A choke coil is needed to operate an arc lamp at 160 V (rms) and 50 Hz. The lamp has an effective resistance of `5 Omega` when running at 10 A (rms). Calculate the inductance of the choke coil. If the same arc lamp is to be operated on 160 V (DC), what additionalresistance is required ? Compare the power loses in both cases.

Answer

`4.84 xx 10^(-2)H; 11 Omega; In case of ac =500W; In case of dc =1100W`

Explanation

As for the arc lamp `V_(R )=IR =10xx5=50V`, so when it is connected to 160V ac source through a choke in series,

`(V^2)=V_(R )^(2) +V_(L)^(2) =sqrt(160^(2)-50^(2))`
and as `V_(L) = I omega L = 2 pi f LI`
so, `L=(V_L)/(2 pi f I) =(152)/(2 xx pi xx 50 xx 10) =4.84 xx 10^(-2)H`
Now the lamp is to be operated at 160V dc, instead of choke if additional resistance r is put in series with it,
`V=1(R+r),i.e., 160=10(5+r)`
i.e., `r=11 Omega`
In case of ac, as choke has no resistance power loss in hte choke will be zero while the bulb will consume,
`P=(I^2)R = 10^(2) xx 5 =500W`
However, in case of dc as resistance r is to be used instead of choke the power loss in resistance r will be.
`PL=10^(2) xx11=1100 W`
While the bulb will still consume 500 W, i.e., when the lamp is run on resistnace r instead if choke more than double the power consumed by the lamp is wasted by the resistance r.