Chapter 8 Solutions - Soln0830 100922

Transcript

Chapter 8, Solution 30. The step responses of a series RLC circuit are v C (t) = [40–10e–2000t–10e–4000t] volts, t > 0 and i L (t) = [3e–2000t+6e–4000t ] m A, t > 0. (a) Find C. (b) Determine what type of damping exhibited by the circuit. Solution Step 1. For a series RLC circuit, i R (t) = i L (t) = i C (t). We can determine C from i C (t) = i L (t) = C(dv C /dt) and we can determine that the circuit is overdamped since the exponent value are real and negative. Step 2. C(dv C /dt) = C[20,000e–2000t+40,000e–4000t] = 0.003e–2000t+0.006e–4000t or C = 0.003/20,000 = 150 F.