30th of April's Class
We were given a set of apparatus to start the day with. We were given a capacitor, battery, light bulb and some alligator clips. The purpose of this experiment is to have first hand experience with the function of a capacitor. It stores energy from the battery source, and as such it sucks up all the voltage within that circuit to within itself. As seen from circuit drawn at the top left corner of the white board, marked 'a', circled in blue. The light bulb did not light up at all.
For the next part, we removed battery from the circuit. This set-up can be seen from the circuit drawn next to the first mentioned, marked 'b', circled in green. The light bulb in this set up lit up, unlike the previous set up. The power is now being supplied by the capacitor that had absorbed electrical energy from the battery in the previous set up.
However, unlike using battery as an energy source, the light from the bulb goes dim fairly quickly. The capacitor has a maximum power that it can store, and it is much less than battery. Once that energy is all expended, the battery would die out.
We were then introduced to Tao, which is the time constant for the time taken for a capacitor to charge up to 63.2% of the total voltage it can take and discharge down to 36.8% of its total voltage capacity. It is directly proportional to Resistance and Capacitance.
The graph for Brightness vs. Time for set up B, which uses the capacitor as an energy source is wrong, and we had forgotten to edit it. The right graph should look something like this:
With the Y-axis being the Brightness of the bulb and X-axis being the time that pass by.
Next, using LoggerPro, we were supposed to create a graph that would plot the capacitor's voltage over time. We hooked the capacitor to a resistor, battery and voltage probe from LoggerPro in series. First, we make sure that the capacitor has zero voltage by not hooking the battery up with it, only the resistor and the voltage probe. After ensuring that the probe is reading 0 voltage from the capacitor, we hooked up the battery to the circuit and let LoggerPro plot the resulting graph.
The following images show our resultant graphs of discharging (in red) and charging (in blue), due to a mistake we made, the order is discharge first then charge.
From the two images above, we can see that the relationship is non-linear and more exponential in nature.
The way we derive that equation is by requesting LoggerPro to find the exponential fit for this graph, which basic form is circled in yellow. We can see from the equation that was given by LoggerPro that the constant A and B of that equation is in Volts. This graph leads us to the understanding that the equation to define the voltage of a capacitor is exponential. This equation can be seen at the bottom left corner of the white board in the image above, boxed up in blue.
We also found a way to calculate the charge held within the capacitor by the calculations done on the left side of the white board. We begin by fiddling around with the definition of Current, one of which is dq/dt. We know that one of the definition for Voltage is IR (Current x Resistance) and also Q/C (Charge / Capacitance). Utilizing these two definition, we substitute the definition for current that we stated earlier and through integration, obtained the equation circled in pink.
Professor Mason then showed us two graphs, depicted in the image above as those at the top part of the whiteboard, written in blue. One of the graphs is Voltage vs. Time, the other is Brightness vs. Time. The question he posed to us was: Predict what the graph for current would look like based on the 2 graphs that he gave to us.
We know from our previous class that Brightness is directly proportional to Power. Power can be defined as Current x Voltage. Therefore, if the equation goes P = IV, then as Power decreases, and the Voltage increase, then the current has to decrease to balance out the equation. This answer of ours was shown at the lower part of the image right above, along with our prediction of what the graph of Current vs. Time would look like.
This image above is the remnant of an explosive demonstration by Professor Mason. The capacitor was placed behind an acrylic shield, and it was being overcharged by an energy source, it boiled up and exploded at the end.
Next, is a series of questions that Professor Mason wants us to practice on. He gave us a description of a circuit, and we were supposed to draw out its diagram relying on what was written on the projection screen. The resultant circuit is shown in the image above, circled in blue. The first question was for us to find the time constant for the circuit if the switch were to remain open. The calculation for that was fairly simple, and we solved it using the identity of the time constant which can be defined with RC (Resistance x Capacitance).
Then, we were supposed to find the Charge in the capacitor if the switch were to remain open. Our calculation was written at the bottom left corner of the white board, written in blue, marked with (b).
From there, we were supposed to find the time taken for the capacitor to charge to its maximum capacity when the switch is closed. Since the battery is now creating a closed circuit with the capacitor, we need to use the formula for Voltage that was we derived earlier, in the exponential form. Isolating the variable t, we obtain time. This calculation is done at the bottom left corner of the white board, written in green.
Next, we were to find the time constant for the capacitor, by using its definition of RC. This calculation can be found to the left of the drawn diagram of the circuit.
The last part of the series of questions was for us to find the time taken for the capacitor to discharge a charge worth 1 electron. To solve this, we used the definition we derived earlier of charge. The solution and calculation done for this question is shown in the image right above.
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