Chapter 2.

1. Chapter 2. Electrical Components and Circuits Components

2. Electrical Components: Electric current; the motion of a charge through a medium. Electric units; the unit of charge (or quantity of electricity) C(coulomb) → 0.001111800g of silver ion → Charge for reduction to silver metal. 1Faraday = 9.649 x 104 coulombs 1Faraday ; Deposition of Ag 107.868g of 1 gram equivalent ↳ (6.02 x 1023 charged particle), I = dQ/dt (Q : charge, A : ampere)

3. 2A Direct-Current Circuits and Measurements • Direct current; Q -> proportional to time. • Alternating current; Q -> periodically change. • 2A-1 Laws of Electricity • Electrical potential (V) ; 공간의 한 점에서 다른 점까지 1개의 전하를 • 움직이는데 는 일. • V ; volt → joule/conlomb (W/Q = V) = (I․R) • R ; ohm → R의 단위 Ω(R = ρℓ/A) ↳ Ohm's law • G ; 저항의 역수(electrical conductance) Ω-1, S • I ; Ampere • P ; Electrical power. joules/sec, W • P = dw/dt = V․dQ/dt = V․I • P = (I․R)․I = I2R. joule's law

4. Kirchhoff's Laws - Current low ; the algebraic sum of currents around any point in a circuit is zero. -Voltage low ; the algebraic sum of the voltages around a closed electrical loop is zero. Power Law P = IV P = I2R = V2/R

5. 2A-2 Direct-Current Circuits • Series circuits Fig 2-1. A battery, a switch, & three resistors in series.

6. ⓐ 점 D에서 kirchhoff's law 적용 I4 - I3 = 0 or I4 = I3 , I3 = I2 at point C. * the current is the same at all points I = I1 = I2 = I3 = I4 ⓑ Voltage low V - V3 - V2 - V1 = 0 or V = V1 + V2 + V3 by ohm's law V = 1(R1 + R2 + R3) = IReq ∵ Req = R1 + R2 + R3 IR1 = V1 , V2 = IR2 , V3 = IR3 V1 = I1 R1 = IR1 (2-9)

7. Voltage dividers ; Fig 2-3 a → series connection of resistor ↳ discrete increment

8. - Potentiometer; continuously variable

9. 2) Parallel Circuits Resistors in parallel at point A Kirchhoff's current law to point A I1 + I2 + I3 - It = 0 It = I1 + I2 + I3

10. - Applying Kirchhoff's voltage law I1 = V/R1 V - I1/R1 =0 V= I1R1 I2 = V/R2 V - I2/R2 =0 V = I2R2 I3 = V/R3V = I3R3 It = I1 + I2 + I3에 위식 代入 V V V V It = --- = --- + --- + --- V1 = V2 = V3 = V Rp R1 R2 R3 so that 1 1 1 1 --- = --- + --- + --- Rp R1 R2 R3 G=1/R Gp = G1 + G2 + G3 - Parallel resistances create a current divider. I1 V/R1 1/R1 G1 Rp G1 --- = ----- = ----- = --- or I1 = It --- = It --- It V/Rp 1/Rp Gp R1 Gp

11. (Ex. 2-1) Calculate a) the total resistance, b) the current from the battery, c) the current present in each of the resistors, and d) the potential drop across each of the resistors.

12. 1 1 1 • ( --- + --- ) = --- • R2 R3 R2,3 • 1 1 1 3 • --- = --- + --- = --- R2,3 = 13.3Ω • R 20 40 40 V 15 b) The current ; V = I·R I = --- = ----- = 0.67A Rs22.3 c) V = V1 + V2 + V3 V1 = I1R1 = 6.03 I = I2 = I3이므로 9.0 V1 = 15 x ------------ = 6.0V (9.0 + 13.3) 13.3 V2 = V3 = V2,3 = 15 x ------ = 9.0V 22.3 d) R1에서 I1 = I = 0.67A I2 = 9.0/20 = 0.45A I3 = 9.0/40 = 0.22A

13. 2A-3 Direct Current, Voltage, and Resistance Measurements Digital Volmeters and Multimeters D’Arsonval moving-coil meter  Digital Voltmeters and Multimeters. Power Source, display, A/D converter

