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

Here, `I = 10 A, V = 80 V`
`R = (V)/(I) = (80)/(10) = 8 Omega`
`E_(upsilon) = 220 V, v = 50 Hz, L = ?`
`Z = (E_(upsilon))/(I_(upsilon)) = (220)/(10) = 22 Omega`
As `R^(2) + X_(L)^(2) = Z^(2)`
`X_(L) = sqrt(Z^(2) - R^(2)) = sqrt(22^(2) - 8^(2)) = sqrt(420)`
`=20.49`
`X_(L) = omega L = 2 pi v L = 20.49`
`L = (20.49)/(2 xx 3.14 xx 50)`
`=0.065 H`