Question

How will you find the inductance of a choke coil needed to run an arc lamp with an AC source of 410V supply at 50Hz? The arc runs at 10 A current and has an effective resistance 40 ohm. [Ans:29mH]

Answer 1

Current required by arc lamp `10A`.
Let `Z` be the impedance of the arc lamp and choke coil together. Current `I` is given by
`I=410/Z=10A`
⇒`Z=41Ω` ....(1)

We know that Reactance of the choke coil
`ωL=2πf×L` .....(2)
Where `f` is the frequency of voltage source.

Also we know that in a LR circuit
`Z^2=R^2+(ωL)^2`
Inserting values of `Z` from (1) and given value of `R`

`41^2=40^2+(ωL)^2`

⇒`(ωL)^2=81`
Using (2)
`L=sqrt81/(2π×50)`
⇒`L=0.029H`, rounded to three decimal places.
or `L=29mH`