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If the resistance in the RL circuit of Figure 3.13(a) is

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 4E Chapter 3.5

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 4E

Problem 4E

Problem

If the resistance in the RL circuit of Figure 3.13(a) is zero, show that the current I t is directly proportional to the integral of the applied voltage E( t) . Similarly show that if the resistance in the RC circuit of Figure 3.13(b) is zero, the current is directly proportional to the derivative of the applied voltage. (In engineering applications, it is often necessary to generate a voltage, rather than a current, which is the integral or derivative of another voltage. Group Project E shows how this is accomplished using an operational amplifier.)

Step-by-Step Solution:

Solution :

Step 1 :

  1. :

In this problem we have to show that the current I(t) is directly proportional to the integral of the applied voltage.

We use the below laws of physics in the figure 3.13

  • According to Ohm’s law, the  voltage drop across a resistor is proportional to the current I passing through the resistor.

           .’. …………..(1)

          The proportionality constant R is called the resistance.

  • According to Faraday’s law Lenz’s law that the voltage drop across an inductor is proportional to the instantaneous rate of change of the current I.

         .’. ……………(2)

           The proportionality constant L is called the inductance.

Step 2 of 5

Chapter 3.5, Problem 4E is Solved
Step 3 of 5

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. The answer to “If the resistance in the RL circuit of Figure 3.13(a) is zero, show that the current I t is directly proportional to the integral of the applied voltage E( t) . Similarly show that if the resistance in the RC circuit of Figure 3.13(b) is zero, the current is directly proportional to the derivative of the applied voltage. (In engineering applications, it is often necessary to generate a voltage, rather than a current, which is the integral or derivative of another voltage. Group Project E shows how this is accomplished using an operational amplifier.)” is broken down into a number of easy to follow steps, and 94 words. This full solution covers the following key subjects: voltage, current, Circuit, resistance, applied. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. Since the solution to 4E from 3.5 chapter was answered, more than 333 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 4E from chapter: 3.5 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM.

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If the resistance in the RL circuit of Figure 3.13(a) is