(Solved): Please use the 7 step method to answer the following. Answer in full for a rating. Thanks! Step ...

Please use the 7 step method to answer the following. Answer in full for a rating. Thanks!

Step1. Use DC analysis methods to find \( \mathrm{v}_{\mathrm{C}}\left(0^{-}\right) \) Step2. Determine the time constant \( \tau=R C \) for \( t>0 \) Step3. Find the forced response \( f(\infty) \) Step4. Write the total response as \( f(t)=f(\infty)+\operatorname{Aexp}(-t / \tau) \) Step5. Use \( \boldsymbol{v}_{\mathrm{C}}\left(0^{-}\right) \)to determine the \( \mathrm{f}\left(0^{+}\right) \), then \( \mathrm{A}=\mathrm{f}\left(0^{+}\right)-\mathrm{f}(\infty) \) Step6. Find: \( A=f\left(0^{+}\right)-f(\infty) \) Step7. \( f(t)= \) final \( + \) [initial-final] \( \exp (-t / \tau) \) \( =\mathrm{f}(\infty)+\left(\mathrm{f}\left(0^{+}\right)-\mathrm{f}(\infty)\right) \exp (-\mathrm{t} / \tau) \) 1. (15pts) After having been in position 1 for a long time, the switch in the circuit below was moved to position 2 at \( t=0 \). Given that \( V 0=12 \mathrm{~V}, R 1=30 \mathrm{k} \Omega, R 2=120 \mathrm{k} \Omega, R 3=60 \mathrm{k} \Omega \), and \( C=100 \mathrm{mF} \), determine \( v_{\mathrm{c}}(\mathrm{t}) \) and \( i_{c}(\mathrm{t}) \) for \( t \geq 0 \).