Problem#$2[10+10+5$ Pts$]$

The generalized version of Ohm's law for impedance elements is $V=IZ.$ Assume the current through a $0\mathrm{.}5F$ capacitor is given by $i_C(t)=I_{o}cos(t)A,I_o=1mA,=1000ra\frac{d}{s}.$

a$)$ Express the current in phasor notation.

b$)$ Determine the impedance of the capacitor.

c$)$ Determine the voltage across the capacitor, in phasor notation.