Solved: Much of Europe uses AC power at 230 V rms and 50 Hz. Express this AC voltage in

Two AC signals have the same amplitude but different frequencies.Are their rms amplitudes the same?

Whats meant by the statement, A capacitor acts like a DC opencircuit?

Theres an insulating gap between capacitor plates, so how cancurrent flow in an AC circuit containing a capacitor?

Why does it make sense that inductive reactance increases withfrequency?

The same AC voltage appears across a capacitor and a resistor,and the same rms current flows in each. Is the power dissipationthe same in each?

When a particular inductor and capacitor are connected acrossthe same AC voltage, the current in the inductor is higher than inthe capacitor. Is this true at all frequencies?

An inductor and capacitor are connected in series across an ACgenerator, and the voltage across the inductor is higher thanacross the capacitor. Is the generator frequency above or below resonance?

When the capacitor voltage in an undriven LC circuit reaches zero, why dont the oscillations stop?

Why is Equation 28.5 not a full description of the relation between voltage and current in a capacitor?

The applied voltage in a series RLC circuit lags the current. Is the frequency above or below resonance?

The voltage across two components in series is zero. Is it possible that the voltages across the individual components arent zero? Give an example.

If you measure the rms voltages across the resistor, capacitor, and inductor in a series RLC circuit, will they add to the rms generator voltage?

A step-up transformer increases voltage, or energy per unit charge. Why doesnt this violate energy conservation?

Much of Europe uses AC power at 230 V rms and 50 Hz. Express this AC voltage in the form of Equation 28.3, taking fV = 0.

An industrial electric motor runs at 208 V rms and 400 Hz. What are (a) the peak voltage and (b) the angular frequency?

An AC current is given by I = 495 sin(9.43t), with I in mA and t in ms. Find (a) the rms current and (b) the frequency in Hz.

What are the phase constants for the signals in Fig. 28.24?

Find the rms current in a 1.0@F capacitor connected across 120-V rms, 60-Hz AC power.

A 470@ resistor, 10@F capacitor, and 750-mH inductor are each connected across 6.3-V rms, 60-Hz AC power. Find the rms current in each.

Find the reactance of a 3.3@F capacitor at (a) 60 Hz, (b) 1.0 kHz, and (c) 20 kHz.

A 15@F capacitor carries 1.4 A rms. Whats its minimum safe voltage rating if the frequency is (a) 60 Hz and (b) 1.0 kHz?

A capacitor and a 1.8@k resistor pass the same current when connected across 60-Hz power. Find the capacitance.

A 50-mH inductor is connected across a 10-V rms AC generator, and a 2.0-mA rms current flows. Whats the generator frequency?

Find the resonant frequency of an LC circuit consisting of a 0.22@F capacitor and a 1.7-mH inductor.

An LC circuit with C = 18 mF undergoes oscillations with period 2.4 s. Find the inductance.

Your sister whos building the radio (Chapter 27 Problem 22) wants to use a variable capacitor with her toilet-paper-tube inductor to span the AM radio band (5501600 kHz). What capacitance range do you suggest?

An LC circuit with a 20@F capacitor oscillates with period 5.0 ms. The peak current is 25 mA. Find (a) the inductance and (b) the peak voltage.

A series RLC circuit has R = 75 k, L = 20mH, and resonates at 4.0 kHz. (a) Whats the capacitance? (b) Find the circuits impedance at resonance and (c) at 3.0 kHz.

Find the impedance at 10 kHz of a circuit consisting of a 1.5@k resistor, 5.0@F capacitor, and 50-mH inductor in series.

A series RLC circuit has R = 18 k, C = 14 F, and L = 0.20 H. (a) At what frequency is its impedance lowest? (b) Whats the impedance at this frequency?

If the peak voltage applied to produce the curves in Fig. 28.17 is 100 V, and if R = 10 k, what are the peak currents at resonance for the three curves shown?

