(a)
The expression for the total energy that dissipated by the resistor in one time constant.
(a)
Answer to Problem 17PQ
The expression for the total energy that dissipated by the resistor in one time constant is,
Explanation of Solution
The following figure shows the given diagram-
Figure-(1)
Here,
Write the expression for current pass through the resistor.
Here,
Write the expression for power dissipated in the resistor as function of time.
Here,
Substitute
Write the expression for energy dissipated
Substitute
Integrate the above expression between the limits
Conclusion:
Therefore, the expression for the total energy that dissipated by the resistor in one time constant is
(b)
The expression for the total charge that passes through the resistor in one time constant.
(b)
Answer to Problem 17PQ
The expression for the total charge that passes through the resistor in one time constant is,
Explanation of Solution
Write the expression for decaying current.
Write the expression for power dissipated in the resistor as function of time.
Substitute
Integrate the above expression between the limits
Conclusion:
Therefore, the expression for the total energy that dissipated by the resistor in one time constant is,
(c)
The comparison between the above two results and comment.
(c)
Answer to Problem 17PQ
The energy dissipated in the resistor when the current decays is more than the energy dissipated when the current grows in the circuit.
Explanation of Solution
Write the expression for energy growth that dissipated through the resistor.
Here,
Write the expression for energy decay that dissipated through the resistor.
Here,
Take the ratio of both equations.
Conclusion:
Substitute
Therefore, the energy dissipated in the resistor when the current decays is more than the energy dissipated when the current grows in the circuit.
Want to see more full solutions like this?
Chapter 33 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- 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_forwardIn Figure 33.9A (page 1052), the switch is closed at a at t = 0. Find an expression for the power dissipated by the resistor as a function of time, and sketch your result. Is the power lost greater as soon as the switch is closed or a long time after it has been closed? Does your answer make sense?arrow_forwardA 15.00 µF capacitor, labeled as C below, is charged to 175.0 µC at time t = 0. At t = 0, the capacitor is connected across the ends of a 5.00 mH inductor represented by symbol L. The diagram below shows the system just after the fully charged capacitor C is connected to inductor L. The current I just begins to flow at t = 0, reducing the charge Q on the right plate. (a) What is the angular frequency ω of the charge oscillations in the capacitor after the above connection is made? (b) Find the maximum current IMAX. (c) What is the value of charge Q on the right plate when the current I reaches the maximum value IMAX?arrow_forward
- In an L-C circuit, L = 85.0 mH and C = 3.20 uF. During the oscillations the maximum current in the inductor is 0.850 mA. (a) What is the maximum charge on the capacitor? (b) What is the magnitude of the charge on the capacitor at an instant when the current in the inductor has magnitude 0.500 mA?arrow_forwardAn LC circuit contains a 20 mH inductor and a 50 µF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.(a) What is the total energy stored initially? Is it conserved during LC oscillations?(b) What is the natural frequency of the circuit?(c) At what time is the energy stored(i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)?(d) At what times is the total energy shared equally between the inductor and the capacitor?(e) If a resistor is inserted in the circuit, how much energy iseventually dissipated as heat?arrow_forwardIn the figure, the capacitor is initially charged when switch 1 is open and switch 2 is closed. Switch 2 is then opened, and removing the battery from circuit, and the capacitor remains charged. Switch 1 is then closed, so that the capacitor is connected directly across the inductor. A) Find the frequency of oscillation of the circuit. B) What are the maximum values of charge on the capacitor and current in the circuit? C) Determine the charge and current as a functions of time.arrow_forward
- A 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_forwardA 521-turn solenoid has a radius of 7.00 mm and an overall length of 15.0 cm. a) What is its inductance? b) If the solenoid is connected in series with a 2.50-Ω resistor and a battery, what is the time constant of the circuit?arrow_forwardA 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 the wire? (c) How long is the resulting solenoid? (d) What is the self-inductance of the solenoid? (e) If the solenoid is attached to a battery with an emf of 6.0 V and internal resistance of 350 mV, compute the time constant of the circuit. (f) What is the maximum current attained? (g) How long would it take to reach 99.9% of its maximum current? (h) What maximum energy is stored in the inductor?arrow_forward
- The drawing shows a straight wire carrying a current I. Above the wire is a rectangular loop that contains a resistor R. If the current I is decreasing in time, what is the direction of the induced current through the resistor R — left-to-right or right-to-left? If the induced current goes from left to right through the resistor, type the letters "LTR" in the box below. If the current goes from right to left through the resistor, type the letters "RTL" in the box.arrow_forwardConsider a transformer, used to recharge rechargeable flashlight batteries, that has 500 turns in its primary coil, 7 turns in its secondary coil, and an input voltage of 120 V. Randomized Variable n = 7 a) What is the voltage output Vs, in volts, of the transformer used for to charge the batteries? b) What input current Ip, in milliamps, is required to produce a 4.8 A output current? c) What is the power input, in watts?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning