(Solved): 1) Consider the following circuit a) Find the time domain current \( i_{o}(t) ...

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1) Consider the following circuit a) Find the time domain current \( i_{o}(t) \) using phasor approach (40 points) b) Find the time domain current \( i_{0}(t) \) using Laplace transform approach. Assume that there is no initial current in transformers and initial voltage on capacitors ( 40 points). c) Determine the transfer function \( H(s)=\frac{I_{0}(s)}{V_{s}(s)} \), where \( I_{o}(s)=\mathcal{L}\left[i_{0}(t)\right] \) is the Laplace transform of \( i_{0}(t) \) and \( V_{s}(s)=\mathcal{L}\left[\mathrm{v}_{s}(t)\right] \) is the Laplace transform of \( v_{s}(t) \) (10 points). d) Determine the inverse Laplace transform \( h(t)=\mathcal{L}^{-1}[\mathrm{H}(\mathrm{s})] \) (10 points)