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

Options

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

Answer

D

Explanation

(d) `R = (V)/(I) = (80)/(10)= 8Omega`
For correct brightness rms current in AC circuit must be the same as current in DC circuit hence impedance can be written as follows :
`Z= (V_("rms"))/(I) = (220)/(10) = 22Omega`
`because Z^(2) =X_(L)^(2) + R^(2)`
`implies (22)^(2) = X_(L)^(2) + (8)^(2) `
`implies X_(L)=20.5`
`implies 100 pi L =20.5`
` implies L = 0.065 ` H
Hence option (d) is correct .