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Question 3.9.7: Modeling Electrical Current in a Wire The electrical circuit...

Modeling Electrical Current in a Wire

The electrical circuit shown in Figure 3.103 includes a 14-ohm resistor, a 2-henry inductor, a 0.05-farad capacitor and a battery supplying 232 volts of AC current modeled by the oscillating function 232 sin 2t, where t is measured in seconds. Find the current in the circuit at any time t.

3.103
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It can be shown (using the elementary laws of electricity) that the charge in this circuit is given by

Q(t)=10 e^{-5 t}+2 t e^{-2 t}+3 \sin 2 t-7 \cos 2 t \text { coulombs. }

The current is then

Q^{\prime}(t)=-50 e^{-5 t}+2 e^{-2 t}-4 t e^{-2 t}+6 \cos 2 t+14 \sin 2 t \text { amps (coulombs per second). }

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