Question

2 First-Order RC Circuit: Natural Response The switch in the circuit in Figure 2 has been in position for a long time. At t = 0, the switch moves to position (the switch opens) and stays there. Assuming that V. > O for the constant voltage source, (a) find vc(0-), vc(0+), ic(0-), and ic(0+); (b) find vc(t) when t 20 (if you want, you can write vo(t) by circuit inspection; you don't need to show the differential equation); and (c) sketch vo(t) when t > 0 (assume V. > 0). Note: the answers to items (a), (b) and (c) can only use the circuit constants Vo, Ri, R2, and C, and the time variable t. xt=0 ict) + uc(t) obat V. O R2Z Figure 2. First-order RC circuit.

Answer 1

delt) Initially switch was at position for a long time and at t=0 it was thrown at position - ② (a) After the long time when switch was at position - @ capacitor will act as open circuit. : Velo) = R2 . Vo voit. Vc (6) Ri+R2 li and Acco) = oA. at tot since capacitoy does not allow sudden change in voltage . Vclot) = R2 RHR₂ . volt. and (ot) = Vc 10) R₂ V. iclot) = amp. R,+R₂

(6) Velt) zo Velt) = Vecco) + [vé (o) - Vecm]e % ot[vc (o)- o] R26 Velt) = So Wolt the is initial volt will be at to which Vo R2 Ri+R2 at t=00 which is ov and volt will be final (C) Graph of Velt) for tzo :- Velt) Vo R2 Ri+R2 Veloft . -:- E=RC E=2RC