A series RCL circuit has a resonant frequency of 1500 Hz.

A 63.0-mF capacitor is connected to a generator operating at a low frequency. The rms voltage of the generator is 4.00 V and is constant. A fuse in series with the capacitor has negligible resistance and will burn out when the rms current reaches 15.0 A. As the generator frequency is increased, at what frequency will the fuse burn out?

Two identical capacitors are connected in parallel to an ac generator that has a frequency of 610 Hz and produces a voltage of 24 V. The current in the circuit is 0.16 A. What is the capacitance of each capacitor?

The reactance of a capacitor is 68 V when the ac frequency is 460 Hz. What is the reactance when the frequency is 870 Hz?

A capacitor is connected to an ac generator that has a frequency of 3.4 kHz and produces a voltage of 2.0 V. The current in the capacitor is 35 mA. When the same capacitor is connected to a second ac generator that has a frequency of 5.0 kHz, the current in the capacitor is 85 mA. What voltage does the second generator produce?

A capacitor is connected across the terminals of an ac generator that has a frequency of 440 Hz and supplies a voltage of 24 V. When a second capacitor is connected in parallel with the fi rst one, the current from the generator increases by 0.18 A. Find the capacitance of the second capacitor

Two parallel plate capacitors are identical, except that one of them is empty and the other contains a material with a dielectric constant of 4.2 in the space between the plates. The empty capacitor is connected between the terminals of an ac generator that has a fi xed frequency and rms voltage. The generator delivers a current of 0.22 A. What current does the generator deliver after the other capacitor is connected in parallel with the fi rst one?

A capacitor is connected across an ac generator whose frequency is 750 Hz and whose peak output voltage is 140 V. The rms current in the circuit is 3.0 A. (a) What is the capacitance of the capacitor? (b) What is the magnitude of the maximum charge on one plate of the capacitor?

A capacitor (capacitance C1) is connected across the terminals of an ac generator. Without changing the voltage or frequency of the generator, * * ** a second capacitor (capacitance C2) is added in series with the fi rst one. As a result, the current delivered by the generator decreases by a factor of three. Suppose that the second capacitor had been added in parallel with the fi rst one, instead of in series. By what factor would the current delivered by the generator have increased?

An 8.2-mH inductor is connected to an ac generator (10.0 V rms, 620 Hz). Determine the peak value of the current supplied by the generator

An inductor has an inductance of 0.080 H. The voltage across this inductor is 55 V and has a frequency of 650 Hz. What is the current in the inductor?

An inductor is to be connected to the terminals of a generator (rms voltage 5 15.0 V) so that the resulting rms current will be 0.610 A. Determine the required inductive reactance

An ac generator has a frequency of 7.5 kHz and a voltage of 39 V. When an inductor is connected between the terminals of this generator, the current in the inductor is 42 mA. What is the inductance of the inductor?

A 40.0-mF capacitor is connected across a 60.0-Hz generator. An inductor is then connected in parallel with the capacitor. What is the value of the inductance if the rms currents in the inductor and capacitor are equal?

An ac generator has a frequency of 2.2 kHz and a voltage of 240 V. An inductance L1 5 6.0 mH is connected across its terminals. Then a second inductance L2 5 9.0 mH is connected in parallel with L1. Find the current that the generator delivers to L1 and to the parallel combination.

A 30.0-mH inductor has a reactance of 2.10 kV. (a) What is the frequency of the ac current that passes through the inductor? (b) What is the capacitance of a capacitor that has the same reactance at this frequency? The frequency is tripled, so that the reactances of the inductor and capacitor are no longer equal. What are the new reactances of (c) the inductor and (d) the capacitor?

Two inductors are connected in parallel across the terminals of a generator. One has an inductance of L1 5 0.030 H, and the other has an inductance of L2 5 0.060 H. A single inductor, with an inductance L, is connected across the terminals of a second generator that has the same frequency and voltage as the fi rst one. The current delivered by the second generator is equal to the total current delivered by the fi rst generator. Find L.

