Question: A conducting rod of length ℓ moves on

> Babies in the United States have a mean birth length of 20.5 inches with a standard deviation of 0.90 inch. The shape of the distribution of birth lengths is approximately Normal. a. Find the birth length at the 2.5th percentile. b. Find the birth length

> Find the sample size required for a margin of error of 3 percentage points, and then find one for a margin of error of 1.5 percentage points; for both, use a 95% confidence level. Find the ratio of the larger sample size to the smaller sample size. To re

> The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100, and the scores are approximately Normally distributed. a. What is the probability that one randomly selected person will have an SAT score of 550 or mor

> Using your list of outcomes in Problem 6.8: a. Find the probability of having 0, 1, or 2 girls in a family of two children and display the probability distribution in a table. b. Make a graph of the probability distribution. Outcomes of Problem 6.8:

> In 2017 the Gallup poll surveyed 1021 adults in the United States and found that 57% supported a ban on smoking in public places. a. Identify the population and the sample. b. What is the parameter of interest? What is the statistic?

> The resonant frequency of a certain series RLC circuit is 2.84 kHz, and the value of its capacitance is 6.50 μF. What is the value of the resonant frequency when the capacitance of the circuit is 9.80 μF?

> An RLC circuit is used in a radio to tune into an FM station broadcasting at f = 99.7 MHz. The resistance in the circuit is R = 12.0 Ω, and the inductance is L = 1.40 μH. What capacitance should be used?

> Consider a series RLC circuit with R = 25 Ω, L = 6.0 mH, and C = 25 μF. The circuit is connected to a 10. - V (rms), 600. - Hz AC source. (a) Is the sum of the voltage drops across R, L, and C equal to 10. V (rms)? (b) Which is greatest, the power delive

> An inductor and a resistor are connected in series. When connected to a 60. - Hz, 90. - V (rms) source, the voltage drop across the resistor is found to be 50. V (rms) and the power delivered to the circuit is 14 W. Find (a) The value of the resistance a

> A series RLC circuit has a resistance of 22.0 Ω and an impedance of 80.0 Ω. If the rms voltage applied to the circuit is 160. V, what average power is delivered to the circuit?

> An RLC circuit has resistance R = 225 Ω and inductive reactance XL = 175 Ω. (a) Calculate the circuit’s capacitive reactance XC if its power factor is cos ( = 0.707. Repeat the calculation for (b) Cos ( = 1.00 and (c) Cos ( = 1.00 x 10-2.

> An AC voltage of the form Δv = (90.0 V) sin (350t) is applied to a series RLC circuit. If R = 50.0 Ω, C = 25.0 μF, and L = 0.200 H, find the (a) Impedance of the circuit, (b) rms current in the circuit, and (c) Average power delivered to the circuit.

> A multimeter in an RL circuit records an rms current of 0.500 A and a 60.0 - Hz rms generator voltage of 104 V. A wattmeter shows that the average power delivered to the resistor is 10.0 W. Determine (a) The impedance in the circuit, (b) The resistance R

> An AC source operating at 60. Hz with a maximum voltage of 170 V is connected in series with a resistor (R = 1.2 kΩ) and a capacitor (C = 2.5 μF). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potenti

> A 1.5 – kΩ resistor is connected to an AC voltage source with an rms voltage of 120 V. (a) What is the maximum voltage across the resistor? (b) What is the maximum current through the resistor? (c) What is the rms current through the resistor? (d) What i

> In which one of the following lists are different types of electromagnetic waves ranked in order of increasing wavelength? (a) X - rays, gamma rays, visible light, radio waves (b) Visible light, radio waves, gamma rays, x – rays (c) Gamma rays, x - rays,

> An AC source with a maximum voltage of 150. V and f = 50.0 Hz is connected between points a and d in Figure P21.29. Calculate the rms voltages between points (a) a and b, (b) b and c, (c) c and d, and (d) b and d. Figure P21.29:

> At what frequency does the inductive reactance of a 57.0 – μH inductor equal the capacitive reactance of a 57.0 - μF capacitor?

