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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

A 100-turn coil with a radius of 10.0 cm is mounted so the coil's axis can be oriented in any horizontal direction. Initially the axis is oriented so the magnetic flux from Earth's field is maximized. If the coil's axis is rotated through 90.0° in 0.080 s, an emf of 0.687 mV is induced in the
A bar magnet is initially far from a circular loop of wire. The magnet is moved at constant speed along the axis of the loop. It moves toward the loop, proceeds to pass through it, and then continues until it is far away on the right side of the loop. Sketch a qualitative graph of the current in
A bar magnet approaches a coil [part (a) of figure].(a) In which direction does current flow through the galvanometer as the magnet approaches?(b) In part (b) of the figure, the magnet is initially at rest inside the coil. It is then pulled out from the left side. In which direction does current
An ideal inductor of inductance L is connected to an ac power supply, which provides an emf ℰ(t) = ℰm sin w t. (a) Write an expression for the current in the inductor as a function of time. (b) What is the ratio of the maximum emf to the maximum current? This ratio is called the reactance. (c)
An airplane is flying due north at 180 m/s. Earth's magnetic field has a northward component of 0.30 mT and an upward component of 0.38 mT. (a) If the wingspan (distance between the wingtips) is 46 m, what is the motional emf between the wingtips? (b) Which wingtip is positively charged?
Repeat Problem 88 if the plane flies 30.0° west of south at 180 m/s instead. Repeat Problem An airplane is flying due north at 180 m/s. Earth's magnetic field has a northward component of 0.30 mT and an upward component of 0.38 mT. (a) If the wingspan (distance between the wingtips) is 46 m, what
In Fig. 20.6, side 3 of the rectangular coil in the electric generator rotates about the axis at constant angular speed w. The figure with this problem shows side 3 by itself.(a) First consider the right half of side 3. Although the speed of the wire differs depending on the distance from the axis,
The magnetic field between the poles of an electromagnet is 2.6 T. A coil of wire is placed in this region so that the field is parallel to the axis of the coil. The coil has electrical resistance 25 Ω, radius 1.8 cm, and length 12.0 cm. When the current supply to the electromagnet is shut off,
An ideal solenoid (N1 turns, length L1, radius r1) is placed inside another ideal solenoid (N2 turns, length L2 > L1, radius r2 > r1) such that the axes of the two coincide. (a) What is the mutual inductance? (b) If the current in the outer solenoid is changing at a rate ΔI2/Δt, what is the
Explain why there is a phase difference between the current in an ac circuit and the potential difference across a capacitor in the same circuit.
How does adjusting the tuning knob on a radio tune in different stations?
What happens if a 40-W light bulb, designed to be connected to an ac voltage with amplitude 170 V and frequency 60 Hz, is instead connected to a 170-V dc power supply? Explain. What dc voltage would make the light bulb burn with the same brightness as the 170 V peak 60-Hz ac?
How can the lights in a home be dimmed using a coil of wire and a soft iron core?
Explain what is meant by a phase difference. Sketch graphs of i (t) and v C (t), given that the current leads the voltage by π/2 radians
What does it mean if the power factor is 1? What does it mean if it is zero?
Suppose you buy a 120-W light bulb in Europe (where the rms voltage is 240 V). What happens if you bring it back to the United States (where the rms voltage is 120 V) and plug it in?
Let's examine the crossover network of Fig. 21.19 in the limiting cases of very low and very high frequencies.(a) How does the reactance of the capacitor and inductor compare for very low frequencies?(b) How do the rms currents through the tweeter and woofer compare for very low frequencies?(c)
Electric power is distributed long distances over transmission lines by using high ac voltages and therefore small ac currents. What is the advantage of using high voltages instead of safer low voltages?
Explain the differences between average current, rms current, and peak current in an ac circuit.
The United States and Canada use 120 V rms as the standard household voltage, while most of the rest of the world uses 240 V rms for the household standard. What are the advantages and disadvantages of the two systems?
Some electric appliances are able to operate equally well with either dc or ac voltage sources, but other appliances require one type of source or the other and cannot run on both. Explain and give a few examples of each type of appliance.
For an ideal inductor in an ac circuit, explain why the voltage across the inductor must be zero when the current is maximum.
For a capacitor in an ac circuit, explain why the current must be zero when the voltage across the capacitor is maximum.
