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essential university physics

Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions

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. (You’ll need Equation 28.10 and a
A series RLC circuit with R = 1.3 Ω, L = 27 mH, and C = 0.33μF is connected across a sine-wave generator. If the capacitor’s peak voltage rating is 600 V, what’s the maximum safe value for the generator’s peak output voltage when it’s tuned to resonance?
An RLC circuit includes a 3.3μF capacitor and a 27-mH inductor. The capacitor is charged to 35V, and the circuit begins oscillating. Ten full cycles later the capacitor voltage peaks at 28V. Find the resistance.
A power supply like that of Fig. 28.23 is supposed to deliver 22-V DC at a maximum current of 150 mA. The transformer?s 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
A car-battery charger runs off the 120-V rms AC power line and supplies 10-A DC at 14V.(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
You’re 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 Ω. You ask the engineers
A series RLC circuit has power factor 0.764 and impedance 182 Ω at 442 Hz. (a) What’s the resistance? (b) If the inductance is 25.0 mH, what’s the resonant frequency?
A series RLC circuit has resistance 127 Ω and impedance 344 Ω.(a) What’s the power factor?(b) If the rms current is 225 mA, what’s the power dissipation?
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.
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. Vce FIGURE 28.26 Problem 53
The table below shows the ratio of peak voltage to peak current that is, the impedance Z as a function of frequency for a series RLC circuit. Plot the data and use your graph to estimate(a) the resonant frequency ?(b) the resistance Frequency (Hz) 150 200 230 280 350 400 Impedance (N) 320 140 74 77
An RLC circuit includes a 1.5-H inductor and a 250μF 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?
A damped RLC circuit includes a 5.0Ω resistor and a 100-mH inductor. If half the initial energy is lost after 15 cycles, what’s the capacitance?
A damped LC circuit consists of a 0.15μF capacitor and a 20-mH inductor with resistance 1.6 Ω. How many oscillation cycles will occur before the peak capacitor voltage drops to half its initial value?
The 2420?F capacitor in Fig. 28.25 is initially charged to 250V.(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
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?
An LC circuit includes a 0.025μF capacitor and a 340μH inductor.(a) If the peak capacitor voltage is 190 V, what’s the peak inductor current?(b) How long after the voltage peak does the current peak occur?
The FM radio band covers the frequency range 88–108 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?
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
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
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 90V, what’s the rms lamp current?
At 15 kHz an inductor has 12 times the reactance of a capacitor. At what frequency will their reactances be equal?
A 2.0μF capacitor has 1.0kΩ reactance.(a) What’s 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?
(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.
You’re 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 transformer’s primary has 660 turns, how many should the secondary have?(b) You can save money with a transformer whose maximum primary
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. What’s the turns ratio of such a transformer?
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.
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 drill draws 4.6 A rms at 120 V rms. If the current lags the voltage by 25°, what’s the drill’s power consumption?
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? R R 2R Wo Frequency, w FIGURE 28.17 Resonance curves for an RLC circuit with three different resistances. Peak current, Ip.
A series RLC circuit has R = 18 kΩ, C = 14 μF, and L = 0.20 H.(a) At what frequency is its impedance lowest?(b) What’s the impedance at this frequency?
Find the impedance at 10 kHz of a circuit consisting of a 1.5kΩ resistor, 5.0μF capacitor, and 50-mH inductor in series.
A Driven RLC Circuits and Resonance 28. A series RLC circuit has R = 75 kΩ, L = 20mH, and resonates at 4.0 kHz. (a) What’s the capacitance? (b) Find the circuit’s impedance at resonance and (c) at 3.0 kHz.
Your sister who’s 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 (550–1600 kHz). What capacitance range do you suggest?Data From Chapter 27 Problem 22Your little sister is building a radio from scratch.
An LC circuit with C = 18 mF undergoes oscillations with period 2.4 s. Find the inductance.
Find the resonant frequency of an LC circuit consisting of a 0.22μF capacitor and a 1.7-mH inductor.
A 50-mH inductor is connected across a 10-V rms AC generator, and a 2.0-mA rms current flows. What’s the generator frequency?
