$(45$ pts$)$ For the circuit on the right.

$5cos(10t)V$

a$.$ Convert all variables to their phasor form.

b$.$ Find the impedance, resistance, and reactance of the circuit in phasor form.

c$.$ Show the found impedance, resistance, and reactance in step $b$ as vectors in the complex plane.

d$.$ Use nodal analysis to find phasor voltage $V(t)$ at the node shown in the schematic.

e$.$ In phasor domain, find phasor current I.

f$.$ Sketch the phasor $V$ and I found in steps $d$ and $e$ in the complex plane; show both magnitude and phase angles.

g$.$ Find time domain current $i_0(t).$

h$.$ Find the complex power, apparent power, real power, and reactive power of the circuit that is delivered by the source.

Find the power factor of the circuit.

Show the above powers on a complex plane and show the power factor on the figure.