Question

An RC circuit is shown. The equivalent capacitance for the capacitor network is Cac = 12 uF. The equivalent resistance for the resistor network is Rce = 800 12 The capacitors are initially uncharged, and the switch S is closed at t = 0. a) Find C3. [4 points] b) Find R1: [4 points] c) Find the current i(0) in the circuit at t= 0. [4 points] d) Find Vac in the circuit at t = 00. [3 points] e) Find the charge on C3 at t = 00. [4 points] f) Find the time constant, T. [2 points] g) Find the current i(2T) the circuit at t = 27. [4 points] a C = 5 uF b cz C, = 20 uF S C 12 V R d Rz = 1200.12 R, = 300 12 e

Answer 1

a) Cac CI+cz 12- a(z Cita 3 12 V R , = 12UF and Cae = GCZ +z = 12 let (,=54F Ť C3= 12 5420 - 8 le F :C3 25 so C3=8MF (2=2046 Anso b.) Ree = 800 Ree = (Rz +R) X Rę Ri+ R2 R3 R3=12000 9800 = (R,+300) 1200 Ri +300 - 2 3 Rit 1500 R +1500 * 3R,+ 900=2R, +3000 » R, = 21002 Ans. At t=0 V 200 = 0.015 A 800 Ans. a) circan't so Ables long time i=0 through 810 - R2=30on 1200 < 12 0 21 Rec Vac = ? at t=0 Vac = 12V Ans. At t= c. 92- C&V= 8H5X12 = 964C Ans fu = 9.6x10² sec r = Re- Reex Cac=800x 12x10 p=9.6x103 sec Ans. 8.) 2Ñ & 2 Recall - ple q= cvci-e tec) 4 i = ţzte i (=24) = ☆ z s. 2(1=29) = too 12 e² ²=0.11A Ans.