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2. An aging battery generating 200e-5t volts is connected in series with a 20 ohm resistor, and a 0.01 farad capacitor. Assuming q = 0 at t = 0, find the charge and current for all t > 0. Show that the charge reaches a maximum and find the time it is reached.

2. An aging battery generating 200e-5t volts is connected in series with a 20 ohm resistor, and a 0.01 farad capacitor. Assuming q = 0 at t = 0, find the charge and current for all t > 0. Show that the charge reaches a maximum and find the time it is reached.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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22 Q₁ (t) = (1-e-²t), t < 2, Q2(t) = Ae-2t, t > 2, respectively, where the initial condition has been applied to the Q1 equation; A is an arbitrary constant. Because the solution is continuous, we impose Q1(2): 22(2), which gives A = (1/2) (e¹ - 1). So E(t) = (1-e-2t), (e4-1) e-2t, t> 2. 0≤t≤2, = EXERCISES 1. Write the equation that governs an RC circuit with a 12-volt battery, taking R = 1 and C = . Determine the equilibrium solution and its stability. If Q(0) = 5, find a formula for Q(t). Find the current I(t). Plot the charge and the current on the same set of axes. 2. An aging battery generating 200e-5t volts is connected in series with a 20 ohm resistor, and a 0.01 farad capacitor. Assuming q = 0 at t = 0, find the charge and current for all t > 0. Show that the charge reaches a maximum and find the time it is reached. 3. In an arbitrary RC circuit with constant emf E, use the method of sepa- ration of variables to derive the formula Q(t) = Ae-t/RC + EC for the charge on the capacitor, where A is an arbitrary constant. If Q(0) = Qo, what is A? 4. An RCL circuit with an applied emf given by E(t) has initial charge Q(0) = Qo and initial current I(0) = Io. What is I'(0)? Write the circuit equation and the initial conditions in terms of current I(t). Hint: Use Kirchhoff's law in the form LI' + RI+Q/C = E(t). 5. Write the RCL circuit equation with the voltage Ve(t) on the capacitor as the unknown state function.
Transcribed Image Text:22 Q₁ (t) = (1-e-²t), t < 2, Q2(t) = Ae-2t, t > 2, respectively, where the initial condition has been applied to the Q1 equation; A is an arbitrary constant. Because the solution is continuous, we impose Q1(2): 22(2), which gives A = (1/2) (e¹ - 1). So E(t) = (1-e-2t), (e4-1) e-2t, t> 2. 0≤t≤2, = EXERCISES 1. Write the equation that governs an RC circuit with a 12-volt battery, taking R = 1 and C = . Determine the equilibrium solution and its stability. If Q(0) = 5, find a formula for Q(t). Find the current I(t). Plot the charge and the current on the same set of axes. 2. An aging battery generating 200e-5t volts is connected in series with a 20 ohm resistor, and a 0.01 farad capacitor. Assuming q = 0 at t = 0, find the charge and current for all t > 0. Show that the charge reaches a maximum and find the time it is reached. 3. In an arbitrary RC circuit with constant emf E, use the method of sepa- ration of variables to derive the formula Q(t) = Ae-t/RC + EC for the charge on the capacitor, where A is an arbitrary constant. If Q(0) = Qo, what is A? 4. An RCL circuit with an applied emf given by E(t) has initial charge Q(0) = Qo and initial current I(0) = Io. What is I'(0)? Write the circuit equation and the initial conditions in terms of current I(t). Hint: Use Kirchhoff's law in the form LI' + RI+Q/C = E(t). 5. Write the RCL circuit equation with the voltage Ve(t) on the capacitor as the unknown state function.
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