An electric drill draws 4.6 A rms at 120 V rms. If the current lags the voltage by 25, whats the drills power consumption?

A 40-W fluorescent lamp has power factor 0.85 and operates from the 120-V rms AC power line. How much current does it draw?

An electric water heater draws 20 A rms at 240 V rms and is purely resistive. An AC motor has the same current and voltage, but its inductance causes the voltage to lead the current by 20. Find the power consumption in each device

For safety, medical equipment connected to patients is often powered by an isolation transformer, whose primary is connected to 120-V AC power and whose secondary delivers 120-V power. Whats the turns ratio of such a transformer?

Youre planning a semester in China, so you want to purchase a transformer to step the 220-V Chinese power down to 120 V to power your stereo. (a) If the transformers primary has 660 turns, how many should the secondary have? (b) You can save money with a transformer whose maximum primary current is 1.4 A. If your stereo draws 2.9 A, will this transformer work?

(a) A 2.2-H inductor is connected across 120-V rms, 60-Hz power. Find the rms inductor current. (b) Repeat if the same inductor is connected across the 230-V rms, 50-Hz power commonly used in Europe.

A 2.0@F capacitor has 1.0@k reactance. (a) Whats the frequency of the applied voltage? (b) What inductance would give the same reactance at this frequency? (c) How would the reactances compare if the frequency were doubled?

Show that the unit of both capacitive and inductive reactance is the ohm

Electroencephalography (EEG) elucidates brain function by analyzing brain waves, AC voltages resulting from electrical activity in the brain. Alpha waves are brain waves with frequencies from 7.5 Hz to 12.5 Hz. A particular alpha wave has frequency 9.84 Hz and rms amplitude 31.8 V. Express this voltage in the form of Equation 28.3, assuming zero phase constant.

At 15 kHz an inductor has 12 times the reactance of a capacitor. At what frequency will their reactances be equal?

A 0.75-H inductor is in series with a fluorescent lamp, and the combination is across 120-V rms, 60-Hz power. If the rms inductor voltage is 90 V, whats the rms lamp current?

A 2.2-nF capacitor and one of unknown capacitance are in parallel across a 10-V rms sine-wave generator. At 1.0 kHz, the generator supplies a total current of 3.4 mA rms. The generator frequency is then decreased until the rms current drops to 1.2 mA. Find (a) the unknown capacitance and (b) the lower frequency.

Connections to the body for electrocardiography (ECG) and electroencephalography (EEG) are normally made with metal electrodes and conductive gels to ensure good electrical contact. An alternative is the capacitively coupled noncontact electrode, which uses a conductor near but not contacting the skin, to form a capacitor. Clothing can serve as the capacitors insulation, eliminating skin contact. A particular EEG instrument calls for capacitive electrodes with maximum reactance 10 M at a typical EEG beta wave frequency of 25 Hz. Whats the minimum electrode capacitance?

The FM radio band covers the frequency range 88108 MHz. If the variable capacitor in an FM receiver ranges from 10.9 pF to 16.4 pF, what inductor should be used to make an LC circuit whose resonant frequency spans the FM band?

An LC circuit includes a 0.025@F capacitor and a 340@H inductor. (a) If the peak capacitor voltage is 190 V, whats the peak inductor current? (b) How long after the voltage peak does the current peak occur?

One-eighth of a cycle after the capacitor in an LC circuit is fully charged, what are the following as fractions of their peak values: (a) capacitor charge, (b) energy in the capacitor, (c) inductor current, (d) energy in the inductor?

The 2420@F capacitor in Fig. 28.25 is initially charged to 250 V. (a) Describe how you would manipulate switches A and B to transfer all the energy from the 2420@F capacitor to the 605@F capacitor. Include the times you would throw the switches. (b) What will be the voltage across the 605@F capacitor once youve finished?

