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?

In the Fig. shown, all elements used are ideal. For time t<0, S₁ remained closed and S₂ open. At t=0, S₁ is opened and S₂ is closed.If the voltage V_C2 across the capacitor C₂ at t = 0 is zero, the voltage across the capacitor combiation at t = 0⁺ will be

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

The equivalent capacitance of the input loop of the circuit shown in below