An AC source is connected to a series combination of a

Problem 1CQ Identical resistors are connected to separate 12 V AC sources. One source operates at 60 Hz, the other at 120 Hz. In which circuit, if either, does the resistor dissipate the greater average power?

Problem 1P A 200 ? resistor is connected to an AC source with . What is the peak current through the resistor if the emf frequency is (a) 100 Hz? (b) 100 kHz?

Problem 2CQ Consider the three circuits in Figure Q26.2. Rank in order, from largest to smallest, the average total powers dissipated by all the resistors in each circuit. Explain.

Problem 2P Figure P26.2 shows voltage and current graphs for a resistor. a. What is the value of the resistance R? b. What is the emf frequency f ?

Problem 3CQ Lightbulbs in AC circuits “flicker” in intensity, though the flickering is too fast for your eyes to sense it. If a light bulb is connected to a 120 V/60 Hz power supply, how many times a second does the bulb reach peak brightness

Problem 3P A resistor dissipates 2.00 W when the rms voltage of the emf is 10.0 V. At what rms voltage will the resistor dissipate 10.0 W?

Problem 4CQ A household wall outlet can provide no more than 15 A, but you can use this outlet to power an electric soldering iron that drives 150 A through the metal tip. How is this possible?

Problem 4P The heating element of a hair dryer dissipates 1500 W when connected to a 120 V outlet. What is the resistance?

Problem 5CQ A 12 V DC power supply is connected to the primary coil of a transformer. The primary coil has 100 turns and the secondary coil has 200. What is the rms voltage across the secondary?

Problem 5P A toaster oven is rated at 1600 W for operation at 120 V, 60 Hz. a. What is the resistance of the oven heater element? b. What is the peak current through it? c. What is the peak power dissipated by the oven?

Problem 6CQ Figure Q26.7 shows three wires wrapped around an iron core. The figure shows the number of turns and the direction of each of the windings. At one

Problem 6P A 100 ? resistor is connected to a 120 V/60 Hz power line. What is its average power loss?

Problem 7CQ Women usually have higher resistance of their arms and legs than men. Why might you expect to see this variation in resistance?

Problem 7P A generator produces 40 MW of power and sends it to town at an rms voltage of 75 kV. What is the rms current in the transmission lines?

Problem 8CQ A circuit breaker won’t keep you from getting a shock; a GFI will. Explain why this is so.

Problem 8P Soles of boots that are designed to protect workers from electric shock are rated to pass a maximum rms current of 1.0 mA when connected across an 18,000 V AC source. What is the minimum allowed resistance of the sole?

Problem 9CQ Your cell phone charger plugs into an AC electric outlet. A typical charger has a two-prong plug. Either prong can go in the hot side of the outlet; that is, you can reverse the plug and the charger still works. Your cell phone runs on DC current from a battery. If you reverse the battery, the phone won’t operate. Explain why you can reverse the polarity of an AC source like an electric outlet, but not a DC source like a battery.

Problem 9P The primary coil of a transformer is connected to a 120 V wall outlet. The secondary coil is connected to a lamp that dissipates 60 W. What is the rms current in the primary coil?

Problem 10CQ New homes are required to have GFI-protected outlets in bathrooms, kitchens, and any outdoor locations. Why is GFI protection required in these locations but not, say, in bedrooms?

Problem 10P A soldering iron uses an electric current in a wire to heat the tip. A transformer with 100 turns on the secondary coil provides 50 W at an rms voltage of 24 V. a. What is the resistance of the wire in the iron? b. How many turns are in the primary coil? c. What is the current in the primary coil?

Problem 11CQ Your computer has a built-in “surge protector.” A surge is a sudden increase in voltage on the power line. This causes a rapid “current spike” that can destroy sensitive electronic components. After the AC electricity is converted to DC in your computer’s power supply, the current going to the computer processor must pass through a coil of wire wrapped around an iron core. Explain how this coil works as a surge suppressor.

Problem 11P A power pack charging a cell phone battery has an output of 0.40 A at 5.2 V (both rms). What is the rms current at the 120 V wall outlet where the power pack is plugged in?

