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

Here, `E_(v)=160V,v=50 Hz. R=5Omega, I_(v)=10A, L=?`
`Z=(E_(v))/(I_(v))=(160)/(10)=16Omega`
As `R^(2)+X_(L)^(2)=Z^(2) therefore X_(L)=sqrt(Z^(2)-R^(2))=sqrt(16^(2)-5^(2))=sqrt(231)=15.2` ohm
As `x_(L)=omega_(L)`
`L=(X_(L))/(omega)=(X_(L))/(2 piv)=(15.2)/(2xx3.142xx50)=4.84xx10^(-2)H`
If choke coil is not to be used, additional resistance required.
`R'=Z-R=16-5=11ohm`
Addtional power loss in second case `=I_(v)^(2)K'=10^(2)xx11=1100` watt
In 1st case, when choke coil is used, power loss=zero.