Physics Lab 212

Understanding RC Circuits

NAME:______

LAB PARTNERS: ______

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DATE:______

EMAIL ADDRESS:______

Software List

Data Studio

Microsoft Excel

Equipment List

Science Workshop Interface + voltage probes

1 µF capacitor.

A two position switch.

A 100 k resistor

1 F "super-capacitor"

Two 1.5 V batteries + a battery holder

Flashlight bulb + bulb holder

Hookup wires with alligator clips

Summary of relevant concepts:

  • When an initially uncharged capacitor of capacitance C is connected in series with a resistance R and a battery of emf E, the charge on the capacitor and the voltage across the capacitor gradually change from 0 to a final steady state value. This charging process is described by the following equations:

V (t) = E (1 - e-t/RC)

Q (t) = CE(1 - e-t/RC)

  • The quantity "RC" has dimensions of TIME & is called the "time constant" of the circuit.
  • When a capacitor C with an initial charge Q0 = CV0 is connected across a resistance R, it discharges, and the charge on the capacitor and the voltage across the capacitor gradually become 0. This discharging process is described by the following equations:

V(t) = V0 e-t/RC

Q(t) = CV0 e-t/RC

Lab Activity: RC Circuits.

Activity 1: Charging and Discharging of RC Circuit

  • Start Data Studio.
  • Click & drag the "analog plug" icon to the analog channel A.
  • Click & drag the "Graph" icon to the analog channel A.
  • Click & drag the "Table" icon to the analog channel A.
  • Double click anywhere on the x-axis of the graph. When you do this, you will get a screen that allows you to set the parameters for the x-axis. You can leave the settings unchanged for now: but remember that you will need to change them later in this lab.
  • Double click anywhere on the y-axis of the graph. When you do this, you will get a screen that allows you to set the parameters for the y-axis. Since the maximum voltage of your two batteries in series is around 3 V, set the maximum value of the voltage for 4 V.
  • Double click the "sampling options" icon.
  • The default rate at which the program measures data is 10 Hz (i.e. 10 readings per second), which is more than sufficient for your first experiment. This default rate will need to be changed later in the lab.

  • Connect the terminals of the 1 F capacitor to each other for a few seconds using some wire.
  • Set up the circuit shown below, making sure that you connect the batteries to each other with the correct polarities (i.e. "positive" end of one battery connected to the "negative" terminal of the second battery)! Do NOT complete the circuit yet -- i.e. leave the switch OPEN. Note that the switch has two possible closed positions, labeled A and B in the diagram above. Note that the voltage probes from the Science Workshop interface box should already be connected to Analog Channel A.

  • Make sure that the voltage probes are properly connected to measure the voltage VC across the capacitor.
  • Record data.
  • Now, click on the "REC" icon on your program screen and complete the circuit by closing the switch in position A. You will see your data getting recorded in the table and it will also be displayed on the graph.
  • After the capacitor seems to have charged completely, flip the switch to position B.
  • Stop recording data by clicking the "STOP" icon when the capacitor has discharged completely.
  • Note now that you have (a) a graph that displays VC vs. t and (b) a table that shows the actual voltage readings (in volts) at different times (in seconds).
  • You might wish to do this a few times in order to get a reasonable set of data. Note that you can delete any set of data simply by highlighting the name of the data set in the data window and then pressing the "delete" key.

Q1. Sketch (qualitatively) below the time variation of the measured voltage across the capacitor. Label the point at which you switched from charging the capacitor to discharging the capacitor. (Alternatively, you can print the graph and attach it to your lab report, if you so wish.)

Q2. Without doing any explicit fits to the data, use the graph displayed in the Data Studio window to estimate the time constant of this circuit. Explain how you did this!

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Next, repeat the experiment but this time measure the voltage VRacross the BULB.

Q3. Sketch (qualitatively) below the time variation of the measured voltage VRacross the bulb. Label the point at which you switched from charging the capacitor to discharging the capacitor. (Alternatively, you can print the graph and attach it to your lab report, if you so wish.)

Q4. Explain qualitatively why the voltage across the bulb varies as observed.

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Activity 2: Quantitative Analysis of an RC Circuit

In the circuit that you set up earlier, replace:

(a) the 1 F capacitor by the 1 µF capacitor;

(b) the bulb by a 100 kresistor.

  • Change the x-axis parameters in the Data Studio graph to read "milliseconds" instead of "seconds"
  • Change the "sampling options" data rate from 10 Hz to 100 Hz.
  • Then, repeat the first experiment that you carried out earlier: i.e. record the voltage VCacross the capacitor, butSTOP taking data after the capacitor is completely charged. We now have data for the CHARGING of the capacitor only.
  • Leave the switch in position A.
  • Export the measured data to an Excel spreadsheet as follows:
  • Export the measured data to an Excel spreadsheet for analysis as follows:
  • Highlight the column of data containing time & voltage readings
  • Copy this to the clipboard (ctrl-C or from the edit menu)
  • Open Microsoft Excel and start a new spreadsheet
  • Paste (ctrl-V) the copied data into the first two columns.
  • Now, go back to Science Workshop and record data again, this time flipping the switch from A to B (i.e. you are now DISCHARGING the capacitor).
  • Export this data also to an Excel spreadsheet.

Q5. Use Microsoft Excel to make graphs of VC vs t during the charging and discharging of the capacitor. Remember to label the axes on your graphs correctly with proper units, etc. Print out these graphs with your lab report.

Q6. From the graphs that you just made, estimate the time constant of your circuit, explaining how you do this.

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Q7. Next, plot the charging data in such a way that tests whether it obeys the capacitor charging equation. Include this plot with your report. From the plot, determine the value of the time constant. Explain below how you did this.

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Q8. Finally, plot the discharging data in such a way that tests whether it obeys the capacitor discharging equation. Include this plot with your report. From the plot, determine the value of the time constant. Explain below how you did this.

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