东南大学电工电子学试卷.doc

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1、东 南 大 学 考 试 卷（A卷）自 觉 遵 守 考 场 纪 律 如 考 试 作 弊 此 答 卷 无 效学号 姓名 密封线课程名称电工学考试学期11-12-2得分适用专业机械工程及自动化考试形式闭卷考试时间长度120分钟1)Birds routinely land and relax on power lines which carry tens of thousands of volts of electricity. Explain why these birds do not get electrocuted. (6 pts)The resistance of the air is to

2、o large for current to flow from the line to the bird to the ground.Alternately, the resistance is too large for current to divert from the wire, into the bird, and then back into the wire. It is not because of wire insulation. Birds could land on uninsulated wires justfine. 6 pts for right answer.

3、1 pt for something vaguely correct.2) Suppose your car battery is dead, and you need to charge it using another cars battery. You have a pair of cables电缆which you can use to connect the terminals终端of the batteries. In order to charge your car battery, should you connect the same terminals (positive

4、of one battery to the positive of the other, and the same with the negative) or the opposite terminals (positive of one battery to the negative of the other battery)? Why did you choose this configuration配置；结构? (6 pts)First note that real batteries have internal内部的resistance, so the universe领域will n

5、ot explode爆炸if you directly connect two car batteries. Next, if the opposite terminals are connected, then P=VI and common sense tells us that both batteries will be supplying power, and the internal resistances will be consuming消耗power, so clearly no power is being delivered递送by either battery. If

6、the same terminals are connected, then we can see that if one battery is of a higher voltage than the other, it will provide power to theother battery. Key to this realization实现is to know that battery voltages drop下降；终止as the battery is depleted耗尽的. 6 pts for right answer. 2 pts if you try to say th

7、ere is no current if two batteries are connected + to+ because voltage sources are perfectly balanced.3) A standard procedure for testing the internal resistance of a battery is the “dual双重的pulse脉冲” test. We first attach an ideal 5 mA current source between the terminals of the battery, so that curr

8、ent flows in the usual direction (positive to negative), and measure the voltage across the battery terminals. We then remove the 5 mA source, and attach an ideal 505 mA current source instead,and again measure the battery terminals. (6 pts)i.Suppose that we find a 1.485V voltage with the 5 mA sourc

9、e, and a 1.385 with the 505 mA source, what is the internal resistance?Easy way to solve these is to subtract减去；扣掉 2nd from first, giving , or . 3 pts for right answer. 2 pts if sign error or algebra 代数学mistake.ii. Assuming the battery is perfectly linear 线型的(i.e. accurately modeled 模式化；被效仿by a Thev

10、enin 戴维宁 equivalent), is it possible to find the voltage provided by the battery with no load attached using the data above? If so, what is it? If not, why not?Plug塞住；用插头将与电源接通 in to one of our equations above, e.g., giving , or finally . If you did it with the current source the other way, you shou

11、ld still have gotten 1.486V. 3 pts for right answer.Find the Thevenin or Norton equivalent circuit model.(12 pts ). (6 pts )(6 pts )Find the Voltage v and the currents i1 and i2 for the circuit shown below. (10 pts )SolutionLabel标注 the meshes；网状物:Since i3=2 it is not a variable.Writing KVL around th

12、e first mesh:24*(i2-i3) + 12*i1 = 0Writing KVL around the second mesh:12*i2 + 6*(i2 i3) = 0Substituting代替，取代 for i3 and rearranging36*i1 = 4818*i2 = 12Namelyi1 = 4/3 Ai2 = 2/3A7. Find the current i for the circuit shown below (10 pts )SolutionZeroing the 1A source givesBy the current division princi

13、ple, the contribution of the 2A source to i1 is2*(-1/30) / (1/30+1/5) = -2/7A.Zeroing the 2A source givesBy the current division principle, the contribution of the 1A source to i1 is1*(1/15)/(1/15+1/20) = 4/7A.Hence i1 = 4/7-2/7 = 2/7A.Find the Thevenin and Norton equivalent circuits across terminal

14、s a and b for the following circuitWith an open circuit across terminals a and b the current through the 20 resistor must be 0.5ix and the voltage across it is then 10ix. ByKVL we also get30V = 5ix + 10ixSo ix = 2A and we calculateVTH = 10ix = 20VTo find RTH we zero the independent独立的 source to get

15、the circuit in Figure 4.We wish to determine what resistance this circuit is equivalent 等价的to acrossthe terminals a and b. One way to do this is to imagine connecting anindependent voltage source of voltage VS across the terminals and findingthe current drawn from this voltage source. We therefore c

