a b c d

d

$ tan\phi = \frac{X_L}{R} = 1 $ $\Rightarrow R = X_L $ $ Z = 100\Omega = \sqrt {R^2 + X_L^2}=  X_L \sqrt 2$ $ X_L = \frac{100}{\sqrt 2} = 70.7 \Omega $ $ 2\pi fL = 70.7 \Omega $ $\Rightarrow L = \frac{70.7}{2000\pi} = 1.1 \times 10^{-2} henry$