PhysicsLAB: RC Time Constants

Equipment

DC power supply
blue box with a capacitor and a resistor
connecting leads
digital ammeter

Process

When the switch is in position A, the capacitor is charging.

The voltage across the capacitor will build until it reaches the voltage of the battery at which time no more charge will flow onto the plates of the capacitor and the capacitor will reach a state of dynamic equilibrium.

We will take measurements of the current through the resistor every 20 seconds for five minutes and plot the results to determine your circuit's RC time constant.

Refer to the following information for the next nine questions.

Charging the capacitor. Remember to always use a positive tip and 9V!

What is the filename for your charging data and its graph?

What is the resistance of your resistor?

What is the capacitance of your capacitor?

What is your RC time constant?

What is the value of I_max?

Based on your initial current value, how many seconds had passed during the charging PRIOR to your first observation?

Your exponent on e also tells you your time constant. Suppose your EXCEL equation was y = 230e^-0.005x. Then your time constant can be found by setting -0.005x = -x/RC and solving for RC. Solve for your graph's RC time constant in this manner.

What is the percent error between your two time constants?

Find your closest data point to i(t) = 0.37I_max. At what time was it recorded? Does this agree with what you expected? Why or why not.

When the switch is in position B, the capacitor is discharging.

Now remove the power supply and measure the current passing through the resistor as the capacitor discharges. Once again, take measurements every 20 seconds for five minutes and plot the results to verify your circuit's RC time constant.

Refer to the following information for the next seven questions.

Discharging the capacitor. Unplug your 9V adapter and record the current as the capacitor discharges. Do NOT remove the tip or change it's polarity.

Before discharging, record the voltage across the capacitor.

What is the value of I_max?

What is the filename for your discharging data and its graph?

How does the shape of the discharging compare to the shape of the charging graph?

What is the percent error between your two time constants?

Find your closest data point to i(t) = 0.37I_max. At what time was it recorded?

Refer to the following information for the next question.

Error Analysis

Which time constant (charging or discharging) do you feel is more accurate? Explain.