Experiment #2: A.C. Circuits

Objective: To provide experience with A.C. Ohm's law, to demonstrate the frequency dependence of reactance and impedance, and to investigate the properties of simple filter circuits.

Procedure: All the voltages in this experiment will be measured using the oscilloscope, while the frequencies will be measured with the counter. Be sure its vertical gain control is in the calibrated position. Refer to the previous description.

I. Capacitive Reactance
A. Set up the circuit shown in Figure 1 after using the impedance bridge and ohmmeter to determine the values of the components you are using.

• Be sure both your signal generator, oscilloscope and counter are plugged into the wall with 3-prong adaptors. Otherwise, there is an "invisible" connection between their black or "ground" terminals through the 3rd prong. If this connection exists, your readings will not be accurate. You can test for this effect by connecting the oscilloscope to the signal generator in both possible ways. The wave form should be the same amplitude in both cases.
  请确保你的信号发生器、示波器和计数器都使用3孔插头插在墙上。否则，通过第三个插脚会形成一个“看不见”的连接，将它们的黑色或‘地’端连接在一起。如果这种连接存在，你的读数将不准确。你可以通过将示波器以两种可能的方式连接到信号发生器上，来测试这种效应。波形在两种情况下应具有相同的幅度。

B. At each of 10 different frequency settings between 1 kilohertz and 100 kilohertz (1,2,4,7,10,20,40,70,100kHz), set (the output voltage of the signal generator) to 2.00 as measured by the oscilloscope and then measure and record along with the frequency the peak-to-peak voltages for and (the voltages across R, C, and the generator). Make all three measurement at the same frequency before going to another, and make them without changing the generator amplitude setting.

C. Results and Analysis

1. Calculate the capacitive reactance at each frequency according to . Since R and C are in series, the same current flows through each. Thus . Make two cartesian graphs: one of as a function of f (e.g., f is horizontal and is vertical) and one of as a function of l/f. Why suggest using l/f? Are the results reasonable? Why?
   根据公式计算每个频率下的容抗。由于R和C是串联的，同一电流流过每个元件。因此，有 $ X_C = \frac{1}{\omega C} $。绘制两个直角坐标图：一个是以f为横坐标、$ X_C $为纵坐标的图（例如，f是水平轴，$ X_C $是垂直轴）；另一个是以1/f为横坐标、$ X_C $为纵坐标的图。为什么建议使用1/f？结果是否合理？为什么？
2. Based on your reactance results, calculate the capacitance and compare it to the actual value.
   根据你的电抗结果，计算电容并将其与实际值进行比较。
3. A.C. Ohm's law
   • Note that for each frequency setting . Is this a violation of Kirchoff's laws as learned in connection with D.C. circuits? Explain.
     请注意，对于每个频率设置，这是否违反了与直流电路相关学过的基尔霍夫定律？请解释。
   • Based on impedance considerations and the measured VÃ , compute the current expected at 2 of the frequencies from part I.B. Compare the theoretical values with those actually measured. Is the comparison reasonable? Explain.
     基于阻抗考虑和测量的VÃ，计算部分I.B中两个频率下的预期电流。将理论值与实际测量值进行比较。这种比较是否合理？请解释原因。
   交流欧姆定律
4. Low and High Pass Filters
   • Arranging the circuit from part I as shown below puts it into the configuration know as a "low©pass" filter:
     将第I部分中的电路按上图排列，即可构成一种称为“低通”滤波器的电路：
   • Note that as actually measured, Vin is VÃ and V . For each measurement compute the ratio r = Æ(#¸ Graph the results and explain the terminology "lowªpass."
     注意，实际测量中，Vin 是 V 和 V。对每个测量值计算比值 r = Æ(#¸ 绘制结果图，并解释“低通”这一术语。
   • Considering the circuit to be an A.C. voltage divider, compute the theoretical r = VÃ and show that it is r = 1/(1+RÃ
     将电路视为交流电压分压器，计算理论上的r = VÃ，并证明r = 1/(1+RÃ。
   低通和高通滤波器
   • Similarly the arrangementÆ(# is referred to as a "High pass" filter. Repeat steps (b) and (c) above for this case
     同样，这种安排称为“高通滤波器”。重复上述步骤（b）和（c）进行此情况的处理。

II. Resonance
A. Set up the circuit shown in Figure 2 (your results will be best if it is wired exactly as shown):

B. For 10 frequencies between 2KHz and 40KHz, measure and record the peak-to-peak voltage for V and V

Note: You should observe the VÃ to go through a definite peak (about a factor of VÃ ) over this range. If you observe no such behavior, or if your peak is less pronounced, consult the supervisor.

C. Graph VÃ over the range. The spread of the peak is related to the "Q" of the circuit, while the frequency of the greatest voltage is the resonant frequency. From your graph, estimate the resonant frequency and compare it with the value computed from theoretical considerations.

D. Note that the sum of the values Và at any frequency setting. Explain why this is not a violation of Kirchoff's law of voltages.

E. Rearrange the circuit so that the capacitor and inductor are adjacent as shown below:Æ(# Connect the signal generator as indicated by VÃ , and observe the voltage VÃ as the frequency is adjusted over the 2©20 KHz range. Describe qualitatively what you see. At the frequency of minimum VÃ , observe the value of VÃ . Explain why VÃ alone is much greater than VÃ