Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
Note: For problems in this set, the ac current and voltage are rms values, and the power is an average value, unless indicated otherwise.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 23.1 Capacitors and Capacitive Reactance

| 1 | ssm What voltage is needed to create a current of 35 mA in a circuit containing only a capacitor, when the frequency is 3.4 kHz?

| 2 | The reactance of a capacitor is when the ac frequency is 460 Hz. What is the reactance when the frequency is 870 Hz?

| 3 | 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 first one, the current from the generator increases by 0.18 A. Find the capacitance of the second capacitor.

| 4 | 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?

| 5 | ssm A circuit consists of a and a capacitor connected in series across the terminals of a 510-Hz generator. The voltage of the generator is 120 V. (a) Determine the equivalent capacitance of the two capacitors. (b) Find the current in the circuit.

* | 6 | 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?

** | 7 | 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 first one. As a result, the current delivered by the generator decreases by a factor of three. Suppose the second capacitor had been added in parallel with the first one, instead of in series. By what factor would the current delivered by the generator have increased?
Section 23.2 Inductors and Inductive Reactance

| 8 | A 0.047-H inductor is wired across the terminals of a generator that has a voltage of 2.1 V and supplies a current of 0.023 A. Find the frequency of the generator.

| 9 | ssm At what frequency (in Hz) are the reactances of a 52-mH inductor and a capacitor equal?

| 10 | Two ac generators supply the same voltage. However, the first 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 first 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?

| 11 | ssm www 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.

| 12 | 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?

* | 13 | A 30.0-mH inductor has a reactance of . (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?

** | 14 | Two inductors are connected in parallel across the terminals of a generator. One has an inductance of , and the other has an inductance of . 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 first one. The current delivered by the second generator is equal to the total current delivered by the first generator. Find L.
Section 23.3 Circuits Containing Resistance, Capacitance, and Inductance

| 15 | ssm A series RCL circuit includes a resistance of , an inductive reactance of , and a capacitive reactance of . The current in the circuit is 0.233 A. What is the voltage of the generator?

| 16 | A resistor and a capacitor are connected in series across a generator (60.0 Hz, 120 V). Determine the power delivered to the circuit.

| 17 | Suppose that the inductance is zero 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 volt age across the capacitor?

| 18 | A light bulb has a resistance of . It is connected to a standard wall socket (120 V, 60.0 Hz). (a) Determine the current in the bulb. (b) Determine the current in the bulb after a capacitor is added in series in the circuit. (c) It is possible to return the current in the bulb to the value calculated in part (a) by adding an inductor in series with the bulb and the capacitor. What is the value of the inductance of this inductor?

| 19 | ssm Multiple-Concept Example 3 reviews some of the basic ideas that are pertinent to this problem. A circuit consists of a 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.

| 20 | Review Conceptual Example 5 and Figure 23-12. Find the ratio of the current in circuit I to that in circuit II in the high-frequency limit for the same generator voltage.

* | 21 | ssm www A circuit consists of an resistor in series with a capacitor, the two being connected between the terminals of an ac generator. The voltage of the generator is fixed. At what frequency is the current in the circuit one-half the value that exists when the frequency is very large?

* | 22 | In one measurement of the body’s bioelectric impedance, values of and are obtained for the total impedance and the phase angle, respectively. These values assume that the body’s resistance R is in series with its capacitance C and that there is no inductance L. Determine the body’s resistance and capacitive reactance.

* | 23 | Refer to Interactive Solution 23.23 at for help with problems like this one. A series RCL circuit contains only a capacitor , an inductor , and a generator (peak voltage = 32.0 V, ). When t = 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 . (b) What is the instantaneous value of the current when ? (Hint: The instantaneous values of the voltage and current are, respectively, the vertical components of the voltage and current phasors.)

* | 24 | Review Conceptual Example 5 before attempting this problem. Then refer to the drawing, in which the generator delivers four times as much current at very low frequencies as it does at very high frequencies. Find the ratio R2/R1 of the resistances.

Problem 24

** | 25 | 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.
Section 23.4 Resonance in Electric Circuits

| 26 | A series RCL circuit has a resonant frequency of 690 kHz. If the value of the capacitance is , what is the value of the inductance?

| 27 | ssm The resonant frequency of a series RCL circuit is 9.3 kHz. The inductance and capacitance of the circuit are each tripled. What is the new resonant frequency?

| 28 | A series RCL circuit is at resonance and contains a variable resistor that is set to . 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 ?

| 29 | ssm A resistor, a 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?

| 30 | 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 and an inductive reactance of . What are the values of (a) L and (b) C?

| 31 | 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?

* | 32 | Consult Multiple-Concept Example 6 for background on how to approach this problem. 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 kHz. When the search coil (inductor B) is brought near a buried metal object, a beat frequency of 7.3 kHz is heard. By what percentage does the buried object reduce the inductance of the search coil?

* | 33 | ssm Suppose 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?

** | 34 | A resistor, a 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 current-versus-frequency graph (see Figure 23-17), there are two possible values for the frequency that correspond to this current. Obtain these two values.

** | 35 | In a series RCL circuit the dissipated power drops by a factor of two when the frequency of the generator is changed from the resonant frequency to a nonresonant frequency. The peak voltage is held constant while this change is made. Determine the power factor of the circuit at the nonresonant frequency.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.