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]

1 Answer
A08
Aug 29, 2016

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#

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