# Experiment of The Month

## Charge on a capacitor

The MU Physics Department does not claim to have invented these labs. In fact the origins of these labs are generally unknown to us, and we would appreciate any information on where they were first performed.

Our labs do not have written instructions. In keeping with this spirit, the description given here will be brief and general. The intent is that each performance of the lab will be unique; in each nature will reveal a slightly different face to the observer.

When we do this lab, we have defined current and have stipulated that an ammeter measures current. (Most of us prefer moving coil Ammeters, because their action illustrates some of the basic physics of electricity and magnetism.)

We connect the circuit shown below. We have not learned much about resistors at this point, but we do know that they conduct electricity, albeit not very well. When the battery (a power supply set to about 15 Volts) is connected the Ammeter registers current in the microAmp range.

When the power supply is disconnected the Ammeter current slowly falls as the charge on the capacitor is depleted. The time to fall from the initial current to a sequence of final currents is measured. (Because of the coarse scale on our Ammeter, this is easier than measuring the current at 1 second, 2 second, ... etc.) This current may be plotted versus time, as sketched above.

The current is the rate of decrease of charge on the capacitor. Thus if the current is integrated as a function of time from t=0 to infinity, the value of the integral is the original charge on the capacitor. The integration can be done numerically or graphically. Graphical integration is interesting because it raises the issue of the meaning of the units of the area. Numerical integration is interesting because one can imagine the lumps of charge which flowed to make each measured current value. In either case, some sort of approximation must be made to account for the fact that the data do not extend to infinity.

If you know the original charge and the original potential difference across the capacitor, you can calculate the capacitance. Be careful, however, not to leave a Voltmeter connected to the capacitor while the current fall is being measured: The input impedance of the Voltmeter is low enough to draw significant (unmeasured) current. This give the appearance of less capacitance.

Sometimes we repeat this experiment later in the semester with the same capacitor, a smaller resistor, a square wave generator and an oscilloscope to measure time in milliseconds rather than in seconds. The measured capacitance is consistently lower than that measured on a slow time scale. This may be related to slow relaxations in the dielectric. (We use non-polar electrolytic capacitors.)

## Experiment Of The Month

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