14. The Loading Error in Potential Measurements The Loading Error in Current Measurements

15. See equations 2-19 and 2-20

16. 2B Alternating current Circuits Alternating voltage and current: 시간에 따라 방향과 크기가 변화하며 똑같은 변화가 계속 반복되는 전압 또는 전류. (the simplest alternating waveform is sine-wave volt or current.) - Period (Tp); The time required for the completion of one cycle - Cycle; one complete revolution - Frequency(f) [HZ]; time number of cycles per second f = 1/tp (2-21)

17. 2B-1 Sinusoidal Signals The AC: produced by rotation of a coil in a magnetic field. A pure sine wave → 일정한 각속도로 회전 하는(시계방향) IP의 vector로 표시. (여기서 Ip : amplitude.) 주기 t 내에 2π radian 의 속도로 회전 할 때 ω = 2π/tp = 2πf Any time t에서 instantaneous value → Vpsin ωt Vp; maximum or peak voltage; the amplitude 순간 전류 : ⅰ= Ip sin ωt = Ip sin 2πft 순간 전압 : v = Vp sin ωt = Vp sin 2πft Out of phase by 90o Phase difference : phase angle(φ) 일반식 ; ⅰ= Ip sin(ωt + φ) = Ip sin(2πft + φ)

18. Sinusoidal signals ;

19. 일반식 ; ⅰ= Ip sin(ωt + φ) = Ip sin(2πft + φ)

20. (rms current & voltage) ; DC, AC의 크기비교 ; 두 전류에 의한 저항에서 야기되는 Joule heat DC = the effective value of a sinusoidal, current Report, heating effect of AC is calculated by averaging I2R losses even complete cycle

21. 1 Hz 중의 평균 열손실 = 직류일 때의 ohm손실 square wave ; 파행도 1.00 파고율 1.00 sine wave ; 파행율 = 1.11 파고율 = 1.41 삼각파 ; 파행율 = 1.15 파고율 = 1.73

22. 2B-2 Reactance in Electrical Circuits Reactance - capacitance : capacitor inductance : inductor Use ; ① converting alternating current to DC or the converse ② discriminating among signals of different frequencies or separating ac & dc signals. Capacitors 구성; a pair of conductors separated by a thin layer of a dielectric substance

23. Position 1 Position 2 Figure 2-8. (a) A series RC circuit. Time response of circuit when switch S is (b) in position 1 and (c) in position 2.

25. 2B-3 Capacitors and Capacitance 1) Capacitance ① a momentary current ② current ceases → to be changed ③ switch을 2로 discharge. Capacitor ① 과 ② 사이에서 switch off; 전하가 저장 The quantity of electricity Q → 판 넓이, 모양, 공간, 절연체 의 유전상수에 의해 결정 (one-farad capacitor stores 1 Q of charge per applied volt.)

26. Rate of current and voltage changes in an RC circuit By Kirchhoff 의 voltage law Vi = vc + vR Vi = constant Vi = q/C + iR : Instantaneous voltage across the resistor

27. : Ohm’s law to eq. 2-35 Phase relations between current and voltage in an RC circuit Fig.2-8c

28. Rate of Current & Potential Change across RL circuit. RC circuit와 동일한 방법으로 처리 vR = Vi( I - e-tR/L ) vL = Vi e-tR/L L/R : time constant

29. 2B-4 Response of Series RC Circuits to Sinusoidal Inputs signal

32. Ip

33. (1/ωC = Xc) At sufficiently high frequencies & capacitance, φ become negligible & I & v are in phase. 1/ωC은 저항 R에 비해 무시 可. ↳ 전류가 잘 흐름 At very low frequencies, the phase angle; π/2

34. Voltage, current and phase Relationships for series RL circuit

35. Figure 2-9 90o phase difference between v and i

36. Capacitive & Inductive Reactance ; impedance Xc = 1/wC = 1/2πfC XL = wL = 2πfL Impedance Z ; 교류회로에서 전압과 전류의 크기의 비(직류회로의 저항에 해당) At, RC circuit Z = √R2 + Xc2 Z = √R2 + XL2 Ip = Vp/Z 저항과 차이점 : ① frequency dependent ② current와 voltage 사이에 phase difference