A damped LC circuit consists of a 0.15@F capacitor and a 20-mH inductor with resistance 1.6 . How many oscillation cycles will occur before the peak capacitor voltage drops to half its initial value?

A damped RLC circuit includes a 5.0@ resistor and a 100-mH inductor. If half the initial energy is lost after 15 cycles, whats the capacitance?

An RLC circuit includes a 1.5-H inductor and a 250@F capacitor rated at 400 V. The circuit is connected across a sine-wave generator with Vp = 32 V. What minimum resistance will ensure that the capacitor voltage does not exceed its rated value when the circuit is at resonance?

The table below shows the ratio of peak voltage to peak current that is, the impedance Zas a function of frequency for a series RLC circuit. Plot the data and use your graph to estimate (a) the resonant frequency and (b) the resistance R

Figure 28.26 shows the phasor diagram for an RLC circuit. (a) Is the driving frequency above or below resonance? (b) Complete the diagram by adding the applied voltage phasor, and from your diagram determine the phase difference between applied voltage and current.

An AC voltage of fixed amplitude is applied across a series RLC circuit. The components are such that the current at half the resonant frequency is half the current at resonance. Show that the current at twice the resonant frequency is also half the current at resonance.

A series RLC circuit has resistance 127 and impedance 344 . (a) Whats the power factor? (b) If the rms current is 225 mA, whats the power dissipation?

A series RLC circuit has power factor 0.764 and impedance 182 at 442 Hz. (a) Whats the resistance? (b) If the inductance is 25.0 mH, whats the resonant frequency?

Youre Chief Financial Officer for a power company, and you consult your engineering department in an effort to minimize powerline losses. Your power plant produces 60-Hz power at 365 kV rms and 200 A rms, and delivers it via transmission lines with total resistance 100 . You ask the engineers for the percentage of power thats lost. They reply that it depends on the power factor. Whats the percentage loss for power factors of (a) 1.0 and (b) 0.60?

A car-battery charger runs off the 120-V rms AC power line and supplies 10-A DC at 14 V. (a) If the charger is 80% efficient in converting the line power to the DC power it supplies to the battery, how much current does it draw from the AC line? (b) If electricity costs 9.5/kWh, how much does it cost to run the charger for 10 hours if the power factor is 1?

A power supply like that of Fig. 28.23 is supposed to deliver 22-V DC at a maximum current of 150 mA. The transformers peak output voltage can charge the capacitor to a full 22 V, and the primary is supplied with 60-Hz AC. What capacitance will ensure that the output voltage stays within 3% of the rated 22 V?

An RLC circuit includes a 3.3@F capacitor and a 27-mH inductor. The capacitor is charged to 35 V, and the circuit begins oscillating. Ten full cycles later the capacitor voltage peaks at 28 V. Find the resistance.

A series RLC circuit with R = 1.3 , L = 27 mH, and C = 0.33F is connected across a sine-wave generator. If the capacitors peak voltage rating is 600 V, whats the maximum safe value for the generators peak output voltage when its tuned to resonance?

Differentiate Equation 28.9 to find the current in the LC circuit, and use q = CV to find the voltage. From these, obtain the electric energy in the capacitor and the magnetic energy in the inductor, and sum to show that the total energy remains constant. (Hint: Youll need Equation 28.10 and a familiar trig identity.)

Find a second frequency where the current in the speaker of Example 28.4 has half its maximum value.

Two capacitors are connected in parallel across a 24-V rms, 7.5-kHz sine-wave generator, and the generator supplies a total rms current of 56 mA. With capacitors rewired in series, the rms current drops to 2.8 mA. What are the two capacitances?

A black box has two input connections and two output connections. With a 12-V rms, 60-Hz sine wave across the inputs, the output is a 6.0-V, 60-Hz sine wave leading the input voltage by 45. Design a circuit that could be in the black box.

