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Question

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

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Solution

## We know thatIrms=Vrms√R2+ω2L2∴10=160√25+(2π×50×L)2or25+(100πL)2=162⇒25+105L2=256⇒L=√231105=0.05HLet RA be the additioal resistance required for operating the arc lamp with 160V DC source, then10=√160RA+5⇒RA+5=16∴RA=16−5=11ΩAC power consumed by the arc lamp =VrmsIrmscosϕ=Pacwhere cosϕ=RZ=R√R2+ω2L2=516Pac=160×10×516=500WNow DC power consumed by arc lampPdc=160×10=1600WPower loss =1600=500=110W=68.75%

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