An electric heater is plugged into an ac outlet. Since the ac current changes polarity, there is no net movement of electrons through the heating element; the electrons just tend to oscillate back and forth. How, then, does the heating element heat up? Don't we need to send electrons through the
An electric appliance is rated 120 V, 5A, 500 W. The first two are rms values; the third is the average power consumption. Why is the power not 600 W (= 120 V × 5 A)?
A solenoid with 8500 turns per meter has radius 65 cm. The current in the solenoid is 25.0 A. A circular loop of wire with 100 turns and radius 8.00 cm is put inside the solenoid. The current in the circular loop is 2.20 A. What is the maximum possible magnetic torque on the loop? What orientation
You are working as an electrical engineer designing transformers for transmitting power from a generating station producing 2.5 × 106 W to a city 120 km away. The power will be carried on two transmission lines to complete a circuit, each line constructed out of copper with a radius of 5.0 cm. (a)
An electromagnetic rail gun can fire a projectile using a magnetic field and an electric current. Consider two conducting rails that are 0.500 m apart with a 50.0-g conducting projectile that slides along the two rails. A magnetic field of 0.750 T is directed perpendicular to the plane of the rails
An air-filled parallel plate capacitor is used in a simple series RLC circuit along with a 0.650-H inductor. At a frequency of 220 Hz, the power output is found to be less than the maximum possible power output. After the space between the plates is filled with a dielectric with k = 5.50, the
(a) When the resistance of an RLC series circuit that is at resonance is doubled, what happens to the power dissipated? (b) Now consider an RLC series circuit that is not at resonance. For this circuit, the initial resistance and impedance are related by R = XC = XL/2. Determine how the power
An RLC circuit has a resistance of 10.0 Ω, an inductance of 15.0 mH, and a capacitance of 350 μ F. By what factor does the impedance of this circuit change when the frequency at which it is driven changes from 60 Hz to 120 Hz? Does the impedance increase or decrease?
An RLC circuit has a resistance of 255 Ω, an inductance of 146 mH, and a capacitance of 877 nF. (a) What is the resonant frequency of this circuit? (b) If this circuit is connected to a sinusoidal generator with a frequency 0.50 times the resonant frequency and a maximum voltage of 480 V, which
A variable inductor is connected to a voltage source whose frequency can vary. The rms current is Ii. If the inductance is increased by a factor of 3.0 and the frequency is reduced by a factor of 2.0, what will be the new rms current in the circuit? The resistance in the circuit is negligible.
Kieran measures the magnetic field of an electron beam. The beam strength is such that 1.40 × 1011 electrons pass a point every 1.30 μs. What magnetic field strength does Kieran measure at a distance of 2.00 cm from the beam center?
Two long, straight wires, each with a current of 5.0 A, are placed on two corners of an equilateral triangle with sides of length 3.2 cm as shown. One of the wires has a current into the page and one has a current out of the page.(a) What is the magnetic field at the third corner of the
A mass spectrometer (see the figure) is designed to measure the mass m of the 238U+ ion. A source of 238U+ ions (not shown) sends ions into the device with negligibly small initial kinetic energies. The ions pass between parallel accelerating plates and then through a velocity selector designed to
A hydroelectric power plant is situated at the base of a large dam. Water flows into the intake near the bottom of the reservoir at a depth of 100 m. The water flows through 10 turbine generators and exits the power plant 120 m below the top of the reservoir at a speed of about 10 m/s (at
Faraday flashlight uses electromagnetic induction to produce energy when shaken. A magnet in the handle is free to slide back and forth through a loop with 50 000 turns. The energy is stored in a 1.0-F capacitor, which can then be used to power a 0.50-W LED bulb. Suppose the area of the loop is 3.0
Consider an induction stove utilizing a primary heating coil located beneath the stove top. The coil is a solenoid with diameter 5.0 cm, length 1.0 cm, and 18 turns. The circuit elements in the stove supply the coil with a peak ac voltage of 340 V at a frequency of 50 kHz. The resistance of the
A toy race track has a 1.0-m-long straight section connected to a vertical circular loop-the-loop section of radius 15 cm. The straight section has a uniform magnetic field directed upward of magnitude 0.10 T and contains two metal strips with negligible resistance. The toy car has mass 40 g and
Two long, straight wires, each with a current of 12.0 A, are placed on two corners of an equilateral triangle with sides of length 2.50 cm as shown. Both of the wires have a current into the page.(a) What is the magnetic field at the third corner of the triangle?(b) Another wire is placed at the
A loop of wire is connected to a battery and a variable resistor as shown. Two other loops of wire, B and C, are placed inside the large loop and outside the large loop, respectively. As the resistance in the variable resistor is increased, are there currents induced in the loops B and C? If so, do
A cosmic ray muon with the same charge as an electron and a mass of 1.9 Ã— 10ˆ’28 kg is moving toward the ground at an angle of 25 ° from the vertical with a speed of 7.0 Ã— 107 m/s. As it crosses point P, the muon is at a horizontal distance of 85.0 cm from a
A variable capacitor is connected to an ac source. The rms current in the circuit is Ii. If the frequency of the source is reduced by a factor of 2.0 while the overlapping area of the capacitor plates is increased by a factor of 3.0, what will be the new rms current in the circuit? The resistance
Power lines carry electricity to your house at high voltage. This problem investigates the reason for that. Suppose a power plant produces 800 kW of power and wants to send that power for many miles over a copper wire with a total resistance of 12 Ω. (a) If the power is sent at a voltage of 120 V
A circular loop of wire is placed near a long current carrying wire. What happens while the loop is moved in each of the three directions? Does current flow? If so, is it CW or CCW? In what direction does a magnetic force act on the loop, if any?