Problem 12CQ The peak current through a resistor is 2.0 A. What is the peak current if a. The resistance R is doubled? b. The peak emf is doubled? c. The frequency f is doubled?

Problem 12P A neon sign transformer has a 450 W AC output with an rms voltage of 15 kV when connected to a normal household outlet. There are 500 turns of wire in the primary coil. a. How many turns of wire does the secondary coil have? b. When the transformer is running at full power, what is the current in the secondary coil? The current in the primary coil?

Problem 13CQ The average power dissipated by a resistor is 4.0 W. What is the average power if a. The resistance R is doubled? b. The peak emf ?0 is doubled? c. Both are doubled simultaneously?

Problem 13P The “power cube” transformer for a portable CD player has an output of 4.5 V and 600 mA (both rms) when plugged into a 120 V outlet. a. If the primary coil has 400 turns of wire, how many turns are on the secondary coil? b. What is the peak current in the primary coil?

Problem 14CQ The peak current through a capacitor is 2.0 A. What is the peak current if a. The peak emf is doubled? b. The capacitance C is doubled? c. The frequency f is doubled?

Problem 14P A science hobbyist has purchased a surplus power-pole transformer that converts 7.2 kV from neighborhood distribution lines into 120 V for homes. He connects the transformer “backward,” plugging the secondary coil into a 120 V outlet. What rms voltage is induced at the primary?

Problem 15CQ Consider the four circuits in Figure Q26.14. Rank in order, from largest to smallest, the capacitive reactances . Explain.

Problem 15P A typical American family uses 1000 kWh of electricity a month. a. What is the average rms current in the 120 V power line to the house? b. On average, what is the resistance of a household?

Problem 16CQ An inductor is plugged into a 120 V, 60 Hz wall outlet in the U.S. Would the peak current be larger, smaller, or unchanged if this inductor were plugged into a wall outlet in a country where the voltage is 120 V at 50 Hz? Explain.

Problem 16P The wiring in the wall of your house to and from an outlet has a total resistance of typically 0.10 ?. Suppose a device plugged into a 120 V outlet draws 10.0 A of current. a. What is the voltage drop along the wire? b. How much power is dissipated in the wire? c. What is the voltage drop across the device? d. At what rate does the device use electric energy?

Problem 17CQ Figure Q26.17 shows two inductors and the potential difference across them at time t = 0 s. a. Can you tell which of these inductors has the larger current flowing through it at t = 0 s? If so, which one? If not, why not? b. Can you tell through which inductor the current is changing more rapidly at t = 0 s? If so, which one? If not, why not?

Problem 17P The following appliances are connected to a single 120 V, 15 A circuit in a kitchen: a 330 W blender, a 1000 W coffeepot, a 150 W coffee grinder, and a 750 W microwave oven. If these are all turned on at the same time, will they trip the circuit breaker?

Problem 18CQ The peak current passing through an inductor is 2.0 A. What is the peak current if a. The peak emf is doubled? b. The inductance L is doubled? c. The frequency f is doubled?

Problem 18P A 60 W (120 V) night light is turned on for an average of 12 h a day year round. What is the annual cost of electricity at a billing rate of $0.10/kWh?

Problem 19CQ Consider the four circuits in Figure Q26.19. Rank in order, from largest to smallest, the inductive reactances . Explain.

Problem 19P Suppose you leave a 110 W television and two 100 W lightbulbs on in your house to scare off burglars while you go out dancing. If the cost of electric energy in your town is $0.12/kWh and you stay out for 4.0 h, how much does this robbery prevention measure cost?

Problem 20CQ The tuning circuit in a radio uses an RLC circuit. Will adjusting the resistance have any effect on the resonance frequency?

Problem 20P The manufacturer of an electric table saw claims that it has a 3.0 hp motor. It is designed to be used on a normal 120 V outlet with a 15 A circuit breaker. Is this claim reasonable? Explain.

Problem 21CQ The resonance frequency of a driven 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 is doubled? e. The emf frequency f is doubled?

