Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 31, Problem 45AP
To determine
To draw: A graph of the emf across the inductor as a function of time.
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A resistor of resistance R = 10 Ω is connected in series with an inductor of L = 15 mH. The RL combination is connected to a variable voltage power supply (V = 4.5 V) by a switch as shown.
a. What is the time constant (τ) of the combination in seconds?
b. The power supply is set to maintain a constant voltage of V = 4.5 V and the switch is closed. Calculate the current, in amperes, through the circuit at t = 0.29 ms after the switch is closed.
c. Calculate the current through the circuit, in amperes, after the switch has been closed for a long time.
A resistor and inductor are connected to a 9.0 V battery by a switch as shown. The moment the switch is closed, current flows through the circuit. The resistor has a resistance of R = 440 Ω and the inductor has an inductance of L = 150 mH.
a) write an equation that relates the current as a function of time i(t) to the maximum current, imax. Express the equation in terms of imax and α, where α = -t/T (time constant).
b) determine the time, in seconds, at which the current has a value of i(t50) = 50% of imax.
c) determine the time, in seconds, at which the current has a value of i(t99) = 99% of imax.
W
R₂
a
a. What is the potential drop on the inductor?
R₁
m
Two resistors, R₁ = 125 § and R2 = 325 92, an inductor L = 3.7 mH, a 16 V battery, and a switch are connected as shown above. The switch has been in position a for a long time.
What is the current through resistor R₁?
What is the current through resistor R₂?
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L
b. At time t = 0s the switch is moved to position b. What is the time constant of the RL circuit obtained?
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c. Find the current in this RL circuit when the time t is three-quarters of the time constant from part b.
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d. At what time has the current decayed to 0.75% of its initial value?
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Chapter 31 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 31.1 - A coil with zero resistance has its ends labeled a...Ch. 31.2 - Prob. 31.2QQCh. 31.3 - Prob. 31.3QQCh. 31.4 - Prob. 31.4QQCh. 31.5 - (i) At an instant of time during the oscillations...Ch. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4PCh. 31 - Prob. 5P
Ch. 31 - A toroid has a major radius R and a minor radius r...Ch. 31 - Prob. 7PCh. 31 - Prob. 8PCh. 31 - Prob. 9PCh. 31 - Prob. 10PCh. 31 - Prob. 11PCh. 31 - Prob. 12PCh. 31 - Prob. 13PCh. 31 - You are working as a demonstration assistant for a...Ch. 31 - Prob. 15PCh. 31 - Prob. 16PCh. 31 - Prob. 17PCh. 31 - Prob. 18PCh. 31 - Prob. 19PCh. 31 - Prob. 20PCh. 31 - Prob. 21PCh. 31 - Prob. 22PCh. 31 - Prob. 23PCh. 31 - Prob. 24PCh. 31 - Prob. 25PCh. 31 - Prob. 26PCh. 31 - Prob. 27PCh. 31 - Prob. 28PCh. 31 - In the circuit of Figure P31.29, the battery emf...Ch. 31 - Prob. 30PCh. 31 - Prob. 31PCh. 31 - Prob. 32PCh. 31 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 31 - Prob. 34PCh. 31 - Electrical oscillations are initiated in a series...Ch. 31 - Prob. 36APCh. 31 - A capacitor in a series LC circuit has an initial...Ch. 31 - Prob. 38APCh. 31 - Prob. 39APCh. 31 - At the moment t = 0, a 24.0-V battery is connected...Ch. 31 - Prob. 41APCh. 31 - Prob. 42APCh. 31 - Prob. 43APCh. 31 - Prob. 44APCh. 31 - Prob. 45APCh. 31 - At t = 0, the open switch in Figure P31.46 is...Ch. 31 - Prob. 47APCh. 31 - Prob. 48APCh. 31 - Prob. 49APCh. 31 - Prob. 50CPCh. 31 - Prob. 51CPCh. 31 - Prob. 52CPCh. 31 - Prob. 53CP
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- When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P23.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin t represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is Emax=0nAImax. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P23.8arrow_forwardEach of the three situations in Figure P32.68 shows a resistor in a circuit in which currents are induced. Using Lenzs law, determine whether the current in each situation is from a to b or from b to a. a. If the current I in the wire in Figure P32.68A is increased from zero to I, what is the direction of the current induced across the resistor R? b. The switch in Figure P32.68B is initially closed and is thrown open at t = 0. What is the direction of the current induced across the resistor R immediately afterward? c. A bar magnet is brought close to the circuit shown in Figure P32.68C. What is the direction of the current induced across the resistor R?arrow_forwardYour RL circuit has a characteristic time constant of 21.5 ns, and a resistance of 5.40 MΩ. A. What is the inductance (in H) of the circuit? B. What resistance (in MΩ) should you use (instead of the 5.40 MΩ resistor) to obtain a 1.00 ns time constant, perhaps needed for quick response in an oscilloscope?arrow_forward
- Two inductors are placed in a circuit in series with each other. Inductor 1 has an inductance of 3.5e-3 H and inductor 2 has an inductance of 4.7e-6 H. Anytime current is running through the inductors, what is the ratio of energy stored in inductor 1 compared to inductor 2? U1 is the energy in inductor 1 and U2 is the energy in inductor 2. U1 = 25.36 U2 U1 = 1.55e-3 U2 U1 = 744.68 U2 U1 = 3.93e-2 U2arrow_forwardI 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 2A 0.01 s 0.02s Current FIGURE EX32.24arrow_forwardAn LC circuit has a 7.00 mH inductor. The current has its maximum value of 0.580 A at t = 0s. A short time later the capacitor reaches its maximum potential difference of 70.0 V Part A What is the value of the capacitance? Vp ΑΣφ. ? µFarrow_forward
- The current I flowing rightward through inductor L is at a steady rate of 0.1280 A/s. The magnitude I εL I of the difference between the right end and the left end of the inductor is 0.0160 (V). What is the inductance L? Which end of the inductor above is at higher voltage, the left end or the right end? Explain.arrow_forwardAn RLC circuit consists of a 1.34 2 resistor, a 8.44 nF capacitor, and a 5.55 mH inductor. Initially, the voltage across the capacitor is 1.46 V, and no current is flowing in the circuit. How many oscillations occur as the charge amplitude on the capacitor decays to 67.4% of its initial value? It is acceptable to let w' = w. i oscillations (include decimals if needed to keep the appropriate number of significant digits in your answer)arrow_forwardAn inductor in the form of a solenoid contains 410 turns and is 15.0 cm in length. A uniform rate of decrease of current through the inductor of 0.421 A/s induces an emf of 175 µV. What is the radius of the solenoid? mmarrow_forward
- In the circuit of Figure P31.29, the battery emf is 50.0 V, the resistance is 250 V, and the capacitance is 0.500 ?F. The switch S is closed for a long time interval, and zero potential difference is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance?arrow_forwarda 12.0 V ideal battery, a 20.0 resistor, and an inductor are connected by a switch at time t = 0. At what rate is the battery transferring energy to the inductor’s field at t = 1.61tL?arrow_forwardThe current flowing through a circuit is changing at a rate of 6.00 A/s. If the circuit contains a 190.0 H inductor, what is the emf across the inductor?arrow_forward
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