An inductance of negligible resistance whose reactance is $22\mathrm{\Omega }$ at 200Hz, is connected to 200 V, 50Hz power line. Then value of inductance is ____ (in henry)

Reactance depends on the frequency of source, but inductance is constant and independent of frequency.

When frequency $\mathrm{f}=200 \mathrm{Hz}$, ${\mathrm{X}}_{\mathrm{L}}=22 \mathrm{\Omega }$.

$\therefore {\mathrm{X}}_{\mathrm{L}}=2\mathrm{\pi fL} \Rightarrow \mathrm{L}=\frac{{\mathrm{X}}_{\mathrm{L}}}{2\mathrm{\pi f}}=\frac{22}{2\mathrm{\pi }\times 200}=0.0175 \mathrm{H}$.