Download presentation
Presentation is loading. Please wait.
1
實驗6: RC 和 RLC 電路(課本實驗21) 目的: 利用示波器觀察 RC 和 RLC 電路中電荷對時間之變化 A: RC電路
1. 電鍵 S 接到 a 點, R,C,電池 e0串聯 iR + q/C = R(dq/dt) + q/C = e0 q(t) = Ce0[1 – exp(-t/RC)] 電容器 C 充電, 時間常數 = RC 2. 充電到qmax, 電鍵S 接到b 點, R,C串聯 R(dq/dt) + q/C = 0 q(t) = qmexp(-t/RC) 電容器放電, t = = RC (鬆弛時間) q(t) = qm/e = qm/2.718 q(T1/2) = qm/2
2
B. LC 和 RLC 電路 原理: 電容器充電到 qmax,電鍵 S 接上, L,C 串聯
L(di/dt) + q/C = L(d2q/dt2) + q/C = 0 q(t) = qmcos[t/(LC)1/2] = qmcos0t (t = 0, q = qm) 電容器 C 電荷簡諧振盪(harmonic oscillation) 振盪角頻率: 0 = 1/(LC)1/2 但 R ≠ 0(電感器 L 線圈有電阻), 為 RLC 電路 L(di/dt) + Ri + q/C = 0 d2q/dt2 + (R/L)dq/dt + q/LC = 0 d2q/dt2 + 2·dq/dt + 02q = 0 R/2L 電容器C電荷阻尼振盪(damped oscillation)
3
1. b2 < w02 (R2/4L2 < 1/LC) q(t) = [qmexp(-bt)]cos(w1t) 角頻率 w12 = w02 – b2 > 0 振幅 qm(t) = qmexp(-bt) (令q(0) = qm, 相位 d = 0, 鬆弛時間 t = 1/b = 2L/R) 電容器C電荷較長週期(T1 > T0) 之次阻尼振盪 2. b2 = w02 (R2C/4L = 1) w12 = 0 (振盪週期T1 = ) 臨界阻尼(critical damping) 3. b2 > w02 (R2C/4L > 1) w12 < 0 (w1虛數,無振盪) 過阻尼(overdamping) For R, L, C, e0串聯 d2q/dt2 + 2b·dq/dt + w02q = e0/L = A q(t) = (A/w02)[1 - exp(-bt).cos(w1t)] (令d = 0)
![1. b2 < w02 (R2/4L2 < 1/LC) q(t) = [qmexp(-bt)]cos(w1t) 角頻率 w12 = w02 – b2 > 0. 振幅 qm(t) = qmexp(-bt)](http://slidesplayer.com/slide/14759794/90/images/3/1.+b2+%3C+w02+%28R2%2F4L2+%3C+1%2FLC%29+q%28t%29+%3D+%5Bqmexp%28-bt%29%5Dcos%28w1t%29+%E8%A7%92%E9%A0%BB%E7%8E%87+w12+%3D+w02+%E2%80%93+b2+%3E+0.+%E6%8C%AF%E5%B9%85+qm%28t%29+%3D+qmexp%28-bt%29.jpg "(令q(0) = qm, 相位 d = 0, 鬆弛時間 t = 1/b = 2L/R) 電容器C電荷較長週期(T1 > T0) 之次阻尼振盪. 2. b2 = w02 (R2C/4L = 1) w12 = 0 (振盪週期T1 = ) 臨界阻尼(critical damping) 3. b2 > w02 (R2C/4L > 1) w12 < 0 (w1虛數,無振盪) 過阻尼(overdamping) For R, L, C, e0串聯. d2q/dt2 + 2b·dq/dt + w02q = e0/L = A. q(t) = (A/w02)[1 - exp(-bt).cos(w1t)] (令d = 0)")
Similar presentations
