An arc lamp requires a direct current of 10A at 80V to function . 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

When the arc lamp functions with dc, V=80V,I=10 A
Therefore, resistance of the lamp `R=V/I=80/10=80Omega`
When the lamp and the inductor is connected to an ac source, impedance of the circuit,
`Z=sqrt(R^2+omega^2L^2)`
Electric current in the circuit,
`I=(V')/R=(V')/sqrt(R^2omega^2L^2)`or,`R^2+omega^2L^2=((V')/I)^2`
or, `8^2+omega^2L^2=(220/10)^2`or,`omega^2L^2=(22)^2-8^2`
or, `L=sqrt(22^2-8^2)/omega=sqrt(30times14)/(2pitimes50)=0.065H`