A hair dryer has a power rating of 1200 W at 120 V rms. Assume the hair dryer circuit contains only resistance. (a) What is the resistance of the heating element? (b) What is the rms current drawn by the hair dryer? (c) What is the maximum instantaneous power that the resistance must withstand?
Show that over one complete cycle, the average value of a sine function squared is 1/2.
The diagram shows a simplified household circuit. Resistor R1 = 240.0 Î© represents a light bulb; resistor R2 = 12.0Î© represents a hair dryer. The resistors r = 0.50Î© (each) represent the resistance of the wiring in the walls. Assume that the generator supplies a
A variable capacitor with negligible resistance is connected to an ac voltage source. How does the current in the circuit change if the capacitance is increased by a factor of 3.0 and the driving frequency is increased by a factor of 2.0?
At what frequency is the reactance of a 6.0- μ F capacitor equal to 1.0 kΩ?
A 0.400-μ F capacitor is connected across the terminals of a variable frequency oscillator. (a) What is the frequency when the reactance is 6.63 kΩ? (b) Find the reactance for half of that same frequency
A 0.250- μ F capacitor is connected to a 220-V rms ac source at 50.0 Hz. (a) Find the reactance of the capacitor. (b) What is the rms current through the capacitor?
A capacitor is connected across the terminals of a 115-V rms, 60.0-Hz generator. For what capacitance is the rms current 2.3 mA?
Show, from XC = 1 / (w C ), that the units of capacitive reactance are ohms.
A parallel plate capacitor has two plates, each of area 3.0 × 10−4 m2, separated by 3.5 × 10−4 m. The space between the plates is filled with a dielectric. When the capacitor is connected to a source of 120 V rms at 8.0 kHz, an rms current of 1.5 × 10−4 A is measured. (a) What is the
A European outlet supplies 220 V (rms) at 50 Hz. How many times per second is the magnitude of the voltage equal to 220 V?
A capacitor (capacitance = C) is connected to an ac power supply with peak voltage V and angular frequency w. (a) During a quarter cycle when the capacitor goes from being uncharged to fully charged, what is the average current (in terms of C, V, and w)? (b) What is the rms current? (c) Explain
Three capacitors (2.0 μ F, 3.0 μ F, 6.0 μ F) are connected in series to an ac voltage source with amplitude 12.0 V and frequency 6.3 kHz. (a) What are the peak voltages across each capacitor? (b) What is the peak current that flows in the circuit?
A capacitor and a resistor are connected in parallel across an ac source. The reactance of the capacitor is equal to the resistance of the resistor. Assuming that iC(t) = I sin w t, sketch graphs of iC(t) and iR(t) on the same axes.
A variable inductor with negligible resistance is connected to an ac voltage source. How does the current in the inductor change if the inductance is increased by a factor of 3.0 and the driving frequency is increased by a factor of 2.0?
At what frequency is the reactance of a 20.0-mH inductor equal to 18.8 Ω?
What is the reactance of an air core solenoid of length 8.0 cm, radius 1.0 cm, and 240 turns at a frequency of 15.0 kHz?
