BlockSpring Oscillator LC Oscillator 31 4 Damped 31

Block-Spring Oscillator LC Oscillator(§ 31 -4) Damped § 31 -5 微分方程式(31 -24) 解 (31 -25)

Damped § 31 -5 過程 Home Work： • 推導eq. 31 -24, eq. 31 -25(和§ 15 -9 強迫 振盪比較) • 寫出從eq. 31 -26, 到eq. 31 -27之課本的 內容 LC Oscillator(§ 31 -4)

Phasor (上學期教過的, traveling wave) 橫座標是 x

§ 31 -8三種電路 • 電阻性負載 (a resistive load) Fig. 31 -8 V R = IR R • 電容性負載 (a capacitive load) Fig. 31 -10 – 容抗(capacitive reactance) XC = 1 / (ωd C) (31 -39) V c = Ic X C • 電感性負載 (a inductive load) Fig. 31 -12 – 感抗(inductive reactance) XL = ω d L (31 -49) V L = IL X L • see Table 3 -2 • Sample Problem 31 -4～ 31 -5 – Home Work ：Problem 29 (Ch 31)、 Problem 31 (Ch 31)

電阻性負載 (Fig. 31 -8&9) 電動勢ε(t) = εm sinωd t 電流 i(t) = I sin (ωd t －ψ) A resistive load • ε(t) - v. R(t) =0 • v. R (t) = εm sinωd t =VR sinωd t • i. R (t) = v. R (t) /R = (VR / R) sinωd t =IR sin (ωd t －ψ) ¨ ψ = 0 o (Fig. 31 -9) ¨ V R = IR R (31 -33) 例題31 -3

電容性負載 (Fig. 31 -10) 電動勢ε(t) = εm sinωd t a capacitive load • ε(t) - v. C (t) =0 • v. C (t) = εm sinωd t =VC sinωd t • q. C (t) = C v. C (t) = C VC sinωd t • i. C (t) = d q. C (t) /dt =ωd CVC cosωd t = ωd CVC sin (ωd t + 90 o) = IC sin (ωd t－ψ) 電流 i(t) = I sin (ωd t －ψ) u IC = ωd CVC = VC / XC u ψ=－90 o (Fig. 31 -9) u V C = IC X C (31 -42) u XC =1/(ωd C ) (31 -39) Home Work： 例題31 -4

Sample Problem 31 -4 (page 840) C = 15 μF，εm = 36 V， fd = 60 Hz (a)寫出 v C (t) 的表示式及其振幅 VC。 • VC= εm = 36 V • v. C (t) = ε (t)=εm sinωd t = VC sinωd t =(36 V) sin(120π t ) (b)寫出 i C (t) 的表示式及其振幅 IC。 • IC = 0. 203 A • i C (t) = Ic sin(ωd t-ψ) = (0. 203 A) sin(120π t + π/2) Home Work： (Check point 4)

Sample Problem 31 -5 (page 842) L = 230 m. H，εm = 36 V， fd = 60 Hz (a)寫出 v L (t) 的表示式及其振幅 VL。 • VL= εm = 36 V • v. L (t) = ε (t)=εm sinωd t = VL sinωd t =(36 V) sin(120π t ) (b)寫出 i L (t) 的表示式及其振幅 IL。 • IL =(VL/XL) 0. 415 A • i L (t) = IL sin(ωd t-ψ) = (0. 415 A) sin(120π t - π/2) Home Work： (Check point 5) • v. L (t) = VL sinωd t (31 -45) • 如果 fd 增加為 120 Hz， VL 及 IL 會增加、減少還是不變？ • • i. Fig = IL sin (ωd t－ψ) (31 -51) L (t) 31 -13(a)(b)會有什麼改變？

Fig. 31 -14

Fig 31 -14 • • Check point 6 例題： Sample Problem 31 -6 (page 847) Home Work：Problem 39 & Problem 41 Question 9, 10, 11, 12

• 9. Figure 31 -23 shows the current i and driving emf for a series RLC circuit. (a) Does the current lead or lag the emf? (b) Is the circuit's load mainly capacitive or mainly inductive? (c) Is the angular frequency ωd of the emf greater than or less than the natural angular frequency ω? • 11. Figure 31 -25 shows the current i and driving emf for a series RLC circuit. Relative to the emf curve, does the current curve shift leftward or rightward and does the amplitude of that curve increase or decrease if we slightly increase (a) L, (b) C, and (c) ωd ?

Sample Problem 31 -6 (c)(d)(e) 請算出振幅εm, VR, VC, VL 的大小 ψ= -24. 30 請畫出 phasor圖