A series RCL circuit includes a resistance of 275 V, an inductive reactance of 648 V, and a capacitive reactance of 415 V. The current in the circuit is 0.233 A. What is the voltage of the generator?

A series RCL circuit contains a 47.0-V resistor, a 2.00-mF capacitor, and a 4.00-mH inductor. When the frequency is 2550 Hz, what is the power factor of the circuit?

Multiple-Concept Example 3 reviews some of the basic ideas that are pertinent to this problem. A circuit consists of a 215-V resistor and a 0.200-H inductor. These two elements are connected in series across a generator that has a frequency of 106 Hz and a voltage of 234 V. (a) What is the current in the circuit? (b) Determine the phase angle between the current and the voltage of the generator

An ac series circuit has an impedance of 192 V, and the phase angle between the current and the voltage of the generator is f 5 2758. The circuit contains a resistor and either a capacitor or an inductor. Find the resistance R and the capacitive reactance XC or the inductive reactance XL, whichever is appropriate

When only a resistor is connected across the terminals of an ac generator (112 V) that has a fi xed frequency, there is a current of 0.500 A in the resistor. When only an inductor is connected across the terminals of this same generator, there is a current of 0.400 A in the inductor. When both the resistor and the inductor are connected in series between the terminals of this generator, what are (a) the impedance of the series combination and (b) the phase angle between the current and the voltage of the generator?

A 2700-V resistor and a 1.1-mF capacitor are connected in series across a generator (60.0 Hz, 120 V). Determine the power delivered to the circuit.

Suppose that the inductance is zero (L 5 0 H) in the series RCL circuit shown in Figure 23.10. The rms voltages across the generator and the resistor are 45 and 24 V, respectively. What is the rms voltage across the capacitor?

Part a of the drawing shows a resistor and a charged capacitor wired in series. When the switch is closed, the capacitor discharges as charge moves from one plate to the other. Part b shows the amount q of charge remaining on each plate of the capacitor as a function of time. In part c of the drawing, the switch has been removed and an ac generator has been inserted into the circuit. The circuit elements in the drawing have the following values: R 5 18 V, Vrms 5 24 V for the generator, and f 5 380 Hz for the generator. The time constant for the circuit in part a is t 5 3.0 3 1024 s. What is the rms current in the circuit in part c?

A circuit consists of an 85-V resistor in series with a 4.0-mF capacitor, and the two are connected between the terminals of an ac generator. ** * * The voltage of the generator is fi xed. At what frequency is the current in the circuit one-half the value that exists when the frequency is very large?

In one measurement of the bodys bioelectric impedance, values of Z 5 4.50 3 102 V and f 5 29.808 are obtained for the total impedance and the phase angle, respectively. These values assume that the bodys resistance R is in series with its capacitance C and that there is no inductance L. Determine the bodys resistance and capacitive reactance.

A series RCL circuit contains only a capacitor (C 5 6.60 mF), an inductor (L 5 7.20 mH), and a generator (peak voltage 5 32.0 V, frequency 5 1.50 3 103 Hz). When t 5 0 s, the instantaneous value of the voltage is zero, and it rises to a maximum one-quarter of a period later. (a) Find the instantaneous value of the voltage across the capacitor/ inductor combination when t 5 1.20 3 1024 s. (b) What is the instantaneous value of the current when t 5 1.20 3 1024 s? (Hint: The instantaneous values of the voltage and current are, respectively, the vertical components of the voltage and current phasors.)

An 84.0-mH inductor and a 5.80-mF capacitor are connected in series with a generator whose frequency is 375 Hz. The rms voltage across the capacitor is 2.20 V. Determine the rms voltage across the inductor.

