b
\(\mathrm{L}=0.7 \mathrm{\,H}, \mathrm{R}=220 \Omega, \mathrm{E}_{0}=220 \mathrm{\,V}, v=50 \mathrm{\,Hz}\)

This is an \(L - R\) circuit Phase difference,

\(\tan \phi=\frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}}=\frac{\omega \mathrm{L}}{\mathrm{R}}=\frac{2 \pi v \mathrm{L}}{\mathrm{R}}\)

\(\left[\mathrm{X}_{\mathrm{L}}=2 \pi v \mathrm{L}=2 \times \frac{22}{7} \times 50 \times 0.7=220 \Omega\right]\)

\(=\frac{220}{220}=1\) or, \(\phi=45^{\circ}\)

Wattless component of current

\(=I_{0} \sin \phi=\frac{I_{0}}{\sqrt{2}}=\frac{1}{\sqrt{2}} \cdot \frac{E_{0}}{Z}\)

\(=\frac{1}{\sqrt{2}} \frac{220}{\sqrt{\mathrm{X}_{\mathrm{L}}^{2}+\mathrm{R}^{2}}}=\frac{1}{\sqrt{2}} \cdot \frac{220}{\sqrt{220^{2}+220^{2}}}\)

\(=\frac{1}{2}=0.5 \mathrm{\,A}\)