Problem 21P If you touch the terminal of a battery, the small area of contact means that the skin resistance will be relatively large; 50 k? is a reasonable value. What current will pass through your body if you touch the two terminals of a 9.0 V battery with your two hands? Will you feel it? Will it be dangerous?

Problem 22CQ Consider the four circuits in Figure Q26.22. They all have the same resonance frequency . Explain.

Problem 22P A person standing barefoot on the ground 20 m from the point of a lightning strike experiences an instantaneous potential difference of 300 V between his feet. If we assume a skin resistance of 1.0 k?, how much current goes up one leg and back down the other?

Problem 23MCQ A transformer has 1000 turns in the primary coil and 100 turns in the secondary coil. If the primary coil is connected to a 120 V outlet and draws 0.050 A, what are the voltage and current of the secondary coil? A. 1200 V, 0.0050 A B. 1200 V, 0.50 A C. 12 V, 0.0050 A D. 12 V, 0.50 A

Problem 23P Electrodes used to make electrical measurements of the body (such as those used when recording an electrocardiogram) use a conductive paste to reduce the skin resistance to very low values. If you have such an electrode on one wrist and one ankle, what are the lowest AC and DC voltages that will give you a perceptible shock? A potentially fatal shock?

Problem 24MCQ An inductor is connected to an AC generator. As the generator’s frequency is increased, the current in the inductor A. Increases. B. Decreases. C. Does not change.

Problem 24P A fisherman has netted a torpedo ray. As he picks it up, this electric fish creates a short-duration 50 V potential difference between his hands. His hands are wet with salt water, and so his skin resistance is a very low 100 ?. What current passes through his body? Will he feel this DC pulse?

Problem 25MCQ A capacitor is connected to an AC generator. As the generator’s frequency is increased, the current in the capacitor A. Increases. B. Decreases. C. Does not change.

Problem 25P Problem concern a high-voltage transmission line. Such lines are made of bare wire; they are not insulated. Assume that the wire is 100 km long, has a resistance of 7.0 ?, and carries 200 A. A bird is perched on the wire with its feet 2.0 cm apart. What is the potential difference between its feet?

Problem 26MCQ An AC source is connected to a series combination of a lightbulb and a variable inductor. If the inductance is increased, the bulb’s brightness A. Increases. B. Decreases. C. Does not change.

Problem 26P Problem concern a high-voltage transmission line. Such lines are made of bare wire; they are not insulated. Assume that the wire is 100 km long, has a resistance of 7.0 ?, and carries 200 A. Would it be possible for a person to safely hang from this wire? Assume that the hands are 15 cm apart, and assume a skin resistance of 2200 ?.

Problem 27MCQ An AC source is connected to a series combination of a lightbulb and a variable capacitor. If the capacitance is increased, the bulb’s brightness A. Increases. B. Decreases. C. Does not change.

Problem 27P A 0.30 ?F capacitor is connected across an AC generator that produces a peak voltage of 10.0 V. What is the peak current through the capacitor if the emf frequency is (a) 100 Hz? (b) 100 kHz?

Problem 28MCQ The circuit shown in Figure Q26.28 has a resonance frequency of 15 kHz. What is the value of L? A. 1.6 ?H B. 2.4 ?H C. 5.2 ?H D. 18 ?H E. 59 ?H

Problem 28P A 20 ?F capacitor is connected across an AC generator that produces a peak voltage of 6.0 V. The peak current is 0.20 A. What is the oscillation frequency in Hz?

Problem 29P The peak current through a capacitor is 10.0 mA. What is the current if a. The emf frequency is doubled? b. The emf peak voltage is doubled (at the original frequency)? c. The frequency is halved and, at the same time, the emf is doubled?

Problem 30P 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 ?

Problem 31P A capacitor is connected to a 15 kHz oscillator that produces an rms voltage of 6.0 V. The peak current is 65 mA. What is the value of the capacitance C?

Problem 32P The peak current through a capacitor is 8.0 mA when connected to an AC source with a peak voltage of 1.0 V. What is the capacitive reactance of the capacitor?

Problem 33P What is the potential difference across a 10 mH inductor if the current through the inductor drops from 150 mA to 50 mA in 10 ?s?

