A 50 W, 100 V lamp is to be connected to an ac mains of 200 V, 50 Hz. What capacitor is essential to be put in series with the lamp?

As resistance of the lampR=VS2Po=100250=200ΩThe rms current I=VR=100200=12ASo when the lamp is put in series with a capacitance and run at 200 V ac, from V = IZ, we haveZ=VI=2001/2=400ΩNow as in case of C-R circuit,Z=R2+1ωC2i.e., R2+1ωC2=160000or, 1ωC2=16×104-2002=12×1041ωC=12×102C=1100π×12×102F=100π12μF=50π3=9.2μF