Question

Derive a solution for the voltage across the capacitor C1 in Fig. 1 as a function of 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. 1. S4 R3 R1 S1 V1+ C1+ R2 V2+ yti Fig. 1. Switched RC circuit. V1-9 V, V2--15 V, R14.7 k2, R2-3.3 kQ, R3 2.2

Answer 1

1) Tiven: t 0ms to125ms Part i Ri S1 C1 To determine the voltage across the capacitor On applying KVL to the above circuit,

Rearranging the above equation, we get By short circuiting the capacitor Determine i(0), 4.7KSQ 18 4.7KO2 -3.83mA and 1(00)-0 Consider the expression for i(t), = 3.83 x 10-3 xe-t 47K×2.2nF = 3.83 x 10"ean Determining voltage across capacitor 396.7t (3.83x1098dr 2.2x10-5J 3.83 x 10-3 Ге-967t 2.2x106-96.7 -18e-96.7t 9+18e-96.7t

From the graph we can observe that, Switch will be closed for 0-25ms , 50-75ms Open for 25-50ms and after 75ms switch is open 2 S c (t) -2671 So at18 e 7 5 29

2S -96'가 46.7 2 S 16-7+ 7S -76-7 SD 22518 e -176-7 -483 5 -22S- -96、7 675 + 13e 947 (75 +

R3 2 R2

g.3k 3.31 2.2k vig Ri+K3 3.3 kx 2.2 K 3.3 K 2.2< oy ms 666.13 J 2.04M

2.i0 no 4 2.704o 2.701, 1 0 o 430, + 900,-岳を48 -34435