# Procedure for Series RC circuit lab

Your printed lab manual describes slightly more steps than I want you to perform. Here are the basic steps you should do today:

1. Start Logger Pro.

2. Discharge the capacitor by throwing the switch to the "short" position.

3. Draw a picture showing the circuit, flow of current, and charges on the capacitor as the circuit charges the capacitor.

4. Measure voltage across capacitor as the circuit charges the capacitor.

5. Use the Logger Pro software to select a range of data values which lie along a smooth curve, and fit the data with a curve of the "Inverse Exponential Function" type. The program will tell you the values of three parameters, which it calls A, B, C. Write down those values, and write down the equation it used to fit the data.

6. Write down an equation for voltage across a capacitor as a function of time as the capacitor charges. Include units.

7. What are the units for each of the computer's three fitted values A, B, C? What is the physical meaning of these variables?

Now, discharge the capacitor, and measure the voltage across the capacitor.

1. Draw a picture showing the circuit, flow of current, and charges on the capacitor as the circuit discharges the capacitor.

2. Measure voltage across capacitor as the circuit discharges the capacitor.

3. Use the Logger Pro software to select a range of data values which lie along a smooth curve, and fit the data with a curve of the "Natural Exponent" type. The program will tell you the values of three parameters, which it calls A, B, C. Write down those values, and write down the equation it used to fit the data.

4. Write down an equation for voltage across capacitor as a function of time as the capacitor discharges. Include units.

5. What are the units for each of the computer's three fitted values A, B, C? What is the physical meaning of these variables?

6. Now, pick the voltages from your measurements at six times: t = 2, 4, 6, 8, 10, 12 seconds. Make a table showing the time, voltage across capacitor, and natural logarithm of voltage across capacitor for these six times. Make a graph showing ln(voltage across capacitor) versus time. Fit a straight line to the graph, and measure its slope and uncertainty.

7. How is your graph, and the line on it, related to the equation for voltage across capacitor as a function of time as the capacitor discharges? What are the units of the slope? What is the physical meaning of the slope?

8. One of the computer's variables A, B, C corresponds to the slope in your hand-drawn graph. Which one? Do the two values agree to within your estimated uncertainty?

You now have one values for the time constant of the circuit, based on measurements while the capacitor was charging up, and two values for the time constant of the circuit, based on measurements while the capacitor was discharging. Do all the values agree? Should they?

Look on the back of the little black box containing resistors and capacitors. Read off the value of the capacitance of the capacitor. Use it, and your calculated time constant, to calculate the resistance of the resistor. What is your value for the resistor? Does it agree with the actual value of the resistor, within the estimated uncertainty?