Question $4(55$ points$)$: Consider the circuit below and do the following,

$($i$)$ Find the current supplied by the source $i(t)(20$ points$)$

$($ii$)$ Find the voltage across the resistors and the inductor $(15$ points$)$

$($iii$)$ Extra credit $(20$ points$)$: Determine the following,

a$.$ RMS value of source voltage,

b$.$ RMS value of source current

c$.$ Average power supplied by the source

d$.$ Average power consumed by the $50$ resistor,

e$.$ Average power consumed by the $100$ resistor

f$.$ Average power consumed by the inductor.