Background –
in a simple rc circuit in which a charged capacitor (or set of connected capacitors, in which case the capacitance that appears in the time constant is ceff, or the effective capacitance) is connected in series to a resistor, once the circuit is closed, the current through the circuit and the voltage across the capacitor are given by the following equations, respectively:
,
and,
.
in the case of this laboratory exercise, there are two circuits that you will analyze the currents and voltages for. the first is a circuit where two capacitors, rated at the same value, are connected in series and the configuration charged to 12 volts. the circuit has a diagram that is as follows:
remember that capacitors in series have an effective capacitance of
and if the capacitors have the same value, this reduces to
where cis the capacitance of an individual capacitor in the configuration.
in the second circuit, the diagram looks like this:
in the case of parallel resistors, the capacitance adds, so the effective capacitance is twice that of an individual capacitor.
the purpose of this lab is two-fold: first, you will verify the exponential behavior of the voltage and current in both of the circuits represented in the above diagrams. secondly, you will identify the capacitance of the system in both cases, and compare the values.
you will have two folders; one labeled series and the other parallel. open the folders and inside will be a series of images. these images contain pictures of a stopwatch, current (in milliamps; be sure to convert to ! ) and voltage (in volts). the times are approximately four seconds apart for two minutes.
procedure 1 - series
open the folder labeled ‘series’. view each image, recording the time (on the left), the current (the middle meter), and the voltage (on the right) in the spreadsheet of your choice. plot the current against time and voltage against time on separate graphs. verify that an exponentially decaying function is the best fit of the data. the resulting equation should have the following form
.
if we compare the resulting equation with the form of the current and voltage equations above, we find that b represents the reciprocal of the time constant, or,
if the resistance is known, this equation can be solved for the effective resistance.
in this experiment, the resistor was measured to have a value of 189,000 ω.
question 1: from the plotted data in both graphs, what function returned the highest r2value?
question 2: from both graphs, record the values for b, ceff, and c, remembering that in this case ceff= c/2.
current vs. time:
b:
ceff:
c:
voltage vs. time:
b:
ceff:
c:
question 3: what is the % difference between your values for the capacitance of a single capacitor in the system between the two methods?
in other words, what is the % difference between the two values for c you just calculated?