16、onsider thecircuit in Figure 5.KVL gives5ix = VS ix = VS/5 A (1)KVL also gives20i1 = VS i1 =VS/20 (2)KCL givesi = i1 + 0.5ix ix = i1 0.5ix (3)Plugging (1) and (2) into (3) yieldsi =VS/20+VS/10=3VS/20Eventually,RTH =VS/i=20/3 The Thevenin equivalent circuit is depicted描述； in Figure 6.From this we get

17、 the Norton equivalent circuit in Figure 7 where we usedWe could have also determined IN by applying a short circuit across theterminals a and b and computing 计算；处理the current through the short circuit短路.This involves analyzing the circuit in Figure 8. Here we have by KVL5ix = 30V ix = 6AThis gives,

18、 by KCLi = ix 0.5ix = 0.5ix = 3Awhich matches the earlier calculation计算；估计.Suppose that v1(t) = 80 cos (t) and v2(t) = 60 sin (t). Use phasors相量 to reduce the sum vs(t) =v1(t) + v2(t) to a single 单一的term of the form Vm cos (t +). Draw a phasor diagram, showing V1, V2, and Vs. State the phase relatio

19、nships between each pair of these phasors. (16 pts )The phasor corresponding tov1(t) = 80 cos (t)isV1 = 800 = 80Equivalently, we get forv2(t) = 60 sin (t) + 60 cos (t /2)the phasorV2 = 60/2 = j60To find the sum using phasors we add the complex numbers which yieldsV = V1 + V2 = 80 j60 = 100ej arctan

20、3/4This corresponds符合，一致 to the time signalvs(t) = 100 cos (t jarctan3/4)The phasor diagram is depicted描述 in Figure 2.Note that V1 leads V2 by /2 and leads Vs by arctan反正切 ( 4/3 ).Find an expression 表达式 for v(t) of the form Vm cos (t +) when v(t) = v1(t) + v2(t) + v3(t) + v4(t) withv1(t) = 20 sin (t

21、)v2(t) = 20 cos (t +/6)v3(t) = 20 sin (t +/3)v4(t) = 10 cos (t)Use phasors. (6 pts )Solution:The phasors corresponding 相应的 to each component 成分；组件；电子 元件signal are given in Table表格 1. The complex numberequivalent 复数等效to each phasor is given as well. Adding all complex numbers giveswhich corresponds t

22、o the phasorwhich can be transformed变形 into the time signalFind the complex impedance阻抗 in polar form 点斜式 极坐标形式 极形式of the network shown below for = 10001/s , = 20001/s ,and = 40001/s . (6 pts )(5 pts)Both capacitors电容器 and inductors电感器 can be used to store energy for use later. Capacitors, though, a

23、re far more popular for energy storage than inductors, because they are easier to keep charged带电荷的 带电的. In lab, for example, you can easily connect up a capacitor to a battery, disconnect it from the source, carry it around in your pocket to grab lunch午餐, go back to lab, and then find that its still

24、 holding a charge even after a long time. Explain why this is relatively difficult with inductors.(5 pts) If youve ever had the batteries on a flash light闪光灯；手电筒 run out,you know that as soon as the light starts dimming调光；变暗,your battery will very soon be dead.This is because a battery supplies its

25、maximum voltage峰点电压 until right before it is depleted耗尽的.On the axis 坐标轴on the left,I have plotted标绘的 the brightness亮度 辉度 of a battery powered flashlight over the life of the battery.We can also power a flashlight using a capacitor.Assuming the brightness of a bulb 电灯泡is proportional比例的 to the volta

26、ge across it,on the right axis,draw (qualitatively定性地) the brightness vs. Time for a capacitor powered flashlight.Draw so that brightness is 1 at time=0,and has dropped to at least 0.1 by time=1.We just want the shape形状,not necessarily the exact values.c) (5 pts) A student is not satisfied with the

27、amount of energy stored in his one-capacitor circuit. He wants to store more energy, so puts 10 capacitors in series串联 and charges them with a single voltage source. Is this a good idea? Why or why not?Find the Thevenin equivalent 戴维南定理 of the circuit电路 below at the two terminals on the far right:e)

28、 Find the Thevenin equivalent of the circuit below between terminals and Think about the various algorithms算法 weve used to find Thevenin equivalents.If you get stuck被困住了,complete the rest of these tricky 棘手的 复杂的problem and come back to this one and maybe some inspiration will reach you:For the circu

29、its below, please find expressions for the specified voltage 表达式指定的电压over the indicated time 表示时间ranges in terms of the circuit parameters电路参数. Plot绘图 the waveform 波形图on the provided axes轴线, and clearly identify. 确定 the key parameters参数 in your graph图表. (3A) Consider the circuit of Fig. 4. The switc

30、h is open for t 0, closed for 0 t -1. The switch is open for t O on the axes below. Using the circuit parameters R1, R2, C, and Vo,indicate on your sketch (i) the initial value初始值 ic(Ot), (ii) the final value ic(oo), and (iii) the time constant时间常数. Problem 1F: 5 points The capacitor in the circuit

