At t = 0 a current of 3 amperes flows in an RLC circuit with resistance 4 ohms, inductance 0.5 henrys, and capacitance 0.001 farads. The initial charge on the capacitor is 9 coulomb. Assume that the impressed voltage, provided by an alternating current generator, is E(t) 10 cos(7t). Note: The phase-angle is between 0 and t. (a) Find the charge in the circuit at time t = 5. (b) Find the amplitude-phase form of the steady state current in the RLC flowing in the circuit, and evaluate it at t = 105. (c) Find the amplitude-phase form of the steady state current in the RLC flowing in the circuit if at t = 0 a current of 6 amperes flowed in the RLC circuit, and the initial charge on the capacitor is 18 coulomb. Evaluate the function you obtain at t = 105.
At t = 0 a current of 3 amperes flows in an RLC circuit with resistance 4 ohms, inductance 0.5 henrys, and capacitance 0.001 farads. The initial charge on the capacitor is 9 coulomb. Assume that the impressed voltage, provided by an alternating current generator, is E(t) 10 cos(7t). Note: The phase-angle is between 0 and t. (a) Find the charge in the circuit at time t = 5. (b) Find the amplitude-phase form of the steady state current in the RLC flowing in the circuit, and evaluate it at t = 105. (c) Find the amplitude-phase form of the steady state current in the RLC flowing in the circuit if at t = 0 a current of 6 amperes flowed in the RLC circuit, and the initial charge on the capacitor is 18 coulomb. Evaluate the function you obtain at t = 105.
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Transcribed Image Text:At t = 0 a current of 3 amperes flows in an RLC circuit with resistance 4 ohms, inductance 0.5 henrys, and
capacitance 0.001 farads. The initial charge on the capacitor is 9 coulomb. Assume that the impressed voltage,
provided by an alternating current generator, is E(t)
10 cos(7t).
Note: The phase-angle is between 0 and r.
(a) Find the charge in the circuit at time t =
5.
(b) Find the amplitude-phase form of the steady state current in the RLC flowing in the circuit, and evaluate it at
t = 105.
(c) Find the amplitude-phase form of the steady state current in the RLC flowing in the circuit if at t = 0 a
current of 6 amperes flowed in the RLC circuit, and the initial charge on the capacitor is 18 coulomb. Evaluate
the function you obtain at t =
105.
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