1- an example of the memo

Rtot =

5. The inductance of the coil is reported by the manufacturer to be ~63 mH. Use this value along with the total circuit resistance to calculate in the space below the expected time constant exp for the circuit.

exp =

6. Set the function generator to a square-wave frequency f corresponding to 20 times the time constant exp. (The current will exceed 99% of its final value after 5 time constants. Thus 10 time constants will allow the current to fully rise, then another 10 time constants will allow it to fully decay again. So a frequency corresponding to 20 time constants will allow you to see a complete cycle of the exponential rise and fall of the current.)

f =

B. Measure coil inductance from inductive time constant

1. Display signal

a. Observe the square-wave voltage of the function generator on channel 1 and the circuit current on channel 2. The square-wave voltage output of the signal generator simulates a battery repeatedly turning on and off; use this signal for the oscilloscope trigger signal. Explain how you use the oscilloscope—a voltage-measuring device—to measure current on channel 2.

b. Adjust the oscilloscope horizontal sensitivity to display 2-3 periods of the circuit current. The function-generator frequency calculated above should produce a waveform cycle like the middle figure below. If instead each cycle looks like the first or last figure, you will need to adjust the frequency to get the middle display.

frequency too low frequency just right frequency too high

Now adjust the function generator voltage output and the vertical sensitivity on the current display so that the waveform fills the entire screen (starts on the bottom grid line and ends on the top grid line).

2. Measure the inductive time constant on both the increasing and the decreasing portion of the current cycle. (Recall: the inductive time constant is the amount of time for the current to increase to 63.2% of its final value or decrease to 36.8% of its initial value.) Your results should be similar to the expected time constant you calculated earlier. Now calculate the average of the two measurements. Use this average value to calculate the inductance in the circuit. Record your results:

inc =

dec =

avg =

L1 =

3. Change the decade resistance to 1000 ; this will change the circuit time constant and the waveform. Change the frequency of the function generator until the display looks like it did in part B. Position the waveform to display either the increasing or decreasing portion of a current cycle (your choice), starting from the left side of the screen. Measure the time and voltage of the waveform each time it crosses one of the screen’s vertical grid lines. Record these time-voltage data pairs in the table below:

4. Enter the data pairs from the table above into Graphical Analysis; the resulting graph should be a duplicate of the oscilloscope display. In the space below, explain which least-squares curve should be fit to the data and why. Now fit that curve to the data. Annotate and print your graph. Record the resulting least-squares equation below. Use that equation to calculate the time constant for the data. Calculate the coil inductance from this time constant. Make sure to show all calculations.

Least-squares equation:

ls =

L2 =

II. RLC Circuits: In this part of the exercise, you will build an RLC circuit and observe the damped oscillations predicted by Kirchhoff’s laws. You will measure the frequency of those oscillations as well as their decay and then use these measurements to calculate the inductance of the inductor.

A. Build RLC Circuit

1. Assemble the RLC circuit shown in Figure 2. Set the decade-resistance box to a resistance Rd of 5000 . Set the function generator square-wave output to an initial frequency of 100 Hz.