A series RLC circuit with R = 47 , L = 250mH, and C = 4.0 F is connected across a sine-wave generator whose peak output voltage is independent of frequency. Find the frequency range over which the peak current will exceed half its value at resonance.

A sine-wave generator with 20-V peak output is applied across a series RLC circuit. At the resonant frequency of 2.0 kHz, the peak current is 50 mA; at 1.0 kHz, its 15 mA. Find R, L, and C.

For RLC circuits in which the resistance isnt too high, the Q factor may be defined as the ratio of the resonant frequency to the difference between the two frequencies where the power dissipated in the circuit is half the power dissipated at resonance. Using suitable approximations, show that this definition leads to Q = v0L/R, with v0 the resonant frequency.

A triangle wave swings linearly between voltages -Vp and +Vp. Show that the rms voltage of a triangle wave is Vp/13

Substitute the expression for q1t2 in Equation 28.11 into the differential equation for an LC circuit with resistance, and find an expression for the angular frequency of the damped oscillations in terms of R, L, and C

Although the maximum current flows in the speaker circuit of Example 28.4 at the 1-kHz resonant frequency, the peak voltage across the capacitor is a maximum at a somewhat lower frequency. Find that frequency and the corresponding peak voltage

Your professor tells you about the days before digital computers when engineers used electric circuits to model mechanical systems. Suppose a 5.0-kg mass is connected to a spring with k = 1.44 kN/m. This is then modeled by an LC circuit with L = 2.5 H. What should C be in order for the LC circuit to have the same resonant frequency as the massspring system?

A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range of frequencies while attenuating signals with frequencies outside the band. Filters are widely used in electronics. Applications include tone and equalizer controls in audio equipment; filters to separate nearby frequencies at cell phone towers; and filters to eliminate unwanted electrical noise in biomedical instruments such as electrocardiographs. A simple design for an RC filter is shown in Fig. 28.27. The circuit shown in Fig. 28.27 is a. a low-pass filter. b. a high-pass filter. c. a band-pass filter. d. impossible to tell without knowing the component values.

A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range of frequencies while attenuating signals with frequencies outside the band. Filters are widely used in electronics. Applications include tone and equalizer controls in audio equipment; filters to separate nearby frequencies at cell phone towers; and filters to eliminate unwanted electrical noise in biomedical instruments such as electrocardiographs. A simple design for an RC filter is shown in Fig. 28.27. When the angular frequency v of the input voltage Vin is such that the capacitors reactance is equal to the resistance, the output voltage is a. Vin /4. b. Vin /2. c. Vin /12. d. 2Vin.

A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range of frequencies while attenuating signals with frequencies outside the band. Filters are widely used in electronics. Applications include tone and equalizer controls in audio equipment; filters to separate nearby frequencies at cell phone towers; and filters to eliminate unwanted electrical noise in biomedical instruments such as electrocardiographs. A simple design for an RC filter is shown in Fig. 28.27. The circuit of Fig. 28.27 a. exhibits resonance at frequency v = 1/RC. b. exhibits resonance at frequency v = 1/1RC. c. produces an output voltage whose frequency differs from that of the input. d. produces an output voltage whose phase differs from that of the input

A filter is a circuit designed to pass AC signals in some frequency range and to attenuate others. Common filters include low-pass filters, which allow low-frequency signals to pass but attenuate high frequencies; high-pass filters, which do the opposite; and band-pass filters, which pass a range of frequencies while attenuating signals with frequencies outside the band. Filters are widely used in electronics. Applications include tone and equalizer controls in audio equipment; filters to separate nearby frequencies at cell phone towers; and filters to eliminate unwanted electrical noise in biomedical instruments such as electrocardiographs. A simple design for an RC filter is shown in Fig. 28.27. If you replace the capacitor in Fig. 28.27 with an inductor, the circuit a. continues to function as before. b. becomes the opposite kind of filter. c. produces zero output voltage because the inductor is a short circuit. d. produces an output voltage that exceeds the input voltage.