How many 200 W/200 V incandescent lamps connected in series would consume the same total power as a single 100 W/200 V incandescent lamp?

The current through the $$2\,\,k\Omega $$ resistance in the circuit shown in Fig. is

The Thevenin's equivalent of a circuit operating at $$\omega = 5\,\,rad/s\,\,{V_{oc}} = 3.71\angle - {15.9^ \circ }$$ and $${Z_0} = 2.38 - j0.667\Omega .$$ At this frequency, the minimal realization of the Thevenin's independence will have a

In the figure given below the value of $$R$$ is