The voltage and current in a circuit are given by e= 100 sin (wt+300) and i=50sin (wt+600). Determine the impedance of the circuit. Assuming the circuit to contain 2 elements in series find resistance, reactance and power factor of the circuit.. -

$e=100 \sin(wt+30^0)\\ \bar{E}=70.7107 \angle 30^0 V \\ i=50 \sin (wt+60^0) \\ \bar{I}=35.355 \angle60^0A \\ \bar{Z}=\dfrac EI=Z \angle-30^0\Omega \\ =(1.732-j1)\Omega \\ R=1.732 \Omega \\ X=1 \Omega \\ pf= \cos \theta = \dfrac RZ =0.866 (Leading)$