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$(20$ points$)$ Consider the circuit below. Assume the switch has been in its initial position for a long time, and it switches position as indicated at $t=0.$

a$.$ Find $i(t)$ for all $t>0.($Answer: $i(t)=0\mathrm{.}9e^{-(2{10}^6)t}mA)$

b$.$ Sketch $i(t)$ as current vs$.$ time.

c$.$ How much energy is stored in the inductor at $t=0?($Answer: $20\mathrm{.}25$ nJ $)$