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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?

a
252μF
b
50π3μF
c
502μF
d
100π3μF

detailed solution

Correct option is B

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

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In the circuit given in figure, VC=50 V and R=50Ω The values of C and VR are


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