the circuit doubles. Find the initial capacitive reactance in terms of R.

Why is the following situation impossible? A series circuit consists of an ideal AC source (no inductance or capacitance in the source itself) with an rms voltage of DV at a frequency f and a magnetic buzzer with a resistance R and an inductance L. By carefully adjusting the inductance L of the circuit, a power factor of exactly 1.00 is attained.

A series RLC circuit has a resistance of 45.0 V and an impedance of 75.0 V. What average power is delivered to this circuit when DVrms 5 210 V?

An AC voltage of the form Dv 5 100 sin 1 000t, where Dv is in volts and t is in seconds, is applied to a series RLC circuit. Assume the resistance is 400 V, the capacitance is 5.00 mF, and the inductance is 0.500 H. Find the average power delivered to the circuit.

A series RLC circuit has a resistance of 22.0 V and an impedance of 80.0 V. If the rms voltage applied to the circuit is 160 V, what average power is delivered to the circuit?

An AC voltage of the form Dv 5 90.0 sin 350t, where Dv is in volts and t is in seconds, is applied to a series RLC circuit. If R 5 50.0 V, C 5 25.0 mF, and L 5 0.200 H, find (a) the impedance of the circuit, (b) the rms current in the circuit, and (c) the average power delivered to the circuit

In a certain series RLC circuit, Irms 5 9.00 A, DVrms 5 180 V, and the current leads the voltage by 37.0. (a) What is the total resistance of the circuit? (b) Calculate the reactance of the circuit (XL 2 XC).

Suppose you manage a factory that uses many electric motors. The motors create a large inductive load to the electric power line as well as a resistive load. The electric company builds an extra-heavy distribution line to supply you with two components of current: one that is 90 out of phase with the voltage and another that is in phase with the voltage. The electric company charges you an extra fee for reactive volt-amps in addition to the amount you pay for the energy you use. You can avoid the extra fee by installing a capacitor between the power line and your factory. The following problem models this solution. In an RL circuit, a 120-V (rms), 60.0-Hz source is in series with a 25.0-mH inductor and a 20.0-V resistor. What are (a) the rms current and (b) the power factor? (c) What capacitor must be added in series to make the power factor equal to 1? (d) To what value can the supply voltage be reduced if the power supplied is to be the same as before the capacitor was installed?

A diode is a device that allows current to be carried in only one direction (the direction indicated by the arrowhead in its circuit symbol). Find the average power delivered to the diode circuit of Figure P33.41 in terms of DVrms and R

A series RLC circuit has components with the following values: L 5 20.0 mH, C 5 100 nF, R 5 20.0 V, and DVmax 5 100 V, with Dv 5 DVmax sin vt. Find (a) the resonant frequency of the circuit, (b) the amplitude of the current at the resonant frequency, (c) the Q of the circuit, and (d) the amplitude of the voltage across the inductor at resonance.

An RLC circuit is used in a radio to tune into an FM station broadcasting at f 5 99.7 MHz. The resistance in the circuit is R 5 12.0 V, and the inductance is L 5 1.40 mH. What capacitance should be used?

The LC circuit of a radar transmitter oscillates at 9.00 GHz. (a) What inductance is required for the circuit to resonate at this frequency if its capacitance is 2.00 pF? (b) What is the inductive reactance of the circuit at this frequency?

A 10.0-V resistor, 10.0-mH inductor, and 100-mF capacitor are connected in series to a 50.0-V (rms) source having variable frequency. If the operating frequency is twice the resonance frequency, find the energy delivered to the circuit during one period.

A resistor R, inductor L, and capacitor C are connected in series to an AC source of rms voltage DV and variable frequency. If the operating frequency is twice the resonance frequency, find the energy delivered to the circuit during one period.

Review. A radar transmitter contains an LC circuit oscillating at 1.00 3 1010 Hz. (a) For a one-turn loop having an inductance of 400 pH to resonate at this frequency, what capacitance is required in series with the loop? (b) The capacitor has square, parallel plates separated by 1.00 mm of air. What should the edge length of the plates be? (c) What is the common reactance of the loop and capacitor at resonance?

