A Choke coil is needed to operate an arc lamp at `160 V` (rms) and `50 Hz`. The lamp has an effective resistnce of `5 Omega` when running at 1`0 A("rms")`. Calculate the inductance of the choke coil. If the same arc lamp is to be operated on `160 V (DC)`, what additional resistance is required ? Compare the power loses in both cases.

Explanation

(i) Here, `E_(v) = 160 V, v = 50 Hz, R = 5 Omega, I_(v) = 10 A, L = ?`
`Z = (E_(v))/(I_(v)) = (160)/(10) = 15 ohm`
From `R^(2) + (omega L)^(2) = Z^(2)`
`omega L = sqrt(Z^(2) - R^(2)) = sqrt(16^(2) - 5^(2)) = sqrt(231)`
`L = (sqrt(231))/(omega) = (sqrt(231))/(2 pi xx 50) = (15.2)/(314) = 0.048 H`
(ii) When same are lamp is operated on d.c. let R' be the additional resistance.
From `I = (E)/(R + R')`
`10 = (160)/(5 + R') :. R' = 11 ohm`
(iii) Power loss in a.c. circuit `= E_(v) I_(v) cos phi = E_(v) I_(v) (R )/(Z)`
`P = 160 xx 10 xx (5)/(16) = 500` watt
Power loss in d.c. circuit `P' = VI = 160 xx 10 = 1600` watt
`(P)/(P') = (500)/(1600) = 0.31`