• BME 210
• # Lab 5: Capacitors & Inductors

## 1. Objectives

By the end of this laboratory session students will be able to:

• Use a function generator and oscilloscope.
• Construct and analyze circuits with resistors, capacitors, and inductors.
• Determine the size of an unknown capacitor given a resistor and time constant.
• Determine the size of an unknown inductor given a resistor and time constant.

## 2. Background

Given a step input, the time constant $$\tau$$ is the amount of time it takes for a capacitor or inductor to reach 63.2% of its final voltage or current, respectively. In the case of decreasing voltage or current, the time constant $$\tau$$ is the amount of time it takes to lose 63.2% of the initial voltage or current. Figure 1 shows the time constant for increasing and decreasing system output. The series RC circuit has a time constant of $$\tau=RC$$. The series RL circuit has a time constant of $$\tau=L/R$$. Figure 1. The figure on the left shows a system where the output is increasing over time. The figure on the right shows a system where the output is decreasing over time. In both, one time constant is 63.2% of the way to the final value.

## 3. Laboratory Equipment

1. Resistors
2. Capacitors
3. Inductors
4. Oscilloscope
5. Function generator
6. Digital multimeter (DMM)
7. RCL meter

## 4. Procedure

### 4.1. RC Circuit

1. The TA will provide you with a 1 k$$\Omega$$ resistor and capacitor of unknown size.
2. Measure and record the value of the 1 k$$\Omega$$ resistor.
3. Construct the circuit shown in Figure 2.
4. Attach the function generator to $$V_s$$. Press Utility → Output Setup → High Z → Done to make sure the proper signal is sent from the function generator. This makes the function generator assume it is delivering a signal into a load with infinite resistance. Adjust the function generator so that it outputs a 1 V peak-to-peak ($$\mathrm{V_{pp}}$$) square wave at 50 Hz. Turn the output on. Figure 2. A series RC circuit designed specifically for BME 210 students.
5. Attach oscilloscope probe 1 across $$V_C$$. Display the output by pressing AUTO. Make sure the probe coupling is set to AC. To do this press the 1 button and then press the top grey button under Coupling until it says AC.

6. Adjust the time and voltage scales as necessary to obtain a good picture on the oscilloscope. Sketch a plot of the oscilloscope screen on paper. Label your axes.

7. Press the Run/Stop button to freeze the waveform.

8. Using the cursors, measure and record the time constant $$\tau$$ of the circuit. To do this press the Cursors button twice until the top box under Mode says Track. Track mode allows your cursors to display time and voltage information simultaneously. Alternate between cursors A and B by using the two bottom grey buttons next to the screen. Move the active cursor by turning the knob on the right that looks like this:

9. If you change the time or voltage scale on the oscilloscope you will need to press the Run/Stop button twice to capture a new waveform and make the cursors available.

10. First, measure the peak-to-peak voltage of your waveform with the oscilloscope. Move cursor A until it is on the bottom of the waveform, right before it begins to rise, and cursor B until it is on the top of the waveform, after it has finished rising. Record the $$\Delta$$Y value. This value is the peak-to-peak voltage of your waveform.

11. Next, calculate the $$\Delta$$Y value for one time constant (see background above).

12. Finally, move cursor B to the left until the $$\Delta$$Y value displayed on the screen matches your calculated value. You now have cursor A positioned at the “0” value and cursor B positioned at the voltage after one time constant.

13. Record the time constant by writing down the value for $$\Delta$$X.

14. Given the measured time constant $$\tau$$, calculate and record the size of the capacitor.

15. Press Run/Stop.

16. Measure and record the capacitor’s value with the RCL meter.

### 4.2. RL Circuit

1. The TA will provide you with a 1 k$$\Omega$$ resistor and inductor of unknown size.
2. Measure and record the value of the 1 k$$\Omega$$ resistor.
3. Construct the circuit shown in Figure 3.
4. Attach the function generator to Vs. Press UtilityOutput SetupHigh ZDone to make sure the proper signal is sent from the function generator. Adjust the function generator so that it outputs a 1 V peak-to-peak ($$\mathrm{V_{pp}}$$) square wave at 15 kHz. Figure 3. A fine series RL circuit.
5. Attach oscilloscope probe 1 across $$V_L$$. Display the output by pressing AUTO. Make sure the probe coupling is set to AC. To do this press the 1 button and press the top grey button under Coupling until it says AC.

6. Adjust the time and voltage scales as necessary to obtain a good picture on the oscilloscope. Sketch a plot of the oscilloscope screen on paper. Label your axes.

7. Press the Run/Stop button to freeze the waveform.

8. Using the cursors, measure and record the time constant $$\tau$$ of the circuit. To do this press the Cursors button twice until the top box under Mode says Track. Track mode allows your cursors to display time and voltage information simultaneously. Alternate between cursors A and B by using the two bottom grey buttons next to the screen. Move the active cursor by turning the knob with the clockwise arrow.

9. First, measure the peak voltage of your waveform with the oscilloscope. Move cursor A until it is on the top of the waveform, right before it begins to fall, and cursor B until it is on the bottom of the waveform, after it has finished falling. Record the $$\Delta$$Y value. This value is the peak voltage of your waveform.

10. Next, calculate the $$\Delta$$Y value for one time constant.

11. Then, to calculate the voltage that corresponds with $$\tau$$, subtract the $$\Delta$$Y value for one time constant from the measured peak voltage (right before the waveform begins to fall).

12. Finally, move cursor B to the left until the $$\Delta$$Y value displayed on the screen matches your calculated value. You now have cursor A positioned at the “0” value and cursor B positioned at the voltage after one time constant.

13. Record the time constant by writing down the value for $$\Delta$$X.

14. Given the measured time constant $$\tau$$, calculate and record the size of the inductor.

15. Press Run/Stop.

16. Measure and record the inductor’s value with the RCL meter.

## 5. Results

1. Report results from steps 2,10,11,13,14, and 16 in Section 4.1.
2. Compare the calculated and measured values for C.
3. Simulate the circuit in Figure 2 using Multisim. Include a plot of the input and output signals. See Section 5-8.1 in the Multisim transient response handout for a tutorial on transient circuit analysis.
4. Report results from steps 2, 9, 10, 11, 13, 14, and 16 in Section 4.2.
5. Compare the calculated and measured values for L.
6. Simulate the circuit in Figure 3 using Multisim. Include a plot of the input and output signals.

Last updated:
February 27, 2018