(Solved): (50 points): The voltage vR from the circuit below is to be solved in two ways using s-domain ci ...

(50 points): The voltage $v_R$ from the circuit below is to be solved in two ways using s-domain circuit analysis. You may assume that the circuit has reached steady-state prior to moving the switch at $t=0$. (i) (10 points) Draw the $s$-domain circuit for $t?0$. (ii) (15 points) Solve for $V_R(s)$ (the Laplace transform of $v_R$ ) using mesh analysis. Find $v_R$. (iii) (5 points) Sketch the poles of $V_R(s)$ in an s-plane diagram. (iv) (10 points) Find the Thevénin equivalent $s$-domain circuit as seen by the $10?$ resistor marked with ' $v_R$ '. (v) (10 points) From the circuit you found in (iv), use the s-domain voltage divider formula to solve for $V_R(s)$ and finally $v_R$.