A series circuit contains a capacitor of 4x10-4 F and an inductor of 1 H. The charge on the capacitor and the current in the circuit are both initially zero. Starting at time t = 0 an external voltage of 300 cos(40t) volts is applied to the circuit, where ț is measured in seconds. Resistance is negligible. Consider the differential equation governing the charge Q(t) in Coulombs on the capacitor as a function of time. a. Establish an initial value problem describing the charge on the capacitor as a function of time. b. What is the natural frequency of this system? c. The solution of the IVP above will exhibit beats. What is the beat (angular) frequency of the solution in rad/sec? d. What is the maximum amount of charge the capacitor will hold?
A series circuit contains a capacitor of 4x10-4 F and an inductor of 1 H. The charge on the capacitor and the current in the circuit are both initially zero. Starting at time t = 0 an external voltage of 300 cos(40t) volts is applied to the circuit, where ț is measured in seconds. Resistance is negligible. Consider the differential equation governing the charge Q(t) in Coulombs on the capacitor as a function of time. a. Establish an initial value problem describing the charge on the capacitor as a function of time. b. What is the natural frequency of this system? c. The solution of the IVP above will exhibit beats. What is the beat (angular) frequency of the solution in rad/sec? d. What is the maximum amount of charge the capacitor will hold?
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter20: Capacitance In Ac Circuits
Section: Chapter Questions
Problem 2PA: You are working in an industrial plant. You have been instructed to double the capacitance connected...
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Question
Transcribed Image Text:A series circuit contains a capacitor of 4x10-4 F and an inductor of 1 H. The charge on the capacitor and
the current in the circuit are both initially zero. Starting at time t = 0 an external voltage of 300 cos(40t)
volts is applied to the circuit, where ț is measured in seconds. Resistance is negligible. Consider the
differential equation governing the charge Q(t) in Coulombs on the capacitor as a function of time.
a. Establish an initial value problem describing the charge on the capacitor as a function of time.
b. What is the natural frequency of this system?
c. The solution of the IVP above will exhibit beats. What is the beat (angular) frequency of the
solution in rad/sec?
d. What is the maximum amount of charge the capacitor will hold?
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