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Mathematics, 13.02.2020 21:04 john9727

(a) What are the boundary conditions for Ic(t) (i. e. what are Ic(t = 0) and Ic(t β†’ [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 Ξ» 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.

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(a) What are the boundary conditions for Ic(t) (i. e. what are Ic(t = 0) and Ic(t β†’ [infinity])?) (b...
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