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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions
The radar system at an airport broadcasts 11 GHz microwaves with 150 kW of power. An approaching airplane with a 31 m2 cross section is 30 km away. Assume that the radar broadcasts uniformly in all directions and that the airplane scatters microwaves uniformly in all directions. What is the
Large quantities of dust should have been left behind after the creation of the solar system. Larger dust particles, comparable in size to soot and sand grains, are common. They create shooting stars when they collide with the earth’s atmosphere. But very small dust particles are conspicuously
Consider current I passing through a resistor of radius r, length L, and resistance R.a. Determine the electric and magnetic fields at the surface of the resistor. Assume that the electric field is uniform throughout, including at the surface.b. Determine the strength and direction of the Poynting
FIGURE Q32.1 shows emf phasors a, b, and c. a. For each, what is the instantaneous value of the emf?b. At this instant, is the magnitude of each emf increasing, decreasing, or holding constant? 100 V b. -100 V 100 V a --100 V FIGURE Q32.1
The emf phasor in FIGURE EX32.1 is shown at t = 2.0 ms. a. What is the angular frequency ω? Assume this is the first rotation.b. What is the peak value of the emf? 135° at t= 2.0 ms -So V -50 V
A resistor is connected across an oscillating emf. The peak current through the resistor is 2.0 A. What is the peak current if:a. The resistance R is doubled?b. The peak emf Ԑ0 is doubled?c. The frequency ω is doubled?
The emf phasor in FIGURE EX32.2 is shown at t = 15 ms. a. What is the angular frequency ω? Assume this is the first rotation.b. What is the instantaneous value of the emf? 30° Phasor at E = 12 V t= 15 ms FIGURE EX32.2
A capacitor is connected across an oscillating emf. The peak current through the capacitor is 2.0 A. What is the peak current if:a. The capacitance C is doubled?b. The peak emf Ԑ0 is doubled?c. The frequency ω is doubled?
A 110 Hz source of emf has a peak voltage of 50 V. Draw the emf phasor at t = 3.0 ms.
A low-pass RC filter has a crossover frequency fc = 200 Hz. What is fc if:a. The resistance R is doubled?b. The capacitance C is doubled?c. The peak emf Ԑ0 is doubled?
Draw the phasor for the emf Ԑ = (170 V) cos((2π × 60 Hz)t) at t = 60 ms.
An inductor is connected across an oscillating emf. The peak current through the inductor is 2.0 A. What is the peak current if:a. The inductance L is doubled?b. The peak emf Ԑ0 is doubled?c. The frequency ω is doubled?
FIGURE EX32.5 shows voltage and current graphs for a resistor. a. What is the emf frequency f ?b. What is the value of the resistance R?c. Draw the resistor??s voltage and current phasors at t = 15 ms. VR iR Voltage 10 V- Current 0.50 A 0+ 0.00 s 0.02 s 0.04 s F-0.50 A -10 V- FIGURE EX32.5
The resonance frequency of a series RLC circuit is 1000 Hz. What is the resonance frequency if:a. The resistance R is doubled?b. The inductance L is doubled?c. The capacitance C is doubled?d. The peak emf Ԑ0 is doubled?
A 200 Ω resistor is connected to an AC source with Ԑ0 = 10 V. What is the peak current through the resistor if the emf frequency is(a) 100 Hz?(b) 100 kHz?
In the series RLC circuit represented by the phasors of FIGURE Q32.7, is the emf frequency less than, equal to, or greater than the resonance frequency ω0? Explain. FIGURE Q32.7
The peak current to and from a capacitor is 10 mA. What is the peak current ifa. The emf frequency is doubled?b. The emf peak voltage is doubled (at the original frequency)?
The resonance frequency of a series RLC circuit is less than the emf frequency. Does the current lead or lag the emf? Explain.
A 0.30 μF capacitor is connected across an AC generator that produces a peak voltage of 10 V. What is the peak current to and from the capacitor if the emf frequency is(a) 100 Hz?(b) 100 kHz?
The current in a series RLC circuit lags the emf by 20°. You cannot change the emf. What two different things could you do to the circuit that would increase the power delivered to the circuit by the emf?