A solenoid with a radius of 8.0×10−3 m and 200 turns / cm is used as an inductor in a circuit. When the solenoid is connected to a source of 15 V rms at 22 kHz, an rms current of 3.5 × 10−2 A is measured. Assume the resistance of the solenoid is negligible. (a) What is the inductive
A 4.00-mH inductor is connected to an ac voltage source of 151.0 V rms. If the rms current in the circuit is 0.820 A, what is the frequency of the source?
Two ideal inductors (0.10 H, 0.50 H) are connected in series to an ac voltage source with amplitude 5.0 V and frequency 126 Hz. (a) What are the peak voltages across each inductor? (b) What is the peak current that flows in the circuit?
Suppose that current flows to the left through the inductor in Fig. 21.6a so that i is negative.(a) If the current is increasing in magnitude, what is the sign of Î”i /Î”t?(b) In what direction is the induced emf that opposes the increase in current?(c) Show that Eq. (21-8)
A 1500-W heater runs on 120 V rms. What is the peak current through the heater?
Suppose that an ideal capacitor and an ideal inductor are connected in series in an ac circuit. (a) What is the phase difference between vC(t) and vL (t)? (b) If the rms voltages across the capacitor and inductor are 5.0 V and 1.0 V, respectively, what would an ac voltmeter (which reads rms
The voltage across an inductor and the current through the inductor are related by vL = L Δ i /Δ t. Suppose that i (t) = I sin w t. (a) Write an expression for vL (t) (b) From your expression for vL (t), show that the reactance of the inductor is XL = wL. (c) Sketch graphs of i (t) and vL (t)
Make a figure analogous to Fig. 21.4 for an ideal inductor in an ac circuit. Start by assuming that the voltage across an ideal inductor is vL (t) = VL sin w t. Make a graph showing one cycle of vL (t) and i (t) on the same axes. Then, at each of the times t = 0, 1/8 T, 2/8 T, . . . ,T, indicate
A 25.0-mH inductor, with internal resistance of 25.0 Ω, is connected to a 110-V rms source. If the average power dissipated in the circuit is 50.0 W, what is the frequency? (Model the inductor as an ideal inductor in series with a resistor.)
An inductor has an impedance of 30.0 Ω and a resistance of 20.0 Ω at a frequency of 50.0 Hz. What is the inductance? (Model the inductor as an ideal inductor in series with a resistor.)
A 6.20-mH inductor is one of the elements in a simple RLC series circuit. When this circuit is connected to a 1.60-kHz sinusoidal source with an rms voltage of 960.0 V, an rms current of 2.50 A lags behind the voltage by 52.0°. (a) What is the impedance of this circuit? (b) What is the resistance
A series combination of a resistor and a capacitor are connected to a 110-V rms, 60.0-Hz ac source. If the capacitance is 0.80 μ F and the rms current in the circuit is 28.4 mA, what is the resistance?
A 300.0-Ω resistor and a 2.5- μ F capacitor are connected in series across the terminals of a sinusoidal emf with a frequency of 159 Hz. The inductance of the circuit is negligible. What is the impedance of the circuit?
A series RLC circuit has a 0.20-mF capacitor, a 13-mH inductor, and a 10.0-Ω resistor, and is connected to an ac source with amplitude 9.0 V and frequency 60 Hz. (a) Calculate the voltage amplitudes VL, VC, VR, and the phase angle. (b) Draw the phasor diagram for the voltages of this circuit.
(a) Find the power factor for the RLC series circuit of Example 21.4. (b) What is the average power delivered to each element (R, L, C)?
A circuit breaker trips when the rms current exceeds 20.0 A. How many 100.0-W light bulbs can run on this circuit without tripping the breaker? (The voltage is 120 V rms.)
A computer draws an rms current of 2.80 A at an rms voltage of 120V. The average power consumption is 240 W. (a) What is the power factor? (b) What is the phase difference between the voltage and current?
An RLC series circuit is connected to an ac power supply with a 12-V amplitude and a frequency of 2.5 kHz. If R = 220 Ω, C = 8.0 μ F, and L = 0.15 mH, what is the average power dissipated?
