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R at t = 0 i(t) = + CH V.(t) Việt) C2 Problem 3: Consider the circuit in Figure 3, for t 2 0. Pri- or to t = 0, the capacitors have been charged with charges, Qi and Q2 respectively, such that Vi(0-) = Qi/Cand V2(0-) = Q2/C2. Assume that C1 = 151F, C2 = 5nF, R = 200 Ohms, and Q1 =-Q2 = 8 nanoCoulumbs. (a) Derive a differential equation in terms of the current through the resistor, i(t), that governs circuit operation for t 20. (b) What is the time constant of the circuit for operation Figure 3 during t 2 0? Express it in terms of nanoseconds. (c) Determine the boundary values, Vi(0+), V2(0+), i(0+), and Vi(.), V2(0), i). (d) Derive an expression for the voltages across the capacitors, Vi(t) and V2(t), for all time t 20. (e) Draw a sketch of Vi(t) and Vz(t) as a function of time from t = 0 to t = 5000ns on the same a graph. Clearly mark the initial and final values of Vi(t) and Vz(t), on your sketch. (f) Draw a sketch of i(t) as a function of time from t = 0 to t = 5000ns. Clearly mark the initial and final values of i(t) on your sketch. (g) Briefly describe the how the Vl(t), V2(t), and i(t) waveforms would look for the case where R is very small (close to zero).