31、in Figure 6 has an initial 初始 最初的 voltage VO on its terminals at t =0 when a step of voltage Vu(t) is applied at t = 0. Find an expression for the voltage across the capacitor vC for t 0. Consider the current divider circuit分流电路 shown below:1a. How many branches分支 are there in the circuit?1b. How ma

32、ny nodes节点 are there in the circuit?2. Derive an expression派生一个表达式 for the output current 输出电流(Iout, shown above) as a function of theinput current (Iin) and the two resistors (R1 and R2). Use any technique youd like.3. How should the resistors be chosen such that twice as much current flows through

33、R1 compared to R2?4. Using the equation 方程 等式you obtained in #2, show what happens to Iout输出电流 if R2 is replacedwith a short circuit (i.e. R2 = 0). Repeat if R2 is replaced with an open circuit.(think about what R2 should be replaced with here)Now suppose the following values are used: Iin = 3 A, R1

34、 = 5 W, R2 = 20 W, and we wish to find the Thevenin equivalent circuit across the two indicated terminals below:5. Find Voc and Isc across the two terminals indicated on the circuit.6. Draw the Thevenin equivalent circuit for the two terminals indicated above.7. Suppose a load is now attached across

35、 the two terminals of the Theveninequivalent circuit:a. Write an equation for I in terms of V.b. Sketch the IV characterstics伏安特性. Use I as the “y-axis Y轴” and V as the“x-axis”. Label标注all relevant points相关点.8. Suppose the load has an IV characteristic given as follows:a. What are the values of I an

36、d V if the load is attached to the Thevenin equivalent circuit 等效电路?b. Looking at the IV characteristic, what is the load? (describe the load as much as you can)For problems 9 through 12, consider the following circuit:9. Using KVL and mesh analysis, write down the equations needed to solve the circ

37、uit. Convert转变 the resistor voltages into currents.10. The dependent source requires one additional equation附加方程 to be generated产生. Write down that equation by looking at the 3 W resistor.11. Solve the equations simultaneously同时地to determine the two mesh currents网孔电流.12. To check your answer, confir

38、m确认that power is conserved守恒in the circuit. Find the power dissipated浪费的in each resistor. Find the power generated生成的(or dissipated in each source). Be clear in your answers whether power is being generated or dissipated in each circuit element.For problems 17, consider the following circuit:1. Find

39、 the transfer转移 function, i.e. Vout输出电压(w)/Vin(w), in terms of R, L, and w.2. What is the magnitude大小of the transfer function传递函数, i.e. | H(w) |, in dB?3a. What is | H(w) | equal to (in dB) for very low frequencies频率?3b. What happens to | H(w) | at high frequencies? What kind of a filter滤波器do we hav

40、e here?4. Derive the equation for the break frequency推导出方程为截止频率. The break frequency is definedas the frequency where | H(w) | = 3.0103 dB.5. Sketch the magnitude Bode波特图plot for this filter滤波器. Label标注all critical points andslopes. Show how you obtained the value for any non-zero slopes零斜坡.6. Suppo

41、se R = 1 W, L = 2 H, and Vin = 3 cos(5t + 30o). Find Vout(t).7. Draw a phasor diagram, indicating the voltage and current phasors of all thecircuit elements电路参量 .For problems 812, consider the following circuit:8a. Find the current that appears on the output side of the transformer变压器.8b. What is th

42、e voltage that appears across the capacitor. (phasor form is acceptable,assume an angular frequency角频率of 1 rad/s)9. Find the voltage that appears on each side of the transformer.10. Find the voltage that appears across the current source.11. Replace the transformer and input circuitry with an equiva

43、lent current sourceand inductor. In other words, draw a circuit which will have a current source,an inductor, and a 3 F capacitor all in series. Label the values for the current source and the inductor.Check your answer to #11 by comparing the amount of power generated by the currentsource in each c

44、ircuit.12. Find the amount of power generated by the current source in the new circuit.Compare this with the amount of power generated by the current source in theoriginal circuit原电路 (they should be the same)For problems 47, consider the following circuit:4. Find the transfer function, i.e. Vout(w)/

45、Vin(w), in terms of R, L, and w (or f).5. What is the magnitude of the transfer function, i.e. | H(w) |?6. What is | H(w) | equal to for very low frequencies? For very high frequencies?What happens at resonance谐振? (i.e. w = wo =LC1) What kind of a filter滤波器do we have here?7. Sketch the magnitude Bode plot for this filter. Label all critical points andslopes斜率. Use R = 2 W, L =41H, and C =81F. Show how you obtained the valuefor any non-zero slopes.In order to measure the voltage across a resistor in a circ