CAPACITOR CHARGING (CBL)

Gunn Physics

PURPOSE:

The purpose of this lab is to examine the pattern of voltage vs time and current vs time for charging and discharging capacitors. In the process, you will examine the mathematical equation that describes the data.

CIRCUIT:

MATERIALS:

CBL [or ULI]
TI-82 [or computer]
Link Cable
2 Voltage Probes
Capacitor Charge/Discharge Apparatus
Capacitors & Resistors

PROCEDURE:

1. Connect the Voltage Probes to Channel 1 (CH1) and Channel 2 (CH2) on the CBL. Connect the CBL to the TI-82 graphing calculator with the Link Cable. Turn on the TI-82 and the CBL.


2. Connect the CBL voltage probes to the Capacitor Charge/Discharge Apparatus as shown. Use 50 µF for the capacitor and 10 K_ for the resistor. Make sure the switch is in "DIS" or discharge position. To make sure the capacitor is fully discharged, touch a piece of wire between points A and B. Remove this wire for the following steps.


3. Launch the program "CAPACITO". Enter the resistance in ohms and the capacitance in micro-farads (µF) when asked. Press <ENTER> to begin collecting data. When the display on the CBL indicates "SAMPLING", flip the switch to "CHG".


4. After a few seconds, you will be presented with a menu. Choose "CAPACITOR VOLTS" to look at the voltage across the capacitor; choose "CURRENT-TIME" to look at the current flowing in the circuit, or choose "V-T AND I-T" to look at both graphs. After examining a graph, press <ENTER> to return to the menu.


> > > Sketch and describe the shapes of both graphs for capacitor charging. Describe the relationship between the two graphs and what is happening in the circuit.


5. With the capacitor fully charged, choose "NEW DATA RUN". When you press <ENTER> to begin collecting data, and the CBL displays "SAMPLING", flip the switch to "DIS". Follow the process in step (4) and answer the same questions above.


6. Go to the ANALYSIS section.


7. Try other resistor-capacitor combinations as time permits, obtain the new components from the instructor.

ANALYSIS:

1. At the end of the data collection, 99 voltages and times will have been recorded. L1 will be the times while L2 will be the capacitor voltages.


2. Press <STAT> then use the right arrow to select "CALC". Now use the down arrow go move to "A: ExpReg" and press <ENTER>. At the cursor position, press this sequence: <2nd> <L₁> <,> <2nd> <L₂> and then <ENTER>. The calculator will now evaluate the data for an equation of the form y = a * b^x. Enter the values for a and b in the data table.


3. The value "b" is equivalent to e^-k. If e^-k = b, then k = -ln b. Determine the value for k and enter it in your data table.


4. Write out the exponential equation that describes the voltage drop in your experiment:


y = a e^-kt =


5. Plot the equation above on top of your lab data to check the accuracy of this equation in predicting the voltages encountered while discharging a capacitor.


6. Take the inverse of the product of the resistance and the capacitance. Check the units of this product. and compare the final value to the value of k in your equation in step 4.


What is the percentage difference between your values in steps 4 and 6? To which factor should any difference be primarily attributed, the capacitor value or the resistor value? Why?



DATA:

Exponential Regression: a _______________

Exponential Regression: b _______________

Exponent: (k) _______________

Resistance Capacitance: (RC) _______________

Inverse RC: (RC)^-1 _______________

Percentage Differnce: _______________


Note: The connections for the PC boards are shown here:



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Updated 3/19/98