Question

2r() V and the capacitor initially stores zero energy. (a) Write the time-domain loop equation in terms of the current io). b) Obtain the s-domain representation of this integral equation. (c Solve for io. 50. The s-domain representation of the voltage source in Fig. 14.16 is V, (s)- İ V. The initial voltage across the capacitor, defined using the 200 mF i() passive sign convention in terms of the current i, is 4.5 V. (a) Write the time- domain integral equation that arises from application of KVL. (b) By first solving for l(s), determine the time-domain current İ(1) FIGURE 14.16

Answer 1

V_s (s) = 2/s + 1 BY KVL, v_s (t) = 1/c integral id t + i (t) R v_s (t) = 1/c integral i (t) dt + i (t) R convert into S-domain v_s (s) = 1/cs i (s) - v (0)/s + i (s) R v_s (s) = i (s)/cs - 4.5/s + i (s) 5 ohm 2/s + 1 = i (s) [1/cs + 5] - 4.5/5 2/s + 1 = i (S) [1/200 times 10^- 3 times s + 5] - 4.5/5 = i (s) [1 + s/0.25] Therefore i (s) = [2/s + 1 + 4.5/5] times 0.25/s + 1 = 0.4/(s + 1)^2 + 0.9/s + 1 Therefore i (s) = 0.4/(s + 1)^2 + 0.9/s + 1