Problem 34P A 20 mH inductor is connected across an AC generator that produces a peak voltage of 10.0 V. What is the peak current through the inductor if the emf frequency is (a) 100 Hz? (b) 100 kHz?

Problem 35P The peak current through an inductor is 10.0 mA. What is the current if a. The emf frequency is doubled? b. The emf peak voltage is doubled (at the original frequency)? c. The frequency is halved and, at the same time, the emf is doubled?

Problem 36P A 500 mH inductor 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 ?

Problem 37P An inductor is connected to a 15 kHz oscillator that produces an rms voltage of 6.0 V. The peak current is 65 mA. What is the value of the inductance L?

Problem 38P The peak current through an inductor is 12.5 mA when connected to an AC source with a peak voltage of 1.0 V. What is the inductive reactance of the inductor?

Problem 39P The superconducting magnet in a magnetic resonance imaging system consists of a solenoid with 5.6 H of inductance. The solenoid is energized by connecting it to a 1.2 V DC power supply. Starting from zero, how long does it take for the solenoid to reach its operating current of 100 A?

Problem 40P In a nuclear magnetic resonance spectrometer, a 15 mH coil is designed to detect an emf oscillating at 400 MHz. The coil is part of an RLC circuit. What value of the capacitance C should be used so that the coil circuit resonates at 400 MHz?

Problem 41P A 2.0 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF. What is the range of oscillation frequencies for this circuit?

Problem 42P An FM radio station broadcasts at a frequency of 100 MHz. What inductance should be paired with a 10 pF capacitor to build a receiver circuit for this station?

Problem 43P The inductor in the RLC tuning circuit of an AM radio has a value of 350 mH. What should be the value of the variable capacitor in the circuit to tune the radio to 740 kHz?

Problem 44P At what frequency f do a 1.0 ?F capacitor and a 1.0 ?H inductor have the same reactance? What is the value of the reactance at this frequency?

Problem 45P Two RLC circuits have identical capacitors but different inductors. Circuit 1 has a resonance frequencf0 while circuit 2 has a resonance at 2f0. What is the ratio L2/L1of the inductance in circuit 2 to die inductance in circuit 1?

Problem 46P What capacitor in series with a 100 ? resistor and a 20 mH inductor will give a resonance frequency of 1000 Hz?

Problem 47P What inductor in series with a 100 ? resistor and a 2.5 ?F capacitor will give a resonance frequency of 1000 Hz?

Problem 48P A series RLC circuit has a 200 kHz resonance frequency. What is the resonance frequency if a. The resistor value is doubled? b. The capacitor value is doubled?

Problem 49P A series RLC circuit has a 200 kHz resonance frequency. What is the resonance frequency if a. The resistor value is doubled? b. The capacitor value is doubled and, at the same time, the inductor value is halved?

Problem 50P An RLC circuit with a 10 ?F capacitor is connected to a variable-frequency power supply with an rms output voltage of 6.0 V. The rms current in the circuit as a function of the driving frequency appears as in Figure P26.51. What are the values of the resistor and the inductor?

Problem 51P A series RLC circuit consists of a 280 ? resistor, a 25 ?H inductor, and an 18 ?F capacitor. What is the rms current if the emf is supplied by a standard 120 V, 60 Hz wall outlet?

Problem 52GP A step-down transformer converts 120 V to 24 V, which is connected to a load of resistance 8.0 ?. What is the resistance “seen” by the power supply connected to the primary coil of the transformer? Hint: Resistance is defined as the ratio of two circuit quantities.

Problem 53GP A 15-km-long, 230 kV aluminum transmission line delivers 34 MW to a city. If we assume a solid cylindrical cable, what minimum diameter is needed if the voltage decrease along this run is to be no more than 1.0% of the transmission voltage? The resistivity of aluminum is .

