Multivariable Calculus
8th Edition
ISBN: 9781305266643
Author: James Stewart
Publisher: Cengage Learning
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Chapter 17.3, Problem 13E
To determine
To find: The charge of series RLC circuit at time
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A 10-ohm resistor and a 5-Henry inductor are connected in series
with a voltage source rated at 20 Volts. Which equation best
describes the behavior of the current, I, over time?
O dI
= 4 – 21
dt
O dI
15 + 21
dt
O dI
= 10 – 21
dt
O dI
= 20+4I
dt
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An (open) electrical circuit consists of an inductor, a resistor, and a capacitor. There is an initial charge of 2 coulombs on the capaci-tor. At the instant the circuit is closed, a current of 3 amperes is present and a voltage of E(t) = 20 cos t is applied. In this circuit the voltage drop across the resistor is 4 times the instantaneous change in the charge, the voltage drop across the capacitor is 10 times the charge, and the voltage drop across the inductor is 2 times the instantaneous change in the current. Write an initial value problem to model the circuit.
Find the charge on the capacitor in an LRC-Series circuit if L = 10 henry, R = 20 ohms, C =
0.01 farad, and E(t) = 200 cos 5t Volts. The initial charge and current are both zero.
Chapter 17 Solutions
Multivariable Calculus
Ch. 17.1 - Solve the differential equation. 1. y" y' 6y = 0Ch. 17.1 - Prob. 2ECh. 17.1 - Prob. 3ECh. 17.1 - Solve the differential equation. 4. y" + y' 12y =...Ch. 17.1 - Prob. 5ECh. 17.1 - Prob. 6ECh. 17.1 - Prob. 7ECh. 17.1 - Prob. 8ECh. 17.1 - Solve the differential equation. 9. y" 4y' + 13y...Ch. 17.1 - Prob. 10E
Ch. 17.1 - Prob. 11ECh. 17.1 - Prob. 12ECh. 17.1 - Prob. 13ECh. 17.1 - Prob. 14ECh. 17.1 - Prob. 15ECh. 17.1 - Prob. 16ECh. 17.1 - Prob. 17ECh. 17.1 - Prob. 18ECh. 17.1 - Solve the initial-value problem. 19. 9y" + 12y' +...Ch. 17.1 - Prob. 20ECh. 17.1 - Prob. 21ECh. 17.1 - Prob. 22ECh. 17.1 - Solve the initial-value problem. 23. y" y' 12y =...Ch. 17.1 - Solve the initial-value problem. 24. 4y" + 4y' +...Ch. 17.1 - Prob. 25ECh. 17.1 - Prob. 26ECh. 17.1 - Prob. 27ECh. 17.1 - Prob. 28ECh. 17.1 - Prob. 29ECh. 17.1 - Prob. 30ECh. 17.1 - Prob. 31ECh. 17.1 - Solve the boundary-value problem, if possible. 32....Ch. 17.1 - Prob. 33ECh. 17.1 - If a, b, and c are all positive constants and y(x)...Ch. 17.2 - Prob. 1ECh. 17.2 - Prob. 2ECh. 17.2 - Prob. 3ECh. 17.2 - Prob. 4ECh. 17.2 - Prob. 5ECh. 17.2 - Prob. 6ECh. 17.2 - Prob. 7ECh. 17.2 - Prob. 8ECh. 17.2 - Prob. 9ECh. 17.2 - Prob. 10ECh. 17.2 - Prob. 11ECh. 17.2 - Prob. 12ECh. 17.2 - Prob. 13ECh. 17.2 - Prob. 14ECh. 17.2 - Prob. 15ECh. 17.2 - Prob. 16ECh. 17.2 - Prob. 17ECh. 17.2 - Prob. 18ECh. 17.2 - Prob. 19ECh. 17.2 - Prob. 20ECh. 17.2 - Solve the differential equation using (a)...Ch. 17.2 - Prob. 22ECh. 17.2 - Prob. 23ECh. