Consider the expression for \(i(t)\) given by
\[
i(t)=\sqrt{2} \mathrm{I}_{\mathrm{rms}}\left[\sin \left(\omega t-\theta_{z}ight)+\sin \theta_{z} \cdot e^{-(\omega R / X) t}ight]
\]
where \(\theta_{z}=\tan ^{-1}(\omega L / R)\).

(a) For \((\mathrm{X} / \mathrm{R})\) equal to zero and infinity, plot \(i(t)\) as a function of \((\omega t)\).

(b) Comment on the dc offset of the fault current waveforms.

(c) Find the asymmetrical current factor and the time of peak, \(t_{p}\), in milliseconds, for \((\mathrm{X} / \mathrm{R})\) ratios of zero and infinity.