Question

time from t 0 ms to t 125 ms if the switches are controlled as shown in Fig. 2 The initial capacitor voltage is -9 V. Show all of your work. S4 R3 R1 S1 C1 + +R2 V2+ Fig. 1. Switched RC it. V19 V, V2-15 V, R1 4.7 kQ, R2 3.3 kQ, R3 kQ, C1 2.2 ?F. 2.2

What are the values of v(t) at times 12.5, 37.5, 62.5, 87.5, and 112.5 ms

Answer 1

Given that V_1 = 9v, t = 0ms to 125ms V_c = - 9V, V_2 = - 15 v R_2 = 3.3 k Ohm, C_i = 2.2 MF Part for determine the voltage across the capacitor So, Applying kVt to the above ckt - V_1 + R_1 (I) + 1/c integral I.dt = 0 So, rearranging the above equation we get. R_1 I + 1/c Integral.dt = V_1 By the shrt ck + the capacitor X = Rho (0) � Rho (Infinity) Determine Rho (0): \r\n here I = V_1 � V_c/R_1 = 9 � (-9)/4.7 k Ohm = 18/4.7 k Ohm = 3.88 mA & Rho (Infinity) = 0 We have to consider Rho (+) Rho (+) = Xe^-+ R_1 C_1 X = 3.83 mA = 3.38 times 10^-3 times e^-+ 14.7 k times 2.2 MF = 3.83 times 10^-3 e^-96.7 t We determine voltage across capacitor is V_c (+) = 1/c integral I.dt = 0 So, rearranging the above equation we