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Prob. 27ECh. 17.2 - Prob. 28ECh. 17.3 - A spring has natural length 0.75 m and a 5-kg...Ch. 17.3 - Prob. 2ECh. 17.3 - A spring with a mass of 2 kg has damping constant...Ch. 17.3 - Prob. 4ECh. 17.3 - Prob. 5ECh. 17.3 - Prob. 6ECh. 17.3 - Prob. 7ECh. 17.3 - Prob. 8ECh. 17.3 - Suppose a spring has mass m and spring constant k...Ch. 17.3 - Prob. 10ECh. 17.3 - Prob. 11ECh. 17.3 - Prob. 12ECh. 17.3 - Prob. 13ECh. 17.3 - Prob. 14ECh. 17.3 - Prob. 15ECh. 17.3 - The battery in Exercise 14 is replaced by a...Ch. 17.3 - Prob. 17ECh. 17.3 - Prob. 18ECh. 17.4 - Prob. 1ECh. 17.4 - Prob. 2ECh. 17.4 - Prob. 3ECh. 17.4 - Prob. 4ECh. 17.4 - Prob. 5ECh. 17.4 - Prob. 6ECh. 17.4 - Prob. 7ECh. 17.4 - Prob. 8ECh. 17.4 - Prob. 9ECh. 17.4 - Prob. 10ECh. 17.4 - Prob. 11ECh. 17.4 - Prob. 12ECh. 17 - (a) Write the general form of a second-order...Ch. 17 - Prob. 2RCCCh. 17 - (a) Write the general form of a second-order...Ch. 17 - Prob. 4RCCCh. 17 - Prob. 5RCCCh. 17 - Prob. 1RQCh. 17 - Prob. 2RQCh. 17 - Prob. 3RQCh. 17 - Prob. 4RQCh. 17 - Solve the differential equation. 1. 4y" y =0Ch. 17 - Prob. 2RECh. 17 - Prob. 3RECh. 17 - Solve the differential equation. 4. y" + 8y' + 16y...Ch. 17 - Prob. 5RECh. 17 - Prob. 6RECh. 17 - Prob. 7RECh. 17 - Prob. 8RECh. 17 - Prob. 9RECh. 17 - Solve the differential equation. 10....Ch. 17 - Prob. 11RECh. 17 - Solve the initial-value problem. 12. y" 6y' + 25y...Ch. 17 - Solve the initial-value problem. 13. y" 5y' + 4y...Ch. 17 - Prob. 14RECh. 17 - Solve the boundary-value problem, if possible. 15....Ch. 17 - Prob. 16RECh. 17 - Prob. 17RECh. 17 - Prob. 18RECh. 17 - A series circuit contains a resistor with R = 40 ,...Ch. 17 - Prob. 20RECh. 17 - Assume that the earth is a solid sphere of uniform...
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- The pathway for a binary electrical signal between gates in an integrated circuit can be modeled as an RC circuit, as shown in the figure to the right; the voltage source models the transmitting gate, and the capacitor models the receiving gate. Suppose the resistance is 500 £2 and the capacitance is 10-11 F (10 picofarads, pF). If the capacitor is initially uncharged and the transmitting gate changes instantaneously from 0 to 5 V, how long will it take for the voltage at the receiving gate to reach 4 V? What is the charge q(t) on the capacitor at time t? q(t) = 5x10-¹1(1-e-200000 - 200000000t) R www E It will take x 10 seconds. (Type your answer in scientific notation, using the appropriate symbol from the math palette for any multiplication. Round to three decimal places as needed.)arrow_forwardIn the serially connected RL circuit, with the resistor R = 50Ω, the coil L = 10H and when the switch is closed at t = 0, a constant voltage of E = 100V is applied. Obtain the equation for the current.arrow_forward3. An RC circuit has an emf of 120 volts, a resistance of 5 ohms, a capacitance of 0.02 farad, and an initial charge on the capacitor of 12 coulombs. Find (a) the charge on the capacitor after 3 milliseconds and (b) the current at after 6 milliseconds.arrow_forward
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