ME $210$ Electronics & Systems Engineering Homework Problem: Energy$-$Storage Network Using Inductors $-100$ points

Question

Consider an energy$-$storage network for an electric company composed of the inductors shown in the following figure. Assume these inductors are initially charged and are connected to an electric load $($ex$.$ a house, hospital, school, etc.$)$ at $t=0.$

Tasks

Design parameter calculation:

Determine the type of components and connections are considered in the circuit.

Use the equivalent inductance method for series and parallel inductors to determine the value of the unknown inductor $L_2$ needed to ensure that the total energy delivered to the electric load is $80$ J $,$ assuming that $i_1(0)=4A,$ and $i_2(0)=-2A.$

Total current calculation:

Use the current$-$voltage relation for inductors to determine the total current $i(t)$ in the circuit assuming that $v(t)=50e^{-200t}mV$ over a $2-$hour interval.