An ac circuit has a single resistor, capacitor, and inductor in series. The circuit uses 100 W of power and draws a maximum rms current of 2.0 A when operating at 60 Hz and 120 V rms. The capacitive reactance is 0.50 times the inductive reactance. (a) Find the phase angle. (b) Find the values of
Suppose that two sinusoidal voltages at the same frequency are added:V1 sin wt + V2 sin (wt + 0Ï•2) = V sin (wt + Ï•)A phasor representation is shown in the diagram.(a) Substitute t = 0 into the equation. Interpret the result by referring to the phasor diagram.(b) Substitute t =
An ac circuit contains a 12.5-Ω resistor, a 5.00- μ F capacitor, and a 3.60-mH inductor connected in series to an ac generator with an output voltage of 50.0 V (peak) and frequency of 1.59 kHz. Find the impedance, the power factor, and the phase difference between the source voltage and current
A 0.48- μ F capacitor is connected in series to a 5.00-kΩ resistor and an ac source of voltage amplitude 2.0 V. (a) At f = 120 Hz, what are the voltage amplitudes across the capacitor and across the resistor? (b) Do the voltage amplitudes add to give the amplitude of the source voltage (i.e.,
A series combination of a 22.0-mH inductor and a 145.0-Ω resistor are connected across the output terminals of an ac generator with peak voltage 1.20 kV. (a) At f = 1250 Hz, what are the voltage amplitudes across the inductor and across the resistor? (b) Do the voltage amplitudes add to give the
A 3.3-kΩ resistor is in series with a 2.0- μ F capacitor in an ac circuit. The rms voltages across the two are the same. (a) What is the frequency? (b) Would each of the rms voltages be half of the rms voltage of the source? If not, what fraction of the source voltage are they? (In other words,
A series circuit with a resistor and a capacitor has a time constant of 0.25 ms. The circuit has an impedance of 350 Ω at a frequency of 1250 Hz. What are the capacitance and the resistance?
A 1500-W electric hair dryer is designed to work in the United States, where the ac voltage is 120 V rms. What power is dissipated in the hair dryer when it is plugged into a 240-V rms socket in Europe? What may happen to the hair dryer in this case?
(a) What is the reactance of a 10.0-mH inductor at the frequency f = 250.0 Hz? (b) What is the impedance of a series combination of the 10.0-mH inductor and a 10.0-Ω resistor at 250.0 Hz? (c) What is the maximum current through the same circuit when the ac voltage source has a peak value of 1.00
The FM radio band is broadcast between 88 MHz and 108 MHz. What range of capacitors must be used to tune in these signals if an inductor of 3.00 μ H is used?
An RLC series circuit is built with a variable capacitor. How does the resonant frequency of the circuit change when the area of the capacitor is increased by a factor of 2?
In an RLC series circuit, these three elements are connected in series: a resistor of 60.0 Ω, a 40.0-mH inductor, and a 0.0500-F capacitor. The series elements are connected across the terminals of an ac oscillator with an rms voltage of 10.0 V. Find the resonant frequency for the circuit.
An RLC series circuit is driven by a sinusoidal emf at the circuit's resonant frequency. (a) What is the phase difference between the voltages across the capacitor and inductor? (b) At resonance, the rms current in the circuit is 120 mA. The resistance in the circuit is 20 Ω. What is the rms value
An RLC series circuit has a resistance of R = 325 Ω, an inductance L = 0.300 mH, and a capacitance C = 33.0 nF. (a) What is the resonant frequency? (b) If the capacitor breaks down for peak voltages in excess of 7.0 × 102V, what is the maximum source voltage amplitude when the circuit is operated
An RLC series circuit has L = 0.300 H and C = 6.00 μ F. The source has a peak voltage of 440 V. (a) What is the angular resonant frequency? (b) When the source is set at the resonant frequency, the peak current in the circuit is 0.560 A. What is the resistance in the circuit? (c) What are the peak
Finola has a circuit with a 4.00-kΩ resistor, a 0.750-H inductor, and a capacitor of unknown value connected in series to a 440.0-Hz ac source. With an oscilloscope, she measures the phase angle to be 25.0°. (a) What is the value of the unknown capacitor? (b) Finola has several capacitors on
Repeat Problem 38 for an operating frequency of 98.7 Hz. (a) What is the phase angle for this circuit? (b) Draw the phasor diagram. (c) What is the resonant frequency for this circuit?
A 4.0-kW heater is designed to be connected to a 120-V rms source. What is the power dissipated by the heater if it is instead connected to a 120-V dc source?
An RC filter is shown. The filter resistance R is variable between 180 Ω and 2200 Ω and the filter capacitance is C = 0.086 μ F. At what frequency is the output amplitude equal to 1/ √2 times the input amplitude if R = (a) 180 Ω? (b) 2200 Ω? (c) Is this a low-pass or high-pass filter?

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