Answer
See answers.
Work Step by Step
Use equation 21–15, without a capacitive reactance. The inductor’s reactance is given by equation 21–11b.
a.
$$Z=\sqrt{R^2+X_L^2}=\sqrt{R^2+4\pi^2 f^2 L^2}$$
$$Z=\sqrt{(36\times10^3 \Omega)^2+4\pi^2 (50Hz)^2 (55\times10^{-3}H)^2}=3.6\times10^4\Omega$$
At this low frequency, the inductor has negligible effect.
b.
$$Z=\sqrt{R^2+X_L^2}=\sqrt{R^2+4\pi^2 f^2 L^2}$$
$$Z=\sqrt{(36\times10^3 \Omega)^2+4\pi^2 (3.0\times10^4 Hz)^2 (55\times10^{-3}H)^2}=3.7\times10^4\Omega$$