FIGURE EX32.9 shows voltage and current graphs for a capacitor. a. What is the emf frequency f?b. What is the value of the capacitance C? Vc ic Voltage 10 V- 15 mA 0- 0.00 s 0.01 s 0.02 s F-15 mA Current -10 V- FIGURE EX32.9
A 20 nF capacitor is connected across an AC generator that produces a peak voltage of 5.0 V.a. At what frequency f is the peak current 50 mA?b. What is the instantaneous value of the emf at the instant when iC = IC?
The average power dissipated by a resistor is 4.0 W. What is PR if:a. The resistance R is doubled while Ԑ0 is held fixed?b. The peak emf Ԑ0 is doubled while R is held fixed?c. Both are doubled simultaneously?
capacitor is connected to a 15 kHz oscillator. The peak current is 65 mA when the rms voltage is 6.0 V. What is the value of the capacitance C?
A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V.a. What is the capacitance?b. If the peak voltage is held constant, what is the peak current at 500 kHz?
a. Evaluate VCin FIGURE EX32.13 at emf frequencies 1, 3, 10, 30, and 100 kHz.b. Graph VCversus frequency.Draw a smooth curve through your five points. ww 16 N (10 V) cos ot F1.0 µF FIGURE EX32.13
a. Evaluate VRin FIGURE EX32.14 at emf frequencies 100, 300, 1000, 3000, and 10,000 Hz.b. Graph VRversus frequency.Draw a smooth curve through your five points. 1.6 μF (10 V) cos o 100 0 FIGURE EX32.14 ww
A high-pass RC filter is connected to an AC source with a peak voltage of 10.0 V. The peak capacitor voltage is 6.0 V. What is the resistor voltage?
A high-pass RC filter with a crossover frequency of 1000 Hz uses a 100 Ω resistor. What is the value of the capacitor?
A low-pass RC filter with a crossover frequency of 1000 Hz uses a 100 Ω resistor. What is the value of the capacitor?
A low-pass filter consists of a 100 μF capacitor in series with a 159 Ω resistor. The circuit is driven by an AC source with a peak voltage of 5.00 V.a. What is the crossover frequency fc?b. What is VC when f = 1/2 fc, fc, and 2fc?
What are VRand VCif the emf frequency in FIGURE EX32.19 is 10 kHz? 150 N (10 V) cos o ( 80 nF FIGURE EX32.19
A high-pass filter consists of a 1.59 μF capacitor in series with a 100 Ω resistor. The circuit is driven by an AC source with a peak voltage of 5.00 V.a. What is the crossover frequency fc?b. What is VR when f = 1/2fc, fc, and 2fc?
An electric circuit, whether it’s a simple lightbulb or a complex amplifier, has two input terminals that are connected to the two output terminals of the voltage source. The impedance between the two input terminals (often a function of frequency) is the circuit’s input impedance. Most
A 20 mH inductor is connected across an AC generator that produces a peak voltage of 10 V. What is the peak current through the inductor if the emf frequency is(a) 100 Hz?(b) 100 kHz?
The peak current through an inductor is 10 mA. What is the peak current ifa. The emf frequency is doubled?b. The emf peak voltage is doubled (at the original frequency)?
FIGURE EX32.24 shows voltage and current graphs for an inductor. a. What is the emf frequency f?b. What is the value of the inductance L? Voltage 1V 2A 0- 0.00 s 0.02 s -2 A 0.01 s Current - V- FIGURE EX32.24
An inductor is connected to a 15 kHz oscillator. The peak current is 65 mA when the rms voltage is 6.0 V. What is the value of the inductance L?
An inductor has a peak current of 330 μA when the peak voltage at 45 MHz is 2.2 V.a. What is the inductance?b. If the peak voltage is held constant, what is the peak current at 90 MHz?
A series RLC circuit has a 200 kHz resonance frequency. What is the resonance frequency if the capacitor value is doubled and, at the same time, the inductor value is halved?
A series RLC circuit has a 200 kHz resonance frequency. What is the resonance frequency ifa. The resistor value is doubled?b. The capacitor value is doubled?
What capacitor in series with a 100 Ω resistor and a 20 mH inductor will give a resonance frequency of 1000 Hz?
