Use the circuit shown below to answer the following questions. The switch shown in the figure below has been open for a very long time, at t=0s, the switch closes.

The control current for the CCVS is I(2R) which is the current flowing the 2R resistor, towards ground. The value for CCVS is r I(2R), where r is a trans resistance. Given VAV ,R, and r, all answers should be in terms of only the known constants: Va , V.B'R, r,B' and any constants, numbers. No other solutions will be accepted, provide all answers in theA' simplest form, simplify. a) [5pts] Use equivalent circuits to derive an expression for the voltage across the capacitor just before the switch closes. b) [5pts] Using equivalent circuits, derive an expression for the time constant of the circuit in terms of the knowns for t > 0s. c) [5pts] After the switch closes, and t → o, derive an expression for the voltage across the capacitor in terms of the knowns.