A step-down transformer is used for recharging the batteries of portable electronic devices. The turns ratio N2/N1 for a particular transformer used in a DVD player is 1:13. When used with 120-V (rms) household service, the transformer draws an rms current of 20.0 mA from the house outlet. Find (a) the rms output voltage of the transformer and (b) the power delivered to the DVD player.

The primary coil of a transformer has N1 5 350 turns, and the secondary coil has N2 5 2 000 turns. If the input voltage across the primary coil is Dv 5 170 cos vt, where Dv is in volts and t is in seconds, what rms voltage is developed across the secondary coil?

A transmission line that has a resistance per unit length of 4.50 3 1024 V/m is to be used to transmit 5.00 MW across 400 mi (6.44 3 105 m). The output voltage of the source is 4.50 kV. (a) What is the line loss if a transformer is used to step up the voltage to 500 kV? (b) What fraction of the input power is lost to the line under these circumstances? (c) What If? What difficulties would be encountered in attempting to transmit the 5.00 MW at the source voltage of 4.50 kV?

In the transformer shown in Figure P33.51, the load resistance RL is 50.0 V. The turns ratio N1/N2 is 2.50, and the rms source voltage is DVs 5 80.0 V. If a voltmeter across the load resistance measures an rms voltage of 25.0 V, what is the source resistance Rs?

A person is working near the secondary of a transformer as shown in Figure P33.52. The primary voltage is 120 V at 60.0 Hz. The secondary voltage is 5 000 V. The capacitance Cs, which is the stray capacitance between the hand and the secondary winding, is 20.0 pF. Assuming the person has a body resistance to ground of Rb 5 50.0 kV, determine the rms voltage across the body. Suggestion: Model the secondary of the transformer as an AC source.

The RC high-pass filter shown in Figure P33.53 has a resistance R 5 0.500 V and a capacitance C 5 613 mF. What is the ratio of the amplitude of the output voltage to that of the input voltage for this filter for a source frequency of 600 Hz?

Consider the RC highpass filter circuit shown in Figure P33.53. (a) Find an expression for the ratio of the amplitude of the output voltage to that of the input voltage in terms of R, C, and the AC source frequency v. (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?

One particular plug-in power supply for a radio looks similar to the one shown in Figure 33.20 and is marked with the following information: Input 120 V AC 8 W Output 9 V DC 300 mA. Assume these values are accurate to two digits. (a) Find the energy efficiency of the device when the radio is operating. (b) At what rate is energy wasted in the device when the radio is operating? (c) Suppose the input power to the transformer is 8.00 W when the radio is switched off and energy costs $0.110/kWh from the electric company. Find the cost of having six such transformers around the house, each plugged in for 31 days.

Consider 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 DVout DVin 5 1/vC R 2 1 a 1 vCb 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?

A step-up transformer is designed to have an output voltage of 2 200 V (rms) when the primary is connected across a 110-V (rms) source. (a) If the primary winding has exactly 80 turns, how many turns are required on the secondary? (b) If a load resistor across the secondary draws a current of 1.50 A, what is the current in the primary, assuming ideal conditions? (c) What If? If the transformer actually has an efficiency of 95.0%, what is the current in the primary when the secondary current is 1.20 A?

Why is the following situation impossible? An RLC circuit is used in a radio to tune into a North American AM commercial radio station. The values of the circuit components are R 5 15.0 V, L 5 2.80 mH, and C 5 0.910 pF

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 V, and the frequency is 60.0 Hz. Find (a) the maximum voltage DVmax, (b) the phase angle f, (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.

Consider a series RLC circuit having the parameters R 5 200 V, L 5 663 mH, and C 5 26.5 mF. The applied voltage has an amplitude of 50.0 V and a frequency of 60.0 Hz. Find (a) the current Imax and its phase relative to the applied voltage Dv, (b) the maximum voltage DVR across the resistor and its phase relative to the current, (c) the maximum voltage DVC across the capacitor and its phase relative to the current, and (d) the maximum voltage DVL across the inductor and its phase relative to the current.

Energy is to be transmitted over a pair of copper wires in a transmission line at the rate of 20.0 kW with only a 1.00% loss over a distance of 18.0 km at potential difference DVrms 5 1.50 3 103 V between the wires. Assuming the current density is uniform in the conductors, what is the diameter required for each of the two wires?

