The two series-connected capacitors in Figure are connected to the terminals of a black bo...

The two series-connected capacitors in Figure are connected to the terminals of a black box at t = 0. The resulting current i(t) for t > 0 is known to be 800e -25t µA.

a) Replace the original capacitors with an equivalent capacitor and find v0(t) for t  ≥ 0.

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b) Find v1(t) for t ≥ 0.

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c) Find v2(t) for t ≥ 0.

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d) How much energy is delivered to the black box in the time interval 0 < t < ∞?

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e) How much energy was initially stored in the series capacitors?

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f) How much energy is trapped in the ideal capacitors?

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g) Show that the solutions for v1 and v2 agree with the answer obtained in (f).