A generator is connected to a resistor and a 0.032-H inductor in series. The rms voltage across the generator is 8.0 V. When the generator frequency is set to 130 Hz, the rms voltage across the inductor is 2.6 V. Determine the resistance of the resistor in this circuit

A tank circuit in a radio transmitter is a series RCL circuit connected to an antenna. The antenna broadcasts radio signals at the resonant frequency of the tank circuit. Suppose that a certain tank circuit in a shortwave radio transmitter has a fi xed capacitance of 1.8 3 10211 F and a variable inductance. If the antenna is intended to broadcast radio signals ranging in frequency from 4.0 MHz to 9.0 MHz, fi nd the (a) minimum and (b) maximum inductance of the tank circuit.

A series RCL circuit has a resonant frequency of 690 kHz. If the value of the capacitance is 2.0 3 1029 F, what is the value of the inductance?

The power dissipated in a series RCL circuit is 65.0 W, and the current is 0.530 A. The circuit is at resonance. Determine the voltage of the generator.

A 10.0-V resistor, a 12.0-mF capacitor, and a 17.0-mH inductor are connected in series with a 155-V generator. (a) At what frequency is the current a maximum? (b) What is the maximum value of the rms current?

The capacitance in a series RCL circuit is C1 5 2.60 mF, and the corresponding resonant frequency is f01 5 7.30 kHz. The generator frequency is 5.60 kHz. What is the value of the capacitance C2 that should be added to the circuit so that the circuit will have a resonant frequency that matches the generator frequency? Note that you must decide whether C2 is added in series or in parallel with C1.

A series RCL circuit is at resonance and contains a variable resistor that is set to 175 V. The power delivered to the circuit is 2.6 W. Assuming that the voltage remains constant, how much power is delivered when the variable resistor is set to 562 V?

The resonant frequency of an RCL circuit is 1.3 kHz, and the value of the inductance is 7.0 mH. What is the resonant frequency (in kHz) when the value of the inductance is 1.5 mH?

A series RCL circuit has a resonant frequency of 1500 Hz. When operating at a frequency other than 1500 Hz, the circuit has a capacitive reactance of 5.0 V and an inductive reactance of 30.0 V. What are the values of (a) L and (b) C?

In a series RCL circuit the generator is set to a frequency that is not the resonant frequency. This nonresonant frequency is such that the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to be 5.36. The resonant frequency is 225 Hz. What is the frequency of the generator?

Suppose that you have a number of capacitors. Each is identical to the capacitor that is already in a series RCL circuit. How many of these additional capacitors must be inserted in series in the circuit so the resonant frequency triples?

A charged capacitor and an inductor are connected as shown in the drawing (this circuit is the same as that in Figure 23.16a). There is no resistance in the circuit. As Section 23.4 discusses, the electrical energy initially present in the charged capacitor then oscillates back and forth between the inductor and the capacitor. The initial charge on the capacitor has a magnitude of q 5 2.90 mC. The capacitance is C 5 3.60 mF, and the * * inductance is L 5 75.0 mH. (a) What is the electrical energy stored initially by the charged capacitor? (b) Find the maximum current in the inductor.

In the absence of a nearby metal object, the two inductances (LA and LB) in a heterodyne metal detector are the same, and the resonant frequencies of the two oscillator circuits have the same value of 630.0 kHz. When the search coil (inductor B) is brought near a buried metal object, a beat frequency of 7.30 kHz is heard. By what percentage does the buried object increase the inductance of the search coil?

A 108-V resistor, a 0.200-mF capacitor, and a 5.42-mH inductor are connected in series to a generator whose voltage is 26.0 V. The current in the circuit is 0.141 A. Because of the shape of the currentfrequency graph (see Figure 23.17), there are two possible values for the frequency that corresponds to this current. Obtain these two values

A capacitor is attached to a 5.00-Hz generator. The instantaneous current is observed to reach a maximum value at a certain time. What is the least amount of time that passes before the instantaneous voltage across the capacitor reaches its maximum value?

A circuit consists of a resistor in series with an inductor and an ac generator that supplies a voltage of 115 V. The inductive reactance is 52.0 V, and the current in the circuit is 1.75 A. Find the average power delivered to the circuit.

