In Exercises 33 and 34, use the electrical circuit differential equation where is the

Chapter 16, Problem 34

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Electrical Circuits

In Exercises 33 and 34, use the electrical circuit differential equation

\(\frac{d^{2} q}{d t^{2}}+\left(\frac{R}{L}\right) \frac{d q}{d t}+\left(\frac{1}{L C}\right) q=\left(\frac{1}{L}\right) E(t)\)

where R is the resistance (in ohms), C is the capacitance (in farads), L is the inductance (in henrys), E(t) is the electromotive force (in volts), and q is the charge on the capacitor (in coulombs). Find the charge q as a function of time for the electrical circuit described. Assume that q(0) = 0 and q’(0) = 0.

R = 20, C = 0.02, L = 1, E(t) = 10 sin 5t

Text Transcription:

d^2q/dt^2 + (R/L) dq/dt +  (1/LC)q = (1/L) E(t)