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The BK Precision multimeter we use has an internal resistance of 10 M ohm according to the owner's manual. This information from the multimeter's user manual has also been confirmed by a direct measurement at the 20 V (DC) setting we will use for this experiment.
Connectors 1-2 on the "small" box connect to the 5 micro F capacitor that is our unknown C. All of the ones I have checked fall within +/- 0.1 of the nominal 5.0 muF value.
Connectors 3-4 on the "small" box connect to the unknown R you are to insert in parallel with the multimeter. All have values of about 5 M ohm, ranging from 4.7 to 5.6 M ohm. You will need to turn the box over and read the color code on the resistor to determine the nominal value of the one you used. All of the ones I have checked fall within 1 or 2 % of the nominal value, so you can use the color-coded value as "known".
This photo shows a measurement of the RC time constant in progress
back when we were using the Keithley multimeters.
The red lead, which was used to charge up the capacitor to its
initial voltage, has been disconnected so capacitor is no
longer connected to the power supply. It looks like the voltage
has already fallen from 20.0 V to 13.2 V.
This photo shows a different group performing the second part of
this lab. Notice that they disconnected the red lead from the
power supply rather than from the capacitor. This works the
same way as in the example above.
Contact me if you have any questions.