A capacitor and a 1.8kΩ resistor pass the same current when connected across 60-Hz power. Find the capacitance.
A 15μF capacitor carries 1.4 A rms. What’s its minimum safe voltage rating if the frequency is(a) 60 Hz (b) 1.0 kHz?
Find the reactance of a 3.3μF capacitor at(a) 60Hz,(b) 1.0 kHz,(c) 20 kHz.
A 470Ω resistor, 10μF 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 rms current in a 1.0μF capacitor connected across 120-V rms, 60-Hz AC power.
What are the phase constants for the signals in Fig. 28.24? (а) (b) (c) ot 27 (e) (d) FIGURE 28.24 Exercise 17 Voltage
An AC current is given by I = 495 sin(9.43t), with I in mA and t in ms. Find(a) The rms current(b) The frequency in Hz.
An industrial electric motor runs at 208 V rms and 400 Hz. What are(a) the peak voltage (b) the angular frequency
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 ϕv = 0. V, sin(ot + ov) and I 1, sin(@t + d;) (28.3)
Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction?despite the defense?s claim that the defendant didn?t touch the lines.
Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction?despite the defense?s claim that the defendant didn?t touch the lines.
Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction?despite the defense?s claim that the defendant didn?t touch the lines.
Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction?despite the defense?s claim that the defendant didn?t touch the lines.
One way to measure blood flow when blood vessels are exposed during surgery is to use an electromagnetic flowmeter. This device surrounds the blood vessel with an electromagnet, creating a magnetic field perpendicular to the blood flow. Since blood is a modest conductor, a motional emf develops
You and your roommate are headed to Cancun for spring break. Your roommate, who has had only high school physics, has read that an emf can be induced in the wings of an airplane and wonders whether this would give enough voltage to power a portable music player. What’s your answer? (Assume that
Find the magnetic-energy density as a function of radial distance for the coaxial cable of Problem 72, and integrate over the volume between the conductors to show that the total energy per unit length of the cable is given by (?0I2/4?)ln(b/a) Use the expression U = 1/2LI2 to find the inductance
The bar in Problem 46 has mass m and is initially at rest. A constant force F(vector) ?to the right is applied to the bar. Formulate Newton?s second law for the bar, and find its velocity as a function of time. Data From Problem 46 Figure 27.39 shows a pair of parallel conducting rails a distance l
A circular wire loop of radius a and resistance R is pulled with constant speed v into a uniform magnetic field B. The loop is perpendicular to the field, and it begins entering the field at time t = 0. Find an expression for the current in the loop from t = 0 until the loop is fully immersed in
The table below shows the current in a circuit like that of Fig. 27.26, where a current has been established with the switch in position A, and then it?s thrown to position B at time t = 0. The resistance is 180 ?. Determine an appropriate function of current that, when plotted against time, should
A long, straight coaxial cable consists of two thin, tubular conductors, the inner of radius a and the outer of radius b. Current I flows out along one conductor and back along the other. Show that the self-inductance per unit length of the cable is ?. - In (bla)
A conducting disk with radius a, thickness h, and resistivity ρ is inside a solenoid of circular cross section, its axis coinciding with the solenoid axis. The magnetic field in the solenoid is given by B = bt, where b is a constant. Find expressions for(a) the current density in the disk as a
A rectangular conducting loop of resistance R, mass m, and width w falls into a uniform magnetic field as shown in Fig. 27.41.(a) Explain why the loop eventually reaches a terminal speed.(b) Find an expression for the terminal speed. X x x X X XIX X X,xx X В x x'x x X X X X FIGURE 27.41 Problem 70
An electric field and a magnetic field have the same energy density. Find an expression for the ratio E/B and evaluate this ratio numerically. What are its units? Is your answer close to any of the fundamental constants listed inside the front cover?
(a) Use Equation 27.8 to write an expression for the resistor?s power dissipation as a function of time,(b) integrate from t = 0 to t = ? to show that the total energy dissipated is equal to the energy initially stored in the inductor. T= he-Rll. (27.8)
A wire of radius R carries current I distributed uniformly over its cross section. Find an expression for the total magnetic energy per unit length within the wire.
