Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 32, Problem 19P
(a)
To determine
The value of
(b)
To determine
The current in the inductor at the instant the switch is thrown to position b.
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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.
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?
An LR circuit is hooked up to a battery which the switch initially open. The resistance in the circuit is R = 110 Ohm, the inductance is L=4.80H, and battery maintains a voltage of E=47.0V. At time t=0 the switch is closed. What is the current through the circuit after the switch has been closed for t=2.66 times 10-2s? What is the voltage across the inductor after the switch has been closed for t=2.66 times 10-2 seconds?
Chapter 32 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 32.1 - A coil with zero resistance has its ends labeled a...Ch. 32.2 - Prob. 32.2QQCh. 32.3 - Prob. 32.3QQCh. 32.4 - Prob. 32.4QQCh. 32.5 - (i) At an instant of time during the oscillations...Ch. 32 - Prob. 1OQCh. 32 - Prob. 2OQCh. 32 - Prob. 3OQCh. 32 - Prob. 4OQCh. 32 - Prob. 5OQ
Ch. 32 - Prob. 6OQCh. 32 - Prob. 7OQCh. 32 - Prob. 1CQCh. 32 - Prob. 2CQCh. 32 - Prob. 3CQCh. 32 - Prob. 4CQCh. 32 - Prob. 5CQCh. 32 - Prob. 6CQCh. 32 - The open switch in Figure CQ32.7 is thrown closed...Ch. 32 - Prob. 8CQCh. 32 - Prob. 9CQCh. 32 - Prob. 10CQCh. 32 - Prob. 1PCh. 32 - Prob. 2PCh. 32 - Prob. 3PCh. 32 - Prob. 4PCh. 32 - Prob. 5PCh. 32 - Prob. 6PCh. 32 - Prob. 7PCh. 32 - Prob. 8PCh. 32 - Prob. 9PCh. 32 - Prob. 10PCh. 32 - Prob. 11PCh. 32 - Prob. 12PCh. 32 - Prob. 13PCh. 32 - Prob. 14PCh. 32 - Prob. 15PCh. 32 - Prob. 16PCh. 32 - Prob. 17PCh. 32 - Prob. 18PCh. 32 - Prob. 19PCh. 32 - Prob. 20PCh. 32 - Prob. 21PCh. 32 - Prob. 22PCh. 32 - Prob. 23PCh. 32 - Prob. 24PCh. 32 - Prob. 25PCh. 32 - Prob. 26PCh. 32 - Prob. 27PCh. 32 - Prob. 28PCh. 32 - Prob. 29PCh. 32 - Prob. 30PCh. 32 - Prob. 31PCh. 32 - Prob. 32PCh. 32 - Prob. 33PCh. 32 - Prob. 34PCh. 32 - Prob. 35PCh. 32 - Prob. 36PCh. 32 - Prob. 37PCh. 32 - Prob. 38PCh. 32 - Prob. 39PCh. 32 - Prob. 40PCh. 32 - Prob. 41PCh. 32 - Prob. 42PCh. 32 - Prob. 43PCh. 32 - Prob. 44PCh. 32 - Prob. 45PCh. 32 - Prob. 46PCh. 32 - Prob. 47PCh. 32 - Prob. 48PCh. 32 - Prob. 49PCh. 32 - Prob. 50PCh. 32 - Prob. 51PCh. 32 - Prob. 52PCh. 32 - Prob. 53PCh. 32 - Prob. 54PCh. 32 - Prob. 55PCh. 32 - Prob. 56PCh. 32 - Prob. 57PCh. 32 - Prob. 58PCh. 32 - Electrical oscillations are initiated in a series...Ch. 32 - Prob. 60APCh. 32 - Prob. 61APCh. 32 - Prob. 62APCh. 32 - A capacitor in a series LC circuit has an initial...Ch. 32 - Prob. 64APCh. 32 - Prob. 65APCh. 32 - At the moment t = 0, a 24.0-V battery is connected...Ch. 32 - Prob. 67APCh. 32 - Prob. 68APCh. 32 - Prob. 69APCh. 32 - Prob. 70APCh. 32 - Prob. 71APCh. 32 - Prob. 72APCh. 32 - Prob. 73APCh. 32 - Prob. 74APCh. 32 - Prob. 75APCh. 32 - Prob. 76APCh. 32 - Prob. 77APCh. 32 - Prob. 78CPCh. 32 - Prob. 79CPCh. 32 - Prob. 80CPCh. 32 - Prob. 81CPCh. 32 - Prob. 82CPCh. 32 - Prob. 83CP
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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_forwardConsider the circuit in Figure P32.18, taking = 6.00 V, L = 8.00 mH, and R = 4.00 . (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 250 s after the switch is closed. (c) What is the value of the final steady-state current? (d) After what time interval does the current reach 80.0% of its maximum value?arrow_forwardIn the LC circuit in Figure 33.11, the inductance is L = 19.8 mH and the capacitance is C = 19.6 mF. At some moment, UB = UE= 17.5 mJ. a. What is the maximum charge stored by the capacitor? b. What is the maximum current in the circuit? c. At t = 0, the capacitor is fully charged. Write an expression for the charge stored by the capacitor as a function of lime. d. Write an expression for the current as a function of time.arrow_forward
