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A series RLC circuit offers a good review in solving linear, constant coefficient ordinary differential equations. A step voltage V, is applied to the initially unexcited circuit at t=0. itz) r=0 i m a. Write a single differential equation for the current. b. Guess an exponential solution of the form i(t)- test and find the natural frequencies of the circuit. c. What are the initial conditions? What are the steady-state voltages across each element? d. Write and sketch the solution for i(t) when C R R R () ic (27) 2L LC' 2L LC' 2L LC e. What is the voltage across each element? f. After the circuit has reached the steady state, the terminal voltage is instantly short-circuited. What is the short circuit current?