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RLC Series Circuit. In the study of an electrical circuit

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

Solution for problem 34E Chapter 4.3

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 34E

PROBLEM 34E

        

RLC Series Circuit. In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an electromotive force (see Figure 4.9), we are led to an initial value problem of the form

where L is the inductance in henrys, R is the resistance in ohms, C is the capacitance in farads, E(t) is the electromotive force in volts q(t), is the charge in coulombs on the capacitor at time t, and I = dq/ dt is the current in amperes. Find the current at time t if the charge on the capacitor is initially zero, the initial current is zero, L = 10 H, R = 20 Ω, C = (6262)-1 F, and E(t) = 100 (V. [Hint: Differentiate both sides of the differential equation in (20) to obtain a homogeneous linear second-order equation for I(t). Then use (20) to determine dI/dt at t = 0.]

Step-by-Step Solution:

Solution:

Step 1: 

In this problem, we have to find the current at time t if the charge on the capacitor is initially zero.

Step 2 of 4

Chapter 4.3, Problem 34E is Solved
Step 3 of 4

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

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RLC Series Circuit. In the study of an electrical circuit