A single-turn loop of radius R carries current I. How does the magnetic-energy density at the loop center compare with that of a long solenoid of the same radius, carrying the same current, and consisting of n turns per unit length?
A neutron star’s magnetic field is about 108 T. Consult Appendix C to compare the energy density in this field with that of(a) gasoline(b) pure uranium-235 (mass density 19x103 kg/m3).
Your hospital is installing a new MRI scanner using a 3.5-H superconducting solenoid carrying 1.8 kA. Copper is embedded in the coils to carry the current in the event of a quench As safety officer, you’re to specify(a) The maximum resistance that will limit power dissipation to 100 kW
When a nonideal 1.0-H inductor is short-circuited, its magnetic energy drops to one-fourth of its original value in 3.6 s. What is its resistance?
A battery, switch, resistor, and inductor are connected in series. When the switch is closed, the current rises to half its steady state value in 1.0 ms. How long does it take for the magnetic energy in the inductor to rise to half its steady-state value?
In Fig. 27.40, take ?0 = 12 V, R1 = 4.0 ?, R2 = 8.0 ?, and R3 = 2.0 ?. Find current I2? (a) Immediately after the switch is first closed (b) A long time later. (c) After a long time, the switch is reopened. R R3 R2 FIGURE 27.40 Problem 61 ell ww
In Fig. 27.26, take ?0 = 12 V, R = 2.7 ?, and L = 20 H. Initially the switch is in position B and there?s no current anywhere. At t = 0 the switch is thrown to position A, and at t = 10 s it?s returned to B. Find the inductor current at (a) t = 5.0 s and (b) t = 15 s. Świtching to B takes the
You’re a safety engineer reviewing plans for a university’s new high-rise dorm. The elevator motors draw 20 A and behave electrically like 2.5-H inductors. You’re concerned about dangerous voltages developing across the switch when a motor is turned off, and you recommend that a resistor be
A series RL circuit like Fig. 27.23a has ?0?= 60 V, R = 22 ?, and L = 1.5 H. Find the rate of change of the current (a) immediately after the switch is closed (b) 100 ms later. Switch open: No current flows. S R L (a)
In Fig. 27.23a, take R = 2.5 k? and E0 = 50 V. When the switch is closed, the current through the inductor rises to 10 mA in 30 ?s. Find (a) the inductance and (b) the current in the circuit after many time constants. Switch open: No current flows. S R L (a)
The current in a series RL circuit rises to half its final value in 7.6 s. What’s the time constant?
A flip coil is used to measure magnetic fields. It’s a small coil placed with its plane perpendicular to a magnetic field, and then flipped through 180°. The coil is connected to an instrument that measures the total charge Q that flows during this process. If the coil has N turns, area A, and
During lab, you’re given a circular wire loop of resistance R and radius a with its plane perpendicular to a uniform magnetic field. You’re supposed to increase the field strength from B1 to B2 and measure the total charge that moves around the loop. Your lab partner claims that the details of
An electron is inside a solenoid, 28 cm from the axis. It experiences a 1.3-fN electric force. At what rate is the solenoid’s magnetic field changing?
The magnetic field inside a solenoid of circular cross section is given by B(vector) = btk̂, where b = 2.1 T/ms. At time t = 0.40 μs, a proton is inside the solenoid at x = 5.0 cm, y = z = 0, and is moving with velocity v (Vector) = 4.8ĵ Mm/s. Find the electromagnetic force on the
In Fig. 27.39, take l = 10 cm, B = 0.50 T, R = 4.0 ?, and v = 2.0 m/s. Find(a) the current in the resistor,(b) the magnetic force on the bar,(c) the power dissipation in the resistor, and(d) the mechanical power supplied by the agent pulling the bar. Compare your answers to parts (c) and (d). ? В
A battery of emf ? is inserted in series with the resistor in Fig. 27.39, with its positive terminal toward the top rail. The bar is initially at rest, and now nothing?s pulling it.(a) Describe the bar?s subsequent motion.(b) The bar eventually reaches a constant speed. Why? (c) What is that
The resistor in Problem 46 is replaced by an ideal voltmeter.(a) To which rail should the positive meter terminal be connected if it?s to indicate a positive voltage?(b) At what rate does the agent pulling the bar do work? В х хх х_х x x x X x x X .R FIGURE 27.39 Problems 46-49 and 75
Figure 27.39 shows a pair of parallel conducting rails a distance l apart in a uniform magnetic field B(vector). A resistor R is connected across the rails, and a conducting bar of negligible resistance is being pulled along the rails with velocity v ! to the right.(a) What direction is the current
A generator consists of a rectangular coil 75 cm by 1.3 m, spinning in a 0.14-T magnetic field. If it’s to produce a 60-Hz alternating emf with peak value 6.7 kV, how many turns must it have?