> A series AC circuit contains a resistor, an inductor of 150. mH, a capacitor of 5.00 μF, and a generator with ΔVmax = 240. V operating at 50.0 Hz. The maximum current in the circuit is 100. mA. Calculate (a) The inductive reactance, (b) The capacitive re

> A 60.0 - Ω resistor is connected in series with a 30.0 - μF capacitor and a generator having a maximum voltage of 1.20 x 102 V and operating at 60.0 Hz. Find the (a) Capacitive reactance of the circuit, (b) Impedance of the circuit, and (c) Maximum curre

> A person is working near the secondary of a transformer, as shown in Figure P21.25. The primary voltage is 120. V (rms) at 60.0 Hz. The capacitance Cs, which is the stray capacitance between the hand and the secondary winding, is 20.0 pF. Assuming the pe

> An AC source operating at 60. Hz with a maximum voltage of 170 V is connected in series with a resistor (R = 1.2 kΩ) and an inductor (L = 2.8 H). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potentia

> A series RLC circuit has resistance R = 12.0 Ω, inductive reactance XL = 30.0 Ω, and capacitive reactance XC = 20.0 Ω. If the maximum voltage across the resistor is ΔVR = 145 V, find the maximum voltage across (a) The inductor and (b) The capacitor. (c)

> A 50.0 - Ω resistor, a 0.100 - H inductor, and a 10.0 - μF capacitor are connected in series to a 60.0 - Hz source. The rms current in the circuit is 2.75 A. Find the rms voltages across (a) The resistor, (b) The inductor, (c) The capacitor, and (d) The

> A resistor (R = 9.00 x 102 Ω), a capacitor (C = 0.250 μF), and an inductor (L = 2.50 H) are connected in series across a 2.40 x 102 - Hz AC source for which ΔVmax = 1.40 x 102 V. Calculate (a) The impedance of the circuit, (b) The maximum current deliver

> An inductor (L = 400. mH), a capacitor (C = 4.43 μF), and a resistor (R = 500. Ω) are connected in series. A 50.0 - Hz AC generator connected in series to these elements produces a maximum current of 250 mA in the circuit. (a) Calculate the required maxi

> As the bar in Figure CQ20.5 moves perpendicular to the field, is an external force required to keep it moving with constant speed? Figure CQ20.5:

> A certain light-bulb is rated at 60.0 W when operating at an rms voltage of 120. V. (a) What is the peak voltage applied across the bulb? (b) What is the resistance of the bulb? (c) Does a 100. - W bulb have greater or less resistance than a 60.0 - W bul

> A series RLC circuit has resistance R = 50.0 Ω and inductance L = 0.500 H. (a) Find the circuit’s capacitance C if the voltage source operates at a frequency of f = 60.0 Hz and the impedance is Z = R = 50.0 Ω. (b) What is the phase angle between the curr

> A sinusoidal voltage Δv = (80.0 V) sin (150t) is applied to a series RLC circuit with L = 80.0 mH, C = 125.0 μF, and R = 40.0 Ω. (a) What is the impedance of the circuit? (b) What is the maximum current in the circuit?

> Determine the maximum magnetic flux through an inductor connected to a standard outlet (ΔVrms = 120. V, f = 60.0 Hz).

> The output voltage of an AC generator is given by Δv = (1.20 x 102 V) sin (30πt). The generator is connected across a 0.500 - H inductor. Find the (a) Frequency of the generator, (b) Rms voltage across the inductor, (c) Inductive reactance, (d) Rms curre

> In a purely inductive AC circuit as shown in Figure P21.15, ΔVmax = 100. V. (a) The maximum current is 7.50 A at 50.0 Hz. Calculate the inductance L. (b) At what angular frequency ω is the maximum current 2.50 A? Figure P21.15:

> An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 47 - H inductor, determine (a) The inductive reactance and (b) The rms current through the inductor.

> An inductor has a 54.0 - Ω reactance when connected to a 60.0 - Hz source. The inductor is removed and then connected to a 50.0 - Hz source that produces a 100. - V rms voltage. What is the maximum current in the inductor?

> A generator delivers an AC voltage of the form Δv = (98.0 V) sin (80πt) to a capacitor. The maximum current in the circuit is 0.500 A. Find the (a) Rms voltage of the generator, (b) Frequency of the generator, (c) Rms current, (d) Reactance, and (e) Valu

> What maximum current is delivered by an AC source with ΔVmax = 48.0 V and f = 90.0 Hz when connected across a 3.70 - μF capacitor?

> When light (or other electromagnetic radiation) travels across a given region, (a) What is it that oscillates? (b) What is it that is transported?

