Circuits: Measuring Capacitance

"Hello, I am a capacitor," is what it would say.

Similarly to resistors, there is a parallel and series relationship when determining how much capacitance there is within a circuit. But, the relationship is the opposite of resistors. When capacitors are in parallel: C = C_1 + C_2 + ... C_n. When the capacitors are in series: C = 1 / (C_1 + C_2 + C_n).

We were then given a sample circuit and were first asked to find the total capacitance in the circuit. C_1 was 20 nF, C_2 was 50 nF, and C_3 was 40 nF. The first capacitor had 11 V stored in it. Utilizing this information, we found the total capacitance to be 52 nF. Secondly, we wer then asked to find the voltage of the second battery. We found the volts to be 18.3 V. Part D, we were asked to find the potential within this circuit.

The next few pictures are of a few different types of capacitors that were available in the lab.

This was the biggest out of the three and had the highest amount of capacitance.

We stored some energy within the capacitor and then created a