Inductive reactance, \(X_{L}=20 \,\Omega\) at \(50\, \mathrm{Hz}\)

\(\because \quad X_{L}=2 \pi v L\)

\(\therefore \frac{X_{L}}{X_{L}^{\prime}}=\frac{v}{v^{\prime}}\)

\(X_{L}^{\prime}=\frac{v^{\prime}}{v} \times X_{L}=\left(\frac{100}{50}\right) \times 20\, \Omega=40 \,\Omega\)

Impedance, \(Z=\sqrt{R^{2}+\left(X_{L}^{\prime}\right)^{2}}=\sqrt{(30)^{2}+(40)^{2}}\)

\(=50 \,\Omega\)

Current in the coil, \(I=\frac{V}{Z}=\frac{200\, \mathrm{V}}{50\, \Omega}=4\, \mathrm{A}\)