Measure the Capacitance
It is possible to get a DMM that measures capacitance directly. But where is the fun in that? In this lab, you will measure the capacitance of a capacitor by charging it up and timing how long it takes to discharge it through a known resistance.
1)You will need ancapacitor, some BNC cables, a DMM (digital multi-meter), a resistor (measure it with the DMM to find out what it is exactly), a timer (the one on your phone is fine), and a power supply. You will need to figure out ahead of time what resistance you’ll need so that it will take something like a couple of minutes for your capacitor to discharge through it.
2)Make sure your capacitor is uncharged. Do this by putting both wires on it in the ground part of an outlet at the same time. If you are uncomfortable doing this, ask your instructor to do it for you.
3)Charge up your capacitor to 5 volts. Do this by plugging in and turning on your power supply, setting it to output 5 volts, and connecting the + end of the capacitor to the red jack on the power supply and the – end of the capacitor to the black jack on the power supply. You only need to connect it to the power supply for several seconds (perhaps much less) to charge it up completely.
4)Set your DMM to measure DC voltage and connect your DMM across your capacitor using your BNC cables. The capacitor should stay at 5 volts.
5)Start the timer at the moment you connect your resistor across the capacitor. Record the voltage across the capacitor every 10 seconds for as long as it takes to discharge to less than ¼ of its original voltage (at least a minute later). Vo will be the voltage across the capacitor the instant you connect the resistor/start the timer.
6)Make a plot of voltage across the capacitor as a function of time. Does it look like what you expect?
7)Solve for C. Determine the value of C for each (t, V) pair from your data. You will have at least 9 values for C.
8)Determine the average value of these C’s and the standard deviation.
9)Does your measured value of C agree with what the capacitor claims to be? Why or why not? These capacitors are made very cheaply, and can easily be 20% (or more) off from what they claim to be. You should also compare your result with other groups to see if yours is reasonable.
10)Turn in the usual lab report:
Introduction
Theory – Write down equation in 7) above and solve it for C. Define your variables.
Experiment – Include ALL of your data here, and your plot. Describe what you did in enough detail that someone 10 years from now would have no trouble duplicating your experiment.
Analysis – Crunch your numbers. Find all your C’s, their average, and their standard deviation.
Discussion – Talk about your result. Is it reasonable?
Conclusion – Repeat your result for C and its uncertainty.