An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

80 H

0.08 H

0.044 H

0.065 H

Solution

0.065 H

I = 10 A, V = 80 V
R = V/I = 80/10 = 8Ω and ω = 50 Hz
For AC circuit, we have

$straight I space equals space fraction numerator straight V over denominator square root of 8 squared plus straight X subscript straight L superscript 2 end root end fraction rightwards double arrow space 10 space equals space fraction numerator 220 over denominator square root of 64 plus straight X subscript straight L superscript 2 end root end fraction rightwards double arrow space square root of 64 space plus straight X subscript straight L superscript 2 end root space equals space 22 squaring space on space both space sides comma space we space get 64 space plus space straight X subscript straight L superscript 2 space equals space 484 straight X subscript straight L superscript 2 space equals space 484 minus 64 space equals space 420 straight X subscript straight L space equals space square root of 420 2 straight pi space straight x space ωL space equals space square root of 420 Series space induction space on space an space arc space lamp. straight L space equals space fraction numerator square root of 420 over denominator left parenthesis 2 straight pi space straight x space 50 right parenthesis end fraction space equals space 0.065 space straight H$