a
\(36=I_{\text {ms }} R\)

\(36=\frac{120}{\sqrt{\mathrm{X}_{\mathrm{L}}^2+\mathrm{R}^2}} \times \mathrm{R}\)

\(\mathrm{R}=90 \Omega \Rightarrow 36=\frac{120 \times 90}{\sqrt{\mathrm{X}_{\mathrm{L}}^2+90^2}}\)

\(\sqrt{\mathrm{X}_{\mathrm{L}}^2+90^2}=300\)

\(\mathrm{X}_{\mathrm{L}}^2=81900\)

\(\mathrm{X}_{\mathrm{L}}=286.18\)

\(\omega \mathrm{L}=286.18\)

\(\mathrm{~L}=\frac{286.18}{376.8}\)

\(\mathrm{~L}=0.76 \mathrm{H}\)