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 closed to:

Options

A. 80 H
B. 0.08 H
C. 0.044 H
D. 0.065 H

Answer

D

Explanation

`R=V/I=80/10 = 8 Omega` (Fro D.C. current )
Now, `I=V_(rms)/"|z|"` (For A.C. current )
`10=220 /sqrt(R^2+X_L^2)`
`100=(220xx220)/((8)^2+X_L^2)`
`64+X_L^2=484`
`therefore X_L^2`= 420
`therefore X_L = sqrt420`
`therefore 2pif L=sqrt420`
`therefore 2xx3.14xx50xxL = sqrt420`
314 L = `sqrt420`
`therefore L=20.49/314`
`therefore` L=0.6526
`approx` 0.065 H