A series RLC circuit consists of a 50 Ω resistor, a 3.3 mH inductor, and a 480 nF capacitor. It is connected to an oscillator with a peak voltage of 5.0 V. Determine the impedance, the peak current, and the phase angle at frequencies(a) 3000 Hz,(b) 4000 Hz,(c) 5000 Hz.
At what frequency f do a 1.0 μF capacitor and a 1.0 μH inductor have the same reactance? What is the value of the reactance at this frequency?
For the circuit of FIGURE EX32.32, a. What is the resonance frequency, in both rad/s and Hz?b. Find VR and VL at resonance.c. How can VL be larger than Ԑ0? Explain. (10 V) cos ot 10 mH 10 µF: FIGURE EX32.32
For the circuit of FIGURE EX32.33, a. What is the resonance frequency, in both rad/s and Hz?b. Find VR and VC at resonance.c. How can VC be larger than Ԑ0? Explain. 10 0 (10 V) cos ot 1.0 mH 1.0 μF FIGURE EX32.33 ww
The heating element of a hair drier dissipates 1500 W when connected to a 120 V/60 Hz power line. What is its resistance?
A resistor dissipates 2.0 W when the rms voltage of the emf is 10.0 V. At what rms voltage will the resistor dissipate 10.0 W?
For what absolute value of the phase angle does a source deliver 75% of the maximum possible power to an RLC circuit?
The motor of an electric drill draws a 3.5 A rms current at the power-line voltage of 120 V rms. What is the motor’s power if the current lags the voltage by 20°?
A series RLC circuit attached to a 120 V/60 Hz power line draws a 2.4 A rms current with a power factor of 0.87. What is the value of the resistor?
A series RLC circuit with a 100 Ω resistor dissipates 80 W when attached to a 120 V/60 Hz power line. What is the power factor?
a. For an RC circuit, find an expression for the angular frequency at which VR = 1/2Ԑ0.b. What is VC at this frequency?
a. lar frequency at which VC = 1/2Ԑ0.For an RC circuit, find an expression for the angub. What is VR at this frequency?
For an RC filter circuit, show that VR = VC = Ԑ0/√2 at ω = ωc.
A series RC circuit is built with a 12 kΩ resistor and a parallel plate capacitor with 15-cm-diameter electrodes. A 12 V, 36 kHz source drives a peak current of 0.65 mA through the circuit. What is the spacing between the capacitor plates?
Show that Equation 32.27 for the phase angle ϕ of a series RLC circuit gives the correct result for a capacitor-only circuit.
a. What is the peak current supplied by the emf in FIGURE P32.45?b. What is the peak voltage across the 3.0 μF capacitor? 3.0 μF Eo = 10 V f=200 Hz 4.0 µF: -2.0 μF FIGURE P32.45
You have a resistor and a capacitor of unknown values. First, you charge the capacitor and discharge it through the resistor. By monitoring the capacitor voltage on an oscilloscope, you see that the voltage decays to half its initial value in 2.5 ms. You then use the resistor and capacitor to make
FIGURE P32.47 shows a parallel RC circuit. a. Use a phasor-diagram analysis to find expressions for the peak currents IR and IC. b. Complete the phasor analysis by finding an expression for the peak emf current I. iR Eg cos ot FIGURE P32.47
The small transformers that power many consumer products produce a 12.0 V rms, 60 Hz emf. Design a circuit using resistors and capacitors that uses the transformer voltage as an input and produces a 6.0 V rms output that leads the input voltage by 45°.
Use a phasor diagram to analyze the RL circuit of FIGURE P32.49. In particular, a. Find expressions for I, VR, and VL.b. What is VR in the limits ω ?? 0 and ω ?? ???c. If the output is taken from the resistor, is this a low-pass or a high-pass filter? Explain. d. Find an expression for the
A series RLC circuit consists of a 75 Ω resistor, a 0.12 H inductor, and a 30 μF capacitor. It is attached to a 120 V/60 Hz power line. What are(a) The peak current I,(b) The phase angle ϕ,(c) The average power loss?
A series RLC circuit consists of a 25 Ω resistor, a 0.10 H inductor, and a 100 μF capacitor. It draws a 2.5 A rms current when attached to a 60 Hz source. What are(a) The emf Ԑrms,(b) The phase angle ϕ,(c) The average power loss?