> An AC generator with an output rms voltage of 36.0 V at a frequency of 60.0 Hz is connected across a 12.0 - μF capacitor. Find the (a) Capacitive reactance, (b) Rms current, and (c) Maximum current in the circuit. (d) Does the capacitor have its maximum

> (a) What is the resistance of a light-bulb that uses an average power of 75.0 W when connected to a 60.0 - Hz power source having a maximum voltage of 170. V? (b) What is the resistance of a 100. - W light-bulb?

> A conducting rectangular loop of mass M, resistance R, and dimensions w by â„“ falls from rest into a magnetic field B(, as shown in Figure P20.67. During the time interval before the top edge of the loop reaches the field, the loop appro

> An N-turn square coil with side â„“ and resistance R is pulled to the right at constant speed v in the positive x - direction in the presence of a uniform magnetic field B acting perpendicular to the coil, as shown in Figure P20.66. At t

> In Figure P20.65 the rolling axle of length 1.50 m is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resistor R = 0.400 Ω is connected to the rails at points a and b, directly opposite each other. (The wheels make good elec

> An aluminum ring of radius 5.00 cm and resistance 3.00 x 10-4 Ω is placed around the top of a long air-core solenoid with 1000 turns per meter and a smaller radius of 3.00 cm, as in Figure P20.64. If the current in the solenoid is increasing

> The magnetic field shown in Figure P20.63 has a uniform magnitude of 25.0 mT directed into the paper. The initial diameter of the kink is 2.00 cm. (a) The wire is quickly pulled taut, and the kink shrinks to a diameter of zero in 50.0 ms. Determine the a

> The square loop in Figure P20.62 is made of wires with a total series resistance of 10.0 Ω. It is placed in a uniform 0.100-T magnetic field directed perpendicular into the plane of the paper. The loop, which is hinged at each corner, is pull

> The bolt of lightning depicted in Figure P20.61 passes 200. m from a 100-turn coil oriented as shown. If the current in the lightning bolt falls from 6.02 x 106 A to zero in 10.5 μs, what is the average voltage induced in the coil? Assume t

> A long solenoid of radius r = 2.00 cm is wound with 3.50 x 103 turns/m and carries a current that changes at the rate of 28.5 A/s as in Figure P20.60. What is the magnitude of the emf induced in the square conducting loop surrounding the center of the so

> How is electrical energy produced in dams? (That is, how is the energy of motion of the water converted to AC electricity?)

> A spacecraft is in a circular orbit of radius equal to 3.0 x 104 km around a 2.0 x 1030 kg pulsar. The magnetic field of the pulsar at that radial distance is 1.0 x 102 T directed perpendicular to the velocity of the spacecraft. The spacecraft is 0.20 km

> An 820-turn wire coil of resistance 24.0 Ω is placed on top of a 12 500-turn, 7.00-cm-long solenoid, as in Figure P20.57. Both coil and solenoid have cross-sectional areas of 1.00 x 10-4 m2. (a) How long does it take the solenoid current to r

> A conducting bar of length â„“ moves to the right on two frictionless rails, as shown in Figure P20.30. A uniform magnetic field directed into the page has a magnitude of 0.30 T. Assume â„“ = 35 cm and R = 9.0 Î&copy

> A rectangular coil with resistance R has N turns, each of length â„“ and width w, as shown in Figure P20.55. The coil moves into a uniform magnetic field B( with constant velocity v(. What are the magnitude and direction of the total magn

> A circular loop of wire of resistance R = 0.500 Ω and radius r = 8.00 cm is in a uniform magnetic field directed out of the page as in Figure P20.54. If a clockwise current of I = 2.50 mA is induced in the loop, (a) Is the magnetic field incr

> Two circular loops of wire surround an insulating rod as in Figure P20.53. Loop 1 carries a current I in the clockwise direction when viewed from the left end. If loop 1 moves toward loop 2, which remains stationary, what is the direction of the induced

> A 60.0-m length of insulated copper wire is wound to form a solenoid of radius 2.0 cm. The copper wire has a radius of 0.50 mm. (a) What is the resistance of the wire? (b) Treating each turn of the solenoid as a circle, how many turns can be made with th

> A 24-V battery is connected in series with a resistor and an inductor, with R = 8.0 Ω and L = 4.0 H, respectively. Find the energy stored in the inductor (a) When the current reaches its maximum value and (b) One time constant after the switch is closed.

> A 300-turn solenoid has a radius of 5.00 cm and a length of 20.0 cm. Find (a) The inductance of the solenoid and (b) The energy stored in the solenoid when the current in its windings is 0.500 A.