37. 1 Faraday ; 1 V의 전위치에 의해 양극판에 축적된 전하의 크기가 1 C일 때의 capacitance.( μF, PF) V = 1/C ∫idt = 1/C∫ Ip sin wt dt = -1/wc Ip cos wt = 1/wc Ip sin(wt - π/2) ∵ Vp = 1/wc Ip, V = (1/wc) I 1/wc = Xc → capacitive reactance 단위 Ω Xc = -1/wc, V =│Xc│I

38. 2) Inductance Coil에 직류 통과 → 자기작용에 의한 유기전압으로 인해 다른 전류 발생 자기장이 변화 → emf 발생 V = -L(di/dt) - : 전류의 방향과 반대 L : inductance [Henrys] → [H] 1 Henry : 전류변화속도가 one A/1 sec 일 때 1volt의 전압 발생, μH ～ H 범위 V = L(d/dt)(Ip sin ωt) = ωLIp cosωt = ωLIp sin(ωt + π/2) 전압의 위상이 전류보다 π/2 앞선다. V = ωLI 여기서 wL을 inductive reactance라 한다. XL= 2πfL 직류만 통과, 교류 불통 (저주파 chopping coil) 직렬 연결 : L = L1+ L2+ L3

39. Figure 2-10

40. <Vector diagrams for Reactive Circuits> V가 ⅰ보다 90°늦다. at capacitance V가 ⅰ보다 90°빠르다. at inductance Z = √R2 + (XL - Xc)2 Z = √R2 + Xc2 , φ = -arctan Xc/R Z = √R2 + XL2 , φ = -arctan XL/R Z = √R2 + (XL+ Xc)2 φ = -arctan (XL+ Xc) / R(XL> Xc 인 경우) ex) ① peak current ② voltage drop Z = √(50)2 + (40 - 20)2 = 53.8Ω Ip = 10 v/53.8 = 0.186A Vc = 0.186 x 20 = 3.7V VR = 0.186 x 50 = 9.3V VL = 0.186 x 40 = 7.4V

41. 2B-5 Filters Based on RC Circuits High-pass & Low-Pass Filters RC & RL circuits → low f component를 지나는 동안 high-f signals을 낮추기 위해 filter로 사용 (low pass filter) or 역이 성립. ① RC circuit에서 high-pass filter Vo : across the resistor R

42. (a) high pass filter and (b)low-Pass Filters

43. Low pass filter

45. 2B-6 The Response of RC Circuits to Pulsed Inputs <Resonant Circuits> impedance Z가 최소 즉 XL = Xc일 때 전류 I = E/Z = E/R ↳ the condition of Resonance resonant frequency fo ; 1/2πfoC = 2πfoL ∵ fo = 1/2π√LC ex) (Vp)i = 15.0 V (peak voltage), L = 100mH, R = 20Ω, C = 1.200μF.

48. 2B-7 Alternating Current, Voltage, and Impedance Measurements Parallel Resonance Filters Xc = XL fo = 1/2π√LC Z of the parallel circuit Z = √R2 + (XLXc/Xc-XL)2 At parallel circuit at resonance → Z는 최대 → maximum voltage drop 生 → tank circuit Behavior of RC Circuits with pulsed inputs RC 회로에 pulse 加 → various form (with of pulse time const) 사이의 관계에 의존 Simple Electrical Measurements Galvanometers → DC의 전류, 저항 측정원리 : the current in duceol motion of a coil suspended in a fixed magnetic field. ⇒ D'arsonval movement or coil. He Ayrton Shunt : to vary the range of a galvanometers p29. 예제 참조☆ measurement of current and voltage.

50. 2C Semiconductors and Semiconductor Devices • Semiconductors • Electronic circuits contain one or more nonlinear devices, such as transistors, semiconductor diodes, and vacuum or gas-filled tubes. • Nonlinear components ; rectification (from ac to dc ), amplitude modulation, or frequency modulation. • Vacuum tube (in the 1950s)→ Semiconductor based diodes and transistors → integrated circuits (Tr, R, C & conductor) • -Semiconductor 장점 : low cost, low power consumption, small heat generation, long life and compactness.