The tuning circuit in an FM radio receiver is a series RLC circuit with a 0.200 μH inductor.a. The receiver is tuned to a station at 104.3 MHz. What is the value of the capacitor in the tuning circuit?b. FM radio stations are assigned frequencies every 0.2 MHz, but two nearby stations cannot use
A series RLC circuit consists of a 550 Ω resistor, a 2.1 mH inductor, and a 550 nF capacitor. It is connected to a 50 V rms oscillating voltage source with an adjustable frequency. An oscillating magnetic field is observed at a point 2.5 mm from the center of one of the circuit wires, which is
In FIGURE P32.54, what is the current supplied by the emf when(a) The frequency is very small(b) The frequency is very large? 50 0 100 N 10 V rms : 20 μF 50 mH FIGURE P32.54
The current lags the emf by 30° in a series RLC circuit with Ԑ0 = 10 V and R = 50 Ω. What is the peak current through the circuit?
A series RLC circuit consists of a 50 Ω resistor, a 3.3 mH inductor, and a 480 nF capacitor. It is connected to a 5.0 kHz oscillator with a peak voltage of 5.0 V. What is the instantaneous current i whena. Ԑ = Ԑ0?b. Ԑ = 0 V and is decreasing?
A series RLC circuit consists of a 50 Ω resistor, a 3.3 mH inductor, and a 480 nF capacitor. It is connected to a 3.0 kHz oscillator with a peak voltage of 5.0 V. What is the instantaneous emf Ԑ whena. i = I?b. i = 0 A and is decreasing?c. i = -I?
Show that the power factor of a series RLC circuit is cos ϕ = R/Z.
For a series RLC circuit, show thata. The peak current can be written I = Imax cos ϕ.b. The average power can be written Psource = Pmax cos2 ϕ.
A television channel is assigned the frequency range from 54 MHz to 60 MHz. A series RLC tuning circuit in a TV receiver resonates in the middle of this frequency range. The circuit uses a 16 pF capacitor.a. What is the value of the inductor?b. In order to function properly, the current throughout
Lightbulbs labeled 40 W, 60 W, and 100 W are connected to a 120 V/60 Hz power line as shown in FIGURE P32.62. What is the rate at which energy is dissipated in each bulb? 40 W 120 V/60 Hz O100 W 60 W FIGURE P32.62
A generator consists of a 12-cm by 16-cm rectangular loop with 500 turns of wire spinning at 60 Hz in a 25 mT uniform magnetic field. The generator output is connected to a series RC circuit consisting of a 120 Ω resistor and a 35 μF capacitor. What is the average power delivered to the circuit?
Commercial electricity is generated and transmitted as three phase electricity. Instead of a single emf, three separate wires carry currents for the emfs Ԑ1 = Ԑ0 cos ωt, Ԑ2 = Ԑ0 cos(ωt +120°), and Ԑ3 = Ԑ0 cos(ωt - 120°) over three parallel wires, each of which supplies one-third of the
You’re the operator of a 15,000 V rms, 60 Hz electrical substation. When you get to work one day, you see that the station is delivering 6.0 MW of power with a power factor of 0.90.a. What is the rms current leaving the station?b. How much series capacitance should you add to bring the power
Commercial electricity is generated and transmitted as three phase electricity. Instead of a single emf Ԑ = Ԑ0 cos ωt, three separate wires carry currents for the emfs Ԑ1 = Ԑ0 cos ωt, Ԑ2 = Ԑ0 cos(ωt + 120°), and Ԑ3 = Ԑ0 cos(ωt - 120°). This is why the long-distance transmission lines
A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W.a. What is the power factor?b. What is the rms resistor voltage?c. What is the motor’s resistance?d. How much series capacitance needs to be added to increase the power factor to 1.0?