In a series circuit, a generator (1350 Hz, 15.0 V) is connected to a 16.0-V resistor, a 4.10-mF capacitor, and a 5.30-mH inductor. Find the voltage across each circuit element.

Review Conceptual Example 5 and Figure 23.13. Find the ratio of the current in circuit I to the current in circuit II in the high-frequency limit for the same generator voltage.

At what frequency (in Hz) are the reactances of a 52-mH inductor and a 76-mF capacitor equal?

The resistor in a series RCL circuit has a resistance of 92 V, while the voltage of the generator is 3.0 V. At resonance, what is the average power delivered to the circuit?

Two ac generators supply the same voltage. However, the fi rst generator has a frequency of 1.5 kHz, and the second has a frequency of 6.0 kHz. When an inductor is connected across the terminals of the fi rst generator, the current delivered is 0.30 A. How much current is delivered when this inductor is connected across the terminals of the second generator?

A series circuit contains only a resistor and an inductor. The voltage V of the generator is fi xed. If R 5 16 V and L 5 4.0 mH, fi nd the frequency at which the current is one-half its value at zero frequency.

A series RCL circuit contains a 5.10-mF capacitor and a generator whose voltage is 11.0 V. * * At a resonant frequency of 1.30 kHz the power delivered to the circuit is 25.0 W. Find the values of (a) the inductance and (b) the resistance. (c) Calculate the power factor when the generator frequency is 2.31 kHz.

When a resistor is connected by itself to an ac generator, the average power delivered to the resistor is 1.000 W. When a capacitor is added in series with the resistor, the power delivered is 0.500 W. When an inductor is added in series with the resistor (without the capacitor), the power delivered is 0.250 W. Determine the power delivered when both the capacitor and the inductor are added in series with the resistor.

Part a of the fi gure shows a heterodyne metal detector being used. As part b of the fi gure illustrates, this device utilizes two capacitor/ inductor oscillator circuits, A and B. Each produces its own resonant frequency, f0A 5 1/[2p(LAC)1/2] and f0B 5 1/[2p(LBC)1/2]. Any diff erence between these frequencies is detected through earphones as a beat frequency 0 f0B 2 f0A 0 . In the absence of any nearby metal object, the inductances LA and LB are identical. When inductor B (the search coil) comes near a piece of metal, the inductance LB increases, the corresponding oscillator frequency f0B decreases, and a beat frequency is heard. Suppose that initially each inductor is adjusted so that LB 5 LA, and each oscillator has a resonant frequency of 855.5 kHz. Assuming that the inductance of search coil B increases by 1.000% due to a nearby piece of metal, determine the beat frequency heard through the earphones.

Two parallel plate capacitors are fi lled with the same dielectric material and have the same plate area. However, the plate separation of capacitor 1 is twice that of capacitor 2. When capacitor 1 is connected across the terminals of an ac generator, the generator delivers an rms * current of 0.60 A. Concepts: (i) Which of the two capacitors has the greater capacitance? (ii) Is the equivalent capacitance of the parallel combination (CP) greater or smaller than the capacitance of capacitor 1? (iii) Is the capacitive reactance of CP greater or smaller than for C1? (iv) When both capacitors are connected in parallel across the terminals of the generator, is the current from the generator greater or smaller than when capacitor 1 is connected alone? Calculations: What is the current delivered by the generator when both capacitors are connected in parallel across the terminals?

An ac generator has a frequency of 1200 Hz and a constant rms voltage. When a 470-V resistor is connected between the terminals of the generator, an average power of 0.25 W is consumed by the resistor. Then, a 0.080-H inductor is connected in series with the resistor, and the combination is connected between the generator terminals. Concepts: (i) In which case does the generator deliver a greater rms current? (ii) In which case is the greater average power consumed by the circuit? Calculations: What is the average power consumed in the inductorresistor series circuit?