Question

An arc lamp requires a direct current of 10 A at 50 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 ____________.

पर्याय

• 0.08 H

• 0.068 H

• 0.045 H

• 60 H

Answer 1

An arc lamp requires a direct current of 10 A at 50 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 0.068 H.

Explanation:

`"Resistance R" = "V"/"i" = 50/10 = 5  Omega`

For a RL circuit;

`"e" = sqrt("e"_"R"^2 + "e"_"L"^2)`

`therefore "e"_"L"^2 = "e"^2 - "e"_"R"^2`

`"i"_2(2 pi"fL")^2 = "e"^2 - ("iR")^2`

`therefore "L"^2 = ("e"^2 - ("iR")^2)/("i"^2 4 pi^2 "f"^2)`

` = ((220)^2 - (10 xx 5)^2)/(10^2 xx 4 xx (3.14)^2 xx (50)^2)`

`"L"^2 = 0.4666 xx 10^-2`

`therefore "L" = 0.068  "H"`