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Time varying capacitor

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A time varying capacitor is characterized by the charge- voltage equation
q(t) = C(t)v(t)
That is, the capacitance is not a constant but a function of time.
a) Given that i(t) = dq(t)/dt, find the voltage- current relation for this time varying capacitor.
b) Let C(t) = 1 + cos (2Ï?t) and v(t) = cos (2Ï?t). Determine the current i1(t) in the capacitor for all t.
c) Let C(t) = 1 + cos (2Ï?t), delay v(t) by 0.25 seconds. Determine i2(t) for all time. Is the system TI?

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