Energy is to be transmitted over a pair of copper wires in a transmission line at a rate P with only a fractional loss f over a distance , at potential difference DVrms between the wires. Assuming the current density is uniform in the conductors, what is the diameter required for each of the two wires?

A 400-V resistor, an inductor, and a capacitor are in series with an AC source. The reactance of the inductor is 700 V, and the circuit impedance is 760 V. (a) What are the possible values of the reactance of the capacitor? (b) If you find that the power delivered to the circuit decreases as you raise the frequency, what is the capacitive reactance in the original circuit? (c) Repeat part (a) assuming the resistance is 200 V instead of 400 V and the circuit impedance continues to be 760 V.

Show that the rms value for the sawtooth voltage shown in Figure P33.64 is DVmax/!3.

A transformer may be used to provide maximum power transfer between two AC circuits that have different impedances Z1 and Z 2. This process is called impedance matching. (a) Show that the ratio of turns N1/N2 for this transformer is N1 N2 5 Z 1 Z 2 (b) Suppose you want to use a transformer as an impedance-matching device between an audio amplifier that has an output impedance of 8.00 kV and a speaker that has an input impedance of 8.00 V. What should your N1/N2 ratio be?

A capacitor, a coil, and two resistors of equal resistance are arranged in an AC circuit as shown in Figure P33.66 (page 1028). An AC source provides an emf of DVrms 5 20.0 V at a frequency of 60.0 Hz. When the doublethrow switch S is open as shown in the figure, the rms current is 183 mA. When the switch is closed in position a, the rms current is 298 mA. When the switch is closed in position b, the rms current is 137 mA. Determine the values of (a) R, (b)C, and (c) L. (d) Is more than one set of values possible? Explain.

Marie Cornu, a physicist at the Polytechnic Institute in Paris, invented phasors in about 1880. This problem helps you see their general utility in representing oscillations. Two mechanical vibrations are represented by the expressions y1 5 12.0 sin 4.50t and y2 5 12.0 sin (4.50t 1 70.0) where y1 and y2 are in centimeters and t is in seconds. Find the amplitude and phase constant of the sum of these functions (a) by using a trigonometric identity (as from Appendix B) and (b) by representing the oscillations as phasors. (c) State the result of comparing the answers to parts (a) and (b). (d) Phasors make it equally easy to add traveling waves. Find the amplitude and phase constant of the sum of the three waves represented by y1 5 12.0 sin (15.0x 2 4.50t 1 70.0) y2 5 15.5 sin (15.0x 2 4.50t 2 80.0) y3 5 17.0 sin (15.0x 2 4.50t 1 160) where x, y1, y2, and y3 are in centimeters and t is in seconds.

A series RLC circuit has resonance angular frequency 2.00 3 103 rad/s. When it is operating at some input frequency, XL 5 12.0 V and XC 5 8.00 V. (a) Is this input frequency higher than, lower than, or the same as the resonance frequency? Explain how you can tell. (b) Explain whether it is possible to determine the values of both L and C. (c) If it is possible, find L and C. If it is not possible, give a compact expression for the condition that L and C must satisfy

Review. One insulated conductor from a household extension cord has a mass per length of 19.0 g/m. A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude 15.3 mT directed perpendicular to the length of the cord. When the cord carries an AC current of 9.00 A at a frequency of 60.0 Hz, it vibrates in resonance in its simplest standing-wave vibration mode. (a) Determine the relationship that must be satisfied between the separation d of the clamps and the tension T in the cord. (b) Determine one possible combination of values for these variables.

(a) Sketch a graph of the phase angle for an RLC series circuit as a function of angular frequency from zero to a frequency much higher than the resonance frequency. (b) Identify the value of f at the resonance angular frequency v0. (c) Prove that the slope of the graph of f versus v at the resonance point is 2Q /v0.

In Figure P33.71, find the rms current delivered by the 45.0-V (rms) power supply when (a) the frequency is very large and (b) the frequency is very small.