a. Green light shines through a 100-mm-diameter hole and is observed on a screen. If the hole diameter is increased by 20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.b. Green light shines through a 100-μm-diameter hole and
FIGURE CP32.68 shows voltage and current graphs for a series RLC circuit. a. What is the resistance R?b. If L = 200 μH, what is the resonance frequency in Hz? Voltage 10 V E2 A Current 0+ 50 100 us E-2 A -10 V- FIGURE CP32.68
a. Show that the average power loss in a series RLC circuit is b. Prove that the energy dissipation is a maximum at ω = ω0. ms)³R ? – w³)² Pavg w*R? + L²(@°
a. Show that the peak inductor voltage in a series RLC circuit is maximum at frequencyb. A series RLC circuit with Ô0 = 10.0 V consists of a 1.0 Ω resistor, a 1.0 μH inductor, and a 1.0 μF capacitor. What is VL at ω = ω0 and
The telecommunication circuit shown in FIGURE CP32.71 has a parallel inductor and capacitor in series with a resistor. a. Use a phasor diagram to show that the peak current through the resistor is b. What is I in the limits ω ?? 0 and ω ?? ???c. What is the resonance frequency ω0? What is I at
Consider the parallel RLC circuit shown in FIGURE CP32.72. a. Show that the current drawn from the emf is b. What is I in the limits ω ?? 0 and ω ?? ???c. Find the frequency for which I is a minimum.d. Sketch a graph of I versus ω. En cos wt ( FIGURE CP32.72
A double slit is illuminated simultaneously with orange light of wavelength 620 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe. What is the unknown wavelength?
FIGURE Q33.1 shows light waves passing through two closely spaced, narrow slits. The graph shows the intensity of light on a screen behind the slits. Reproduce these graph axes, including the zero and the tick marks locating the double-slit fringes, then draw a graph to show how the light-intensity
Two narrow slits 80 μm apart are illuminated with light of wavelength 620 nm. What is the angle of the m = 3 bright fringe in radians? In degrees?
In a double-slit interference experiment, which of the following actions (perhaps more than one) would cause the fringe spacing to increase?(a) Increasing the wavelength of the light.(b) Increasing the slit spacing.(c) Increasing the distance to the viewing screen.(d) Submerging the entire
A double-slit experiment is performed with light of wavelength 630 nm. The bright interference fringes are spaced 1.8 mm apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of 420 nm?
FIGURE Q33.3 shows the viewing screen in a double-slit experiment. Fringe C is the central maximum. What will happen to the fringe spacing if a. The wavelength of the light is decreased?b. The spacing between the slits is decreased?c. The distance to the screen is decreased?d. Suppose the
Light of wavelength 550 nm illuminates a double slit, and the interference pattern is observed on a screen. At the position of the m = 2 bright fringe, how much farther is it to the more distant slit than to the nearer slit?
FIGURE Q33.3 is the interference pattern seen on a viewing screen behind 2 slits. Suppose the 2 slits were replaced by 20 slits having the same spacing d between adjacent slits. a. Would the number of fringes on the screen increase, decrease, or stay the same?b. Would the fringe spacing increase,
Light of 630 nm wavelength illuminates two slits that are 0.25 mm apart. FIGURE EX33.5 shows the intensity pattern seen on a screen behind the slits. What is the distance to the screen? Intensity x (ст) 2 FIGURE EX33.5
FIGURE Q33.5 shows the light intensity on a viewing screen behind a single slit of width a. The light??s wavelength is λ. Is λ < a, λ = a, λ > a, or is it not possible to tell? Explain. FIGURE Q33.5
In a double-slit experiment, the slit separation is 200 times the wavelength of the light. What is the angular separation (in degrees) between two adjacent bright fringes?
FIGURE Q33.6 shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if a. The wavelength of the light is increased?b. The diameter of the aperture is increased?c. How will the screen appear if the aperture diameter is less than
Light from a sodium lamp (λ = 589 nm) illuminates two narrow slits. The fringe spacing on a screen 150 cm behind the slits is 4.0 mm. What is the spacing (in mm) between the two slits?
Narrow, bright fringes are observed on a screen behind a diffraction grating. The entire experiment is then immersed in water. Do the fringes on the screen get closer together, get farther apart, remain the same, or disappear? Explain.
A double-slit interference pattern is created by two narrow slits spaced 0.25 mm apart. The distance between the first and the fifth minimum on a screen 60 cm behind the slits is 5.5 mm. What is the wavelength (in nm) of the light used in this experiment?
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