(Solved): Electrical AC circuit is given in Fig.1. Please derive the expression of the instantaneous current ...

Electrical AC circuit is given in Fig.1. Please derive the expression of the instantaneous current in the circuit and find its numerical expression if the instantaneous voltage is $v(t)=10\sqrt{2}\sin (10t)\mathrm{V}$ and $\mathrm{C}=0.1\mathrm{F}$ and ${\mathrm{L}}_1={\mathrm{L}}_2=0.15\mathrm{H}$. Show every step of your work. (Please note: Failure to derive the expression of the instantaneous current in the circuit will result in " 0 " (zero) marks for Q-1 even if the final numerical expression of the instantaneous current in the circuit is correct.) Fig.1 Electrical AC circuit is given in Fig.2. Please derive the expression of the equivalent impedance ${\mathrm{Z}}_{\text{eq }}$ in the input of the circuit. Use the result from derivation and calculate the value of the equivalent impedance $Z_{\text{eq }}$ for rectangular frequency $?=100\mathrm{rad}/\mathrm{s}$ if $\mathrm{C}=0.01\mathrm{F},{\mathrm{L}}_1=0.04\mathrm{H},{\mathrm{L}}_2=$ $0.03\mathrm{H}$ and ${\mathrm{L}}_3=0.08\mathrm{H}$. Show every step of your work. (Please note: Failure to derive the expression of the equivalent impedance ${\mathrm{Z}}_{\mathrm{eq}}$ in the input of the circuit will result in " 0 " (zero) marks for Q-2 even if the final numerical value of the equivalent impedance ${\mathrm{Z}}_{\mathrm{eq}}$ is correct.) Fig. 2