- Figure CQ20.7 shows a slidewire generator with motional cmf 0 when the wire at A slides across the top and bottom rails at constant velocity v0. (a) When the wire reaches B so that the area enclosed by the circuit is doubled, determine the ratio of the new cmf to the original cmf, /0. (b) If the wire's speed is doubled so that v = 2v0 determine the ratio /0. Figure CQ20.7arrow_forwardA coil with a self-inductance of 3.0 H and a resistance of 100 2 carries a steady current of 2.0 A. (a) What is the energy stored in the magnetic field of the coil? (b) What is the energy per second dissipated in the resistance of the coil?arrow_forwardShow that Equation 32.28 in the text Ls Kirchhoffs loop rule as applied to the circuit in Figure P32.56 with the switch thrown to position b.arrow_forward
- Each 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_forwardThe magnetic field through a square loop of wire with sides of length 3.00 cm changes with time as shown in Figure P32.8, where the sign indicates the direction of the field relative to the axis of the loop. Plot the emf induced in the loop versus time. FIGURE P32.8arrow_forward(i) When a particular inductor is connected to a source of sinusoidally varying emf with constant amplitude and a frequency of 60.0 Hz, the rms current is 3.00 A. What is the rms current if the source frequency is doubled? (a) 12.0 A (b) 6.00 A (c) 4.24 A (d) 3.00 A (e) 1.50 A (ii) Repeat part (i) assuming the load is a capacitor instead of an inductor. (iii) Repeat part (i) assuming the load is a resistor instead of an inductor.arrow_forward
- In the circuit shown in the Figure with 3.0 mH for the inductance and 6.0 uF for the capacitance, S1 has been closed for a long enough time so that the current reads a steady 3.50 A. Suddenly, S2 is closed and S1 is opened at the same instant. What is the maximum charge that the capacitor will receive? What is the current in the inductor at this time? At an instant when the charge on the capacitor is 0.1 mC, what is the current in the inductor? At an instant when the charge on the capacitor is 0.1 mC, what is the rate at which the current in the inductor is changing?arrow_forwardIn the circuit of Figure P32.48, the battery emf & is 50 V, the resistance R is 190 2, and the capacitance C is 0.500 μF. The switch S is closed for a long time, and no voltage 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 L? 0.173 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. H R ε 000 Figure P32.48 Additional Materialsarrow_forwardA 10.00 μF capacitor C is initially charged to a voltage V of 10.00 (V). It is then connected in series with an inductor L. Charge and current oscillations ensue. (a) What is the total energy U of the circuit? (b) If the maximum current in the inductor is Im = 0.500 (A), then what is the inductance L? What is the charge Q on the positive plate of the capacitor when the current reaches its maximum value Im? (c) What is the angular frequency of the charge oscillations?arrow_forward
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