An arc lamp requires a direct current of 10A at 80V to function. If it is connected to a 220V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

Resistance of lamp by ohm's law, R = V/I = 80/10 = 8Ω
When inductor is connected in series and source is applied, V = IZ
V = I√(R² + (ωL)²)
Given, I = 10 A
for lamp to work, ∴ 220 = 10√(8² + (2 × π × 50 × L)²)
Solving, L = 0.0648 H