Review. In the circuit shown in Figure P33.72, assume all parameters except C are given. Find (a) the current in the circuit as a function of time and (b) the power delivered to the circuit. (c) Find the current as a function of time after only switch 1 is opened. (d) After switch 2 is also opened, the current and voltage are in phase. Find the capacitance C. Find (e) the impedance of the circuit when both switches are open, (f) the maximum energy stored in the capacitor during oscillations, and (g) the maximum energy stored in the inductor during oscillations. (h) Now the frequency of the voltage source is doubled. Find the phase difference between the current and the voltage. (i) Find the frequency that makes the inductive reactance one-half the capacitive reactance.

A series RLC circuit contains the following components: R 5 150 V, L 5 0.250 H, C 5 2.00 mF, and a source with DVmax 5 210 V operating at 50.0 Hz. Our goal is to find the phase angle, the power factor, and the power input for this circuit. (a) Find the inductive reactance in the circuit. (b) Find the capacitive reactance in the circuit. (c) Find the impedance in the circuit. (d) Calculate the maximum current in the circuit. (e) Determine the phase angle between the current and source voltage. (f)Find the power factor for the circuit. (g) Find the power input to the circuit.

A series RLC circuit is operating at 2.00 3 103 Hz. At this frequency, XL 5 XC 5 1 884 V. The resistance of the circuit is 40.0 V. (a) Prepare a table showing the values of XL, XC , and Z for f 5 300, 600, 800, 1.00 3 103, 1.50 3 103, 2.00 3 103, 3.00 3 103, 4.00 3 103, 6.00 3 103, and 1.00 3 104 Hz. (b) Plot on the same set of axes XL, XC , and Z as a function of ln f

A series RLC circuit consists of an 8.00-V resistor, a 5.00-mF capacitor, and a 50.0-mH inductor. A variablefrequency source applies an emf of 400 V (rms) across the combination. Assuming the frequency is equal to one-half the resonance frequency, determine the power delivered to the circuit.

A series RLC circuit in which R 5 1.00 V, L 5 1.00 mH, and C 5 1.00 nF is connected to an AC source delivering 1.00 V (rms). (a) Make a precise graph of the power delivered to the circuit as a function of the frequency and (b) verify that the full width of the resonance peak at half-maximum is R/2pL.

The resistor in Figure P33.77 represents the midrange speaker in a three-speaker system. Assume its resistance to be constant at 8.00 V. The source represents an audio amplifier producing signals of uniform amplitude DVmax 5 10.0 V at all audio frequencies. The inductor and capacitor are to function as a band-pass filter with DVout/DVin 5 1 2 at 200 Hz and at 4.00 3 103 Hz. Determine the required values of (a) L and (b) C. Find (c) the maximum value of the ratio DVout/DVin; (d) the frequency f0 at which the ratio has its maximum value; (e) the phase shift between Dvin and Dvout at 200 Hz, at f0, and at 4.00 3 103 Hz; and (f) the average power transferred to the speaker at 200 Hz, at f0, and at 4.00 3 103 Hz. (g) Treating the filter as a resonant circuit, find its quality factor.

An 80.0-V resistor and a 200-mH inductor are connected in parallel across a 100-V (rms), 60.0-Hz source. (a) What is the rms current in the resistor? (b) By what angle does the total current lead or lag behind the voltage?

A voltage Dv 5 100 sin vt, where Dv is in volts and t is in seconds, is applied across a series combination of a 2.00-H inductor, a 10.0-mF capacitor, and a 10.0-V resistor. (a) Determine the angular frequency v0 at which the power delivered to the resistor is a maximum. (b) Calculate the average power delivered at that frequency. (c) Determine the two angular frequencies v1 and v2 at which the power is one-half the maximum value. Note: The Q of the circuit is v0/(v2 2 v1).

Figure P33.80a shows a parallel RLC circuit. The instantaneous voltages (and rms voltages) across each of the three circuit elements are the same, and each is in phase with the current in the resistor. The currents in C and L lead or lag the current in the resistor as shown in the current phasor diagram, Figure P33.80b. (a) Show that the rms current delivered by the source is Irms 5 DVrms c 1 R 2 1 avC 2 1 vLb 2 d 1/2 (b) Show that the phase angle f between DVrms and Irms is given by tan f 5 R a 1 XC 2 1 XL b

An AC source with DVrms 5 120 V is connected between points a and d in Figure P33.24. At what frequency will it deliver a power of 250 W? Explain your answer.