CAPACITANCE Objectives
Introduction When you first throw the switch (S) which connects the battery to the capacitor, the voltage across the capacitor is not immediately equal to as the battery voltage. The charge moves onto the plates quickly at first, and the capacitor voltage increases quickly. However, as the capacitor becomes charged, the charging rate begins to taper off. Eventually, the capacitor voltage is the same as the battery voltage, and no more charge can be forced onto the plates. At this point, the capacitor is no longer charging. If you analyze voltage of a charging of the charging capacitor over time, you might notice that it models an inverse exponential curve. Incidentally, the following formula describes the charging of a capacitor over time: V_{C} = V_{B} (1e^{t/RC}) V_{C} is the voltage across the charging capacitor at any time (t). V_{B} is the battery voltage, R is the resistance of the circuit, and C is the capacitance. After a capacitor is charged, it will hold its charge even when the power supply is removed. The capacitor can now be used as a voltage source that stores charge until you need it to use it. When a capacitor is used, it will discharge. Its rate of discharge will be great at first. However, that rate tapers off exponentially with time. Eventually, the voltage across the capacitor will be near zero, at which time the capacitor is no longer discharging. Below is an example of a circuit that will discharge a capacitor: If you analyze the voltage of a discharging capacitor over time,you might notice that it models a natural exponential curve. Incidentally, the following formula describes the discharging of a capacitor over time: V_{C} = V_{B} (e^{t/RC}) PRELAB QUESTIONS (to be checked off at the beginning of lab)
MATERIALS
ACTIVITIES Activity 1: Modeling charge and discharge of a capacitor Begin by discharging the capacitor (see below). The discharging circuit for the capacitor is very simple. A capacitor is discharged simply by connecting the ends together with a conductor. Leave it connected for about 10 seconds to make sure it is completely discharged. In the above discharge, resistance will be effectively zero, and the time constant will be very short. Placing a resistor is in the loop will slow the current, increasing the amount of time it takes to charge and discharge. This is important because you are going to analyze these charge and discharge curves.
Now construct the RC circuit above using the resistor and one of the capacitors on your table, but do not connect the battery yet! Do not twist or bend the wires of the resistor or capacitor; use the alligator cables to make the connections. Make sure that the negative end of the capacitor is going to connect to the negative end of the battery! If you don't, the capacitor might overheat and explode! Do not close the switch yet. Attach the voltage probe so that it will measure the voltage across the capacitor. Ask your instructor to check your circuit. When you have received permission from your instructor and the circuit is complete, click "collect." You may now close the switch. You should see the charging curve of the capacitor voltage. After the capacitor is fully charged, you may disconnect the battery and discharge the capacitor using the circuit below. When the circuit is constructed, press the switch and discharge the capacitor while Logger Pro is collecting. With a little practice and some adjustment of the time and voltage scales, you should be able to charge and discharge the capacitor during one collection cycle, so that both curves are displayed, one after another, on the same graph. Examine the equation that models the voltage of a charging capacitor, then use the curve fitting function of Logger Pro to apply that equation to the charging portion of the graph. Next examine the equation that models the voltage of a discharging capacitor, and use the curve fitting function of Logger Pro to apply that equation to the discharging portion of the graph. Print this graph. Repeat for the second capacitor. Be sure to keep track of which capacitor was used for each graph! You will need this information for Activity 2. Activity 2: Accurately determining capacitance First, use the multimeter on the "Ohms" setting to measure the value of the resistance (see above). Make sure the battery is not connected! For this activity, only the discharging curve of each capacitor will be analyzed. This is because the charging circuit contains not only the resistance of the resistor which you measured, but also the internal resistance of the battery, which you did not measure. Examine the discharge equation used in activity 1, and compare it to your curve fit parameters to determine the value of the two capacitors. Using percent difference, compare these to the value that is actually printed on the capacitors. Activity 3: Capacitors in series and parallel
After you have made your predictions, repeat the Activity 2 experiment to determine the total capacitance of the two capacitors placed in series. Repeat for the parallel configuration. Were your predictions correct? Explain. POSTLAB QUESTIONS
Voltage = Resistance · Current


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