Problem 54GP The outer membranes of cells are quite irregular at the submicron level, so the surface area of an apparently spherical cell differs from the value one would calculate from geometry. To determine the actual surface area of a cell membrane, electrophysiologists use intracellular electrodes to measure the membrane’s capacitive reactance. They take advantage of the fact that the capacitance per unit area of all biological membranes is about 1.0 µF/cm2. a. What is the surface area of a 20-µm-diameter sphere? Give your answer in square centimeters. b. The capacitive reactance of the outer membrane of a cell is measured to be 6.4 × 106 ? at 1.0 kHz. What is the surface area of the membrane, in cm2? By what factor is the area greater than your answer to part a? An important biological process is the release of neurotransmitters that are involved in chemical communication between nerve cells and muscles. This release occurs when intracellular vesicles containing the neurotransmitter chemical fuse with the outer cell membrane and release their contents. The vesicle’s membrane becomes part of the cell’s outer membrane, increasing the latter’s area. As a result, the fusion of vesicles with the outer membrane can be detected by monitoring the outer membrane’s capacitive reactance. Indeed, the fusion of a single vesicle can be resolved. c. What is the percentage increase in the capacitive reactance of the cell considered in part b when a single vesicle’s membrane, a smooth sphere 0.10 µm in diameter, fuses with the outer membrane of the cell?

Problem 55GP The voltage across a 60 ?F capacitor is described by the equation , where t is in seconds. a. What is the voltage across the capacitor at t = 0.010 s? b. What is the capacitive reactance? c. What is the peak current?

Problem 56GP The voltage across a 75 ?H inductor is described by the equation , where t is in seconds. a. What is the voltage across the inductor at t = 0.10 s? b. What is the inductive reactance? c. What is the peak current?

Problem 57GP An LC circuit is built with a 20 mH inductor and an 8.0 µF capacitor. The current has its maximum value of 0.50 A at t = 0 s. How long does it take until the capacitor is fully charged?

Problem 58GP An electronics hobbyist is building a radio set to receive the AM band, with frequencies from 520 to 1700 kHz. What range variable capacitor will she need to go with a 230 µH inductor?

Problem 59GP Problem For the circuit of Figure P26.59, a. What is the resonance frequency? b. At resonance, what is the peak current through the circuit?

Problem 60GP For the circuit of Figure P26.60, a. What is the resonance frequency? b. At resonance, what is the peak current through the circuit?

Problem 61GP An RLC circuit consists of a 48 ? resistor, a 200 µF capacitor, and an inductor. The current is 2.5 A rms when the circuit is connected to a 120 V/60 Hz. outlet. a. What is the inductance? b. What would be the current if this circuit were used in France, where the outlets are 220 V/50 Hz?

Problem 62PP Halogen Bulbs Halogen bulbs have some differences from standard incandescent lightbulbs. They are generally smaller, the filament runs at a higher temperature, and they have a quartz (rather than glass) envelope. They may also operate at lower voltage. Consider a 12 V, 50 W halogen bulb for use in a desk lamp. The lamp plugs into a 120 V, 60 Hz outlet, and it has a transformer in its base. The 12 V rating of the bulb refers to the rms voltage. What is the peak voltage across the bulb? A. 8.5 V B. 12 V C. 17 V D. 24 V

Problem 64PP Halogen Bulbs Halogen bulbs have some differences from standard incandescent lightbulbs. They are generally smaller, the filament runs at a higher temperature, and they have a quartz (rather than glass) envelope. They may also operate at lower voltage. Consider a 12 V, 50 W halogen bulb for use in a desk lamp. The lamp plugs into a 120 V, 60 Hz outlet, and it has a transformer in its base. How much current is drawn by the lamp at the outlet? That is, what is the rms current in the primary? A. 0.42 A B. 1.3 A C. 4.2 A D. 13 A

Problem 65PP Halogen Bulbs Halogen bulbs have some differences from standard incandescent lightbulbs. They are generally sm6aller, the filament runs at a higher temperature, and they have a quartz (rather than glass) envelope. They may also operate at lower voltage. Consider a 12 V, 50 W halogen bulb for use in a desk lamp. The lamp plugs into a 120 V, 60 Hz outlet, and it has a transformer in its base. What will be the voltage across the bulb if the lamp’s power cord is accidentally plugged into a 240 V, 60 Hz outlet? A. 2 V B. 24 V C. 36 V D. 48 V