> Receiving radio antennas can be in the form of conducting lines or loops. What should the orientation of each of these antennas be relative to a broadcasting antenna that is vertical?

> (a) If an inductor carrying a 1.70-A current stores an energy of 0.300 mJ, what is its inductance? (b) How much energy does the same inductor store if it carries a 3.00-A current?

> Consider the circuit shown in Figure P20.43. Take ε = 6.00 V, L = 8.00 mH, and R = 4.00 Ω. (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 250. μs after the switch is

> Calculate the resistance in an RL circuit in which L = 2.50 H and the current increases to 90.0% of its final value in 3.00 s.

> A 25-mH inductor, an 8.0-Ω resistor, and a 6.0-V battery are connected in series as in Figure P20.43. The switch is closed at t = 0. Find the voltage drop across the resistor (a) At t = 0 and (b) After one time constant has passed. Also, find

> The battery terminal voltage in Figure P20.43 is ε = 9.00 V and the current I reaches half its maximum value of 2.00 A at t = 0.100 s after the switch is closed. Calculate (a) The time constant τ. (b) What is the emf across the in

> An RL circuit with L = 3.00 H and an RC circuit with C = 3.00 μF have the same time constant. If the two circuits have the same resistance R, (a) What is the value of R and (b) What is this common time constant?

> An electromagnet can be modeled as an inductor in series with a resistor. Consider a large electromagnet of inductance L = 12.0 H and resistance R = 4.50 Ω connected to a 24.0 V battery and switch as in Figure P20.43. After the switch is clos

> An emf of 24.0 mV is induced in a 500-turn coil when the current is changing at a rate of 10.0 A/s. What is the magnetic flux through each turn of the coil at an instant when the current is 4.00 A?

> A solenoid of radius 2.5 cm has 400 turns and a length of 20 cm. Find (a) Its inductance and (b) The rate at which current must change through it to produce an emf of 75 mV.

> Show that the two expressions for inductance given by L = NфB/I and L = -ε / ΔI/Δt have the same units.

> A loop of wire is placed in a uniform magnetic field. (a) For what orientation of the loop is the magnetic flux a maximum? (b) For what orientation is the flux zero?

> The current in a coil drops from 3.5 A to 2.0 A in 0.50 s. If the average emf induced in the coil is 12 mV, what is the self-inductance of the coil?

> A solenoid with 475 turns has a length of 6.00 cm and a cross-sectional area of 2.80 x 10-9 m2. Find (a) The solenoid’s inductance and (b) The average emf around the solenoid if the current changes from +2.00 A to -2.00 A in 8.33 x 10-3 s.

> A coil of 10.0 turns is in the shape of an ellipse having a major axis of 10.0 cm and a minor axis of 4.00 cm. The coil rotates at 100. rpm in a region in which the magnitude of Earth’s magnetic field is 55.0 μT. What is the maximum voltage induced in th

> A motor has coils with a resistance of 30. Ω and operates from a voltage of 240 V. When the motor is operating at its maximum speed, the back emf is 145 V. Find the current in the coils (a) When the motor is first turned on and (b) When the motor has rea

> A generator connected to the wheel or hub of a bicycle can be used to power lights or small electronic devices. A typical bicycle generator supplies 6.00 V when the wheels rotate at ω = 20.0 rad/s. (a) If the generator’s magnetic field has magnitude B =

> A flat coil enclosing an area of 0.10 m2 is rotating at 60 rev/s, with its axis of rotation perpendicular to a 0.20-T magnetic field. (a) If there are 1 000 turns on the coil, what is the maximum voltage induced in the coil? (b) When the maximum induced

> Considerable scientific work is currently under way to determine whether weak oscillating magnetic fields such as those found near outdoor electric power lines can affect human health. One study indicated that a magnetic field of magnitude 1.0 x 10-3 T,

> A 100-turn square wire coil of area 0.040 m2 rotates about a vertical axis at 1500 rev/min, as indicated in Figure P20.32. The horizontal component of Earth’s magnetic field at the location of the loop is 2.0 x 10-5 T. Calculate the max

> A square coil of wire of side 2.80 cm is placed in a uniform magnetic field of magnitude 1.25 T directed into the page as in Figure P20.31. The coil has 28.0 turns and a resistance of 0.780 Ω. If the coil is rotated through an angle of 90.0&A

> Consider the arrangement shown in Figure P20.30 where R = 6.00 Ω, ℓ = 1.20 m, and B = 2.50 T. (a) At what constant speed should the bar be moved to produce a current of 1.00 A in the resistor? (b) What power is delivered to

> (a) Does the phase angle in an RLC series circuit depend on frequency? (b) What is the phase angle for the circuit when the inductive reactance equals the capacitive reactance?

