Charging and Discharging of Capacitors

In this experiment, we saw that connecting the capacitor and light bulb in series like this would temporarily light the bulb. Eventually, the capacitor would not be able to hold any more charge, the current would stop, effectively turning off the light. Then we would take the battery out of the circuit and see the the light glow again. In this discharging process, charge would flow from one end of the capacitor, through the wire and the bulb, onto the other side of the capacitor. Eventually the light would turn off as well.

On the right hand side of the board is the amount of time the bulb would stay lit for the adjacent circuit shown. In the lower left, we predicted that the resulting voltage of this circuit would be the difference between the voltages of the two capacitors. Experimentally we see that the resulting voltage is actually much less that what we predicted. 

This here is a graph of the potential across a capacitor as a function of time during discharging.

This here is the graph of potential as a function of time during a charging cycle. For both of these graphs, we see an exponential relationship.

With the time constant (tao) equal RC, we see that the units of the time constant are in seconds. From the equations provided by logger pro for the exponential function, A and B are both in Volts, and C is 1/s. On the bottom of the board, we see that during discharging, the ratio of a charge at time t divided by the charge when t=0 is equal to e^(-t/RC).

During charging of a capacitor, the voltage across the capacitor starts from zero, then eventually levels off to a constant voltage. The current immediately jumps to a maximum current, and eventually goes to zero. The brightness of a light as a function of time when connected to a capacitor in a closed circuit is almost identical to the current as a function of time graph.

During discharging, we can see that as time goes to infinity, the final charge across the capacitor will eventually go to zero.

For this charging process, we use the formula in the upper left hand corner. We can determine that as time goes to infinity, the potential across the capacitor eventually becomes the voltage originally present in the source before charging.

For this circuit, we found the equivalent resistance of the circuit. Since the capacitance was given, we were able to determine the time constant. Since the original charge charge across the capacitor is equal to the product of the original potential across the capacitor and the capacitance, we are able to easily determine the amount of time it will take for the capacitor to discharge.