Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 31, Problem 12P
Show that i = Iie−t/τ is a solution of the differential equation
where Ii is the current at t = 0 and τ = L/R.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Energy is to be transmitted over a pair of copper wires in a transmission line at the rate of 20.0 kW with only a 1.00% loss over a distance of 18.0 km at potential difference ΔVrms = 1.50 × 103 V between the wires. Assuming the current density is uniform in the conductors, what is the diameter required for each of the two wires?
If instantaneous current is given by I= 4 sin( ωt+ø ) amperes, then the r.m.s. value of current is
a.4 A
b.2√2 A
c.4√2 A
d.zero
A capacitor charging circuit consists of a battery, an uncharged 20 μF capacitor, and a 5.6 kΩkΩ resistor. At t = 0 ss the switch is closed; 0.15 s later, the current is 0.46 mA . What is the battery's emf?
Chapter 31 Solutions
Physics for Scientists and Engineers
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 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 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 - Show that i = Iiet/ is a solution of the...Ch. 31 - Prob. 13PCh. 31 - You are working as a demonstration assistant for a...Ch. 31 - Prob. 15PCh. 31 - The switch in Figure P31.15 is open for t 0 and...Ch. 31 - Prob. 17PCh. 31 - Two ideal inductors, L1 and L2, have zero internal...Ch. 31 - Prob. 19PCh. 31 - Prob. 20PCh. 31 - Prob. 21PCh. 31 - Complete the calculation in Example 31.3 by...Ch. 31 - Prob. 23PCh. 31 - A flat coil of wire has an inductance of 40.0 mH...Ch. 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 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 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 - Review. Consider a capacitor with vacuum between...Ch. 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 - You are working on an LC circuit for an experiment...Ch. 31 - Prob. 43APCh. 31 - Prob. 44APCh. 31 - Prob. 45APCh. 31 - At t = 0, the open switch in Figure P31.46 is...Ch. 31 - Review. The use of superconductors has been...Ch. 31 - Review. A fundamental property of a type 1...Ch. 31 - Prob. 49APCh. 31 - In earlier times when many households received...Ch. 31 - Assume the magnitude of the magnetic field outside...Ch. 31 - Prob. 52CPCh. 31 - Prob. 53CP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- In the RC circuit shown in Figure P29.78, an ideal battery with emf and internal resistance r is connected to capacitor C. The switch S is initially open and the capacitor is uncharged. At t = 0, the switch is closed. a. Determine the charge q on the capacitor at time t. b. Find the current in the branch be at time t. What is the current as t goes to infinity?arrow_forward3.1 A wire of diameter d, length l and resistivity ρ forms a circular loop. A current entersand leaves the loop at points P and Q as shown in the Figure. Show that the resistance R ofthe wire is given by the expression (4) R = 4ρx(l − x) / π*d^2*larrow_forwardQ2. To determine the galvanometer's internal resistor R. and its maximum electric current Is, corresponding to a maximum deviation of its needle, we mount it in series with a rheostat, as shown in the adjacent figure. R a b son Reosta Galvanometre When the needle makes a maximum deviation Vab = V1 = 5 V and Rr= R1 = 80 k 2. When the needle makes 1/2 maximum deviation Vab = V2 = 2 V and Rp = R2 = 60 ko. When the needle makes 44 maximum deviation Vab = V3 = 2 V and Rr = R3 . V a) Write the relationship between V1, R1, Rc and le. b) Write the relationship between V2, R2, Re and Ic. c) Write the relationship between V3, R3, Re and Ic. d) Determine the values of Re and Ic. e) Determine the value of Rs. Answer:arrow_forward
- Considering the closed path and current values in the figure ∮H⃗ .the value of the expression dl→ is true in which of the following options? Please select one: A. -20 A B. 30 A C. 0 D. 10 A E. -10 Aarrow_forwardIn the figure R1 = 9.81 kΩ, R2 = 15.4 kΩ, C = 0.433 μF, and the ideal battery has emf ε = 18.0 V. First, the switch is closed a long time so that the steady state is reached. Then the switch is opened at time t = 0. What is the current in resistor 2 at t = 3.60 ms?arrow_forwardFor the following circuit R1=R2=60 ohms , R3 = 250 ohms , R4= 325 ohms , R5= 260 ohms, and Vtotal = 35V . What is the total current (It)arrow_forward
- You connect a battery, resistor, and capacitor as in Fig. 26.20a, where E = 36.0 V, C = 5.00 mF, and R = 120 Ω. The switch S is closed at t = 0. (a) When the voltage across the capacitor is 8.00 V, what is the magnitude of the current in the circuit? (b) At what time t after the switch is closed is the voltage acrossthe capacitor 8.00 V? (c) When the voltage across the capacitor is 8.00 V, at what rate is energy being stored in the capacitor?arrow_forwardA long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗. The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗=2*I0/πa^2 *[1−(r/a)^2]k for r≤a=0 for r≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes. Part A Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≥a. Part B Obtain an expression for the current I contained in a circular cross section of radius r≤a and centered at the cylinder axis. Part C Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≤a.arrow_forwardIn the circuit below, the switch has been in the open position for a long time. At t=0, the switch is turned on. If the current at time t=3.3 ms reaches half of its maximum value, L=68 mH, and ℰ=17 V, find:the time constant τ= ms,the resistance R= Ω,the maximum value of the current, Imax= A.If the switch is open again, after what time, the current will reach the half of its value?t1/2= ms.arrow_forward
- When the switch S is toggled to the left, the capacitor C charges through the resistor R. When the switch is toggled to the right, the capacitor discharges current through the patient's torso, modeled as the resistor Rtorso, allowing the heart's normal rhythm to be reestablished. (a)If the capacitor is initially uncharged with C = 8.25 µF and = 1270 V, find the value of R (in ohms) required to charge the capacitor to a voltage of 755 V in 1.70 s. answer in Ω b) If the capacitor is then discharged across the patient's torso with Rtorso = 1260 Ω, calculate the voltage (in V) across the capacitor after 4.50 ms. answer in Varrow_forwardThe switch shown has been in position a for a long time. It is changed to position b at t = 0 s. What are the charge Q on the capacitor and the current I through the resistor (a) immediately after the switch is changed? (b) At t = 50 ms? (c) At t = 200 μs?arrow_forwardWhat is the current flowing through the battery immediately after the switch is closed and through the battery a long time after the switch has been closed? Use the following data: EMF = 14.5 V, R1 = 90.0 Ω, R2 = 10.0 Ω, L = 28.0 mH.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
DC Series circuits explained - The basics working principle; Author: The Engineering Mindset;https://www.youtube.com/watch?v=VV6tZ3Aqfuc;License: Standard YouTube License, CC-BY