You’re an electrical engineer designing an alternator (the generator that charges a car’s battery). Mechanical engineers specify a 10-cm-diameter rotating coil, and you determine that you can fit 250 turns in this coil. To charge a 12-V battery, you need a peak output of 14 V when the
A uniform magnetic field is given by B(vector) = btk̂, where b = 0.35 T/s. Find the induced current in a conducting loop with area 240 cm2 and resistance 0.20 Ω that lies in the x–y plane. In what direction is the current, as viewed from the positive z-axis?
A stent is a cylindrical tube, often made of metal mesh, that’s inserted into a blood vessel to overcome a constriction. It’s sometimes necessary to heat the stent after insertion to prevent cell growth that could cause the constriction to recur. One method is to place the patient in a changing
A 2000-turn solenoid is 2.0 m long and 15 cm in diameter. The solenoid current is increasing at 1.0 kA/s. (a) Find the current in a 10-cm-diameter wire loop with resistance 5.0 Ω lying inside the solenoid and perpendicular to the solenoid axis. (b) Repeat for a similarly oriented 25-cm-diameter
A square wire loop 3.0 m on a side is perpendicular to a uniform 2.0-T magnetic field. A 6-V light bulb is in series with the loop, as shown in Fig. 27.38. The magnetic field is reduced steadily to zero over time ?t. (a) Find ?t such that the bulb will shine at full brightness. (b) Which way will
A magnetic field is given by B(vector) = B0(x/x0)2 k̂, where B0 and x0 are constants. Find an expression for the magnetic flux through a square of side 2x0 that lies in the x–y plane with one corner at the origin and sides coinciding with the positive x- and y-axis.
A 5-turn coil 1.0 cm in diameter is rotated at 10 rev/s about an axis perpendicular to a uniform magnetic field. A voltmeter connected to the coil through rotating contacts reads a peak value 360 μV. What’s the magnetic-field strength?
A square wire loop of side l and resistance R is pulled with constant speed v from a region of no magnetic field until it’s fully inside a region of constant, uniform magnetic field B(vector) perpendicular to the loop plane. The boundary of the field region is parallel to one side of the loop.
A conducting loop with area 0.15 m2 and resistance 6.0 Ω lies in the x–y plane. A spatially uniform magnetic field points in the z-direction. The field varies with time according to Bz = at2 - b, where a = 2.0 T/s2 and b = 8.0 T. Find the loop current(a) at t = 3.0 s(b) when Bz = 0.
A conducting loop of area A and resistance R lies at right angles to a spatially uniform magnetic field. At time t = 0, the magnetic field and loop current are both zero. Subsequently, the current increases according to I = bt2, where b is a constant with units A/s2. Find an expression for the
The induced electric field 12 cm from the axis of a 10-cm-radius solenoid is 45 V/m. Find the rate of change of the solenoid’s magnetic field.
Find the magnetic-field strength in a region where the magnetic energy density is 7.8 J/cm3
The world’s strongest magnet that can produce a sustained field is a 45-T device at the National High Magnetic Field Laboratory in Florida. What’s the corresponding magnetic-energy density?
Show that the quantity B2/2μ0 has the units of energy density.
A 1250-turn solenoid 23.2 cm long and 1.58 cm in diameter carries 165 mA. How much magnetic energy does it contain?
A 220-mH inductor carries 350 mA. How much energy must be supplied to the inductor in raising the current to 850 mA?
What’s the current in a 24-mH inductor storing 75 μJ of energy?
How much energy is stored in a 5.0-H inductor carrying 35 A?

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