> Figure P20.29 shows a bar of mass m = 0.200 kg that can slide without friction on a pair of rails separated by a distance ℓ = 1.20 m and located on an inclined plane that makes an angle θ = 25.0° with respect to

> An astronaut is connected to her spacecraft by a 25-m-long tether cord as she and the spacecraft orbit Earth in a circular path at a speed of 3.0 x 103 m/s. At one instant, the voltage measured between the ends of a wire embedded in the cord is measured

> An automobile has a vertical radio antenna 1.20 m long. The automobile travels at 65.0 km/h on a horizontal road where Earth’s magnetic field is 50.0 μT, directed toward the north and downward at an angle of 65.0° below the horizontal. (a) Specify the di

> In one of NASA’s space tether experiments, a 20.0-km-long conducting wire was deployed by the space shuttle as it orbited at 7.86 x 103 m/s around Earth and across Earth’s magnetic field lines. The resulting motional emf was used as a power source. If th

> A pickup truck has a width of 79.8 in. If it is traveling north at 37 m/s through a magnetic field with vertical component of 35 μT, what magnitude emf is induced between the driver and passenger sides of the truck?

> A 2.00 - m length of wire is held in an east–west direction and moves horizontally to the north with a speed of 15.0 m/s. The vertical component of Earth’s magnetic field in this region is 40.0 μT directed downward. Calculate the induced emf between the

> A truck is carrying a steel beam of length 15.0 m on a freeway. An accident causes the beam to be dumped off the truck and slide horizontally along the ground at a speed of 25.0 m/s. The velocity of the center of mass of the beam is northward while the l

> An N - turn circular wire coil of radius r lies in the xy - plane (the plane of the page), as in Figure P20.10. A uniform magnetic field is turned on, increasing steadily from 0 to B0 in the positive z - direction in t seconds. (a) Find a symbolic expres

> To monitor the breathing of a hospital patient, a thin belt is girded around the patient’s chest as in Figure P20.21. The belt is a 200-turn coil. When the patient inhales, the area encircled by the coil increases by 39.0 cm2. The magni

> A circular coil enclosing an area of 100 cm2 is made of 200 turns of copper wire. The wire making up the coil has resistance of 5.0 Ω, and the ends of the wire are connected to form a closed circuit. Initially, a 1.1-T uniform magnetic field points perpe

> Does dropping a magnet down a copper tube produce a current in the tube? Explain.

> A 300-turn solenoid with a length of 20.0 cm and a radius of 1.50 cm carries a current of 2.00 A. A second coil of four turns is wrapped tightly around this solenoid, so it can be considered to have the same radius as the solenoid. The current in the 300

> What is the impedance of a series RLC circuit at resonance? (a) XL (b) XC (c) R (d) XL - XC (e) 0

> A circular loop of wire lies below a long wire carrying a current that is increasing as in Figure P20.17a. (a) What is the direction of the induced current in the loop, if any? (b) Now suppose the loop is next to the same wire as in Figure P20.17b. What

> An inductor and a resistor are connected in series across an AC generator, as shown in Figure CQ21.16. Immediately after the switch is closed, which of the following statements is true? (a) The current is ΔV/R. (b) The voltage across the indu

> Why is the sum of the maximum voltages across each of the elements in a series RLC circuit usually greater than the maximum applied voltage? Doesn’t this violate Kirchhoff’s loop rule?

> A horizontal metal bar oriented east–west drops straight down in a location where Earth’s magnetic field is due north. As a result, an emf develops between the ends. Which end is positively charged? (a) The east end (b) The west end (c) Neither end carri

> A magneto is used to cause the spark in a spark plug in many lawn mowers today. A magneto consists of a permanent magnet mounted on a flywheel so that it spins past a fixed coil. Explain how this arrangement generates a large enough potential difference

> Two circular loops are side by side and lie in the xy - plane. A switch is closed, starting a counterclockwise current in the left-hand loop, as viewed from a point on the positive z - axis passing through the center of the loop. Which of the following s