(a) What are the boundary conditions for Ic(t) (i. e. what are Ic(t = 0) and Ic(t → [infinity])?) (b) Use KVL and the relationship between charge and current (q = R Idt) to find the first order differential equation in terms of the current through the capacitor, Ic. Assume that dVs dt = 0. (Hint: You will need to take a derivative with respect to time to get the equation.) (c) What is the eigenvalue λ of this equation? (d) Using the eigenvalue and boundary conditions found in the previous parts, find an expression for Ic(t) in terms of Vs , R, and C. (e) On what order of magnitude of time (nanoseconds, milliseconds, 10’s of seconds, etc.) does this circuit settle (Ic is < 5% of its initial value)? (f) Give 2 ways to reduce the settling time of the circuit if we are allowed to change one component in the circuit.