Transient Response in RCL Circuits I (7 marks) Consider a parallel RCL circuit, as shown. The switch was in the position shown for a long time, then thrown in the direction of the arrow at t = 0. VC VR R I + iL (a). Calculate VR, VC, and i for t < 0. (b). Calculate and wo for t > 0. (c). What is the damping regime for this circuit for t > 0? (d). Consider the resistor voltage VR for t>0. If the circuit is underdamped, we have: VR(t > 0) = exp(-(wot) [A cos (wat) + A2 sin (wat)], if the circuit is critically damped, we have: VR(t > 0) = (A1 + A2t) exp (-wot), 1 and if the circuit is overdamped we have: VR(t > 0) = A1 exp == + A2 exp As noted in the lessons, wd, T, and 72 are all obtained from ( and wo, found above. Regardless of the damp- ing regime, each expression for VR (t > 0) depends on two coefficients, written here as A and A2. Calculate these two coefficients for vR(t > 0) as appropriate for the values and damping regime found above. The components are defined based on your student number: R = (0,5) kn, L= (12) mH, c= C = (0.75) nF, I = (3.5) mA. Note: For some of you, ( will be very close to critical damping, but not exact. When deciding the damping regime, make sure is accurate to at least one decimal point. You can also leave with more decimal points if your ( is close to critical damping I will consider both answers (i.e. critically damped or just slightly under/overdamped) to be correct. For the majority of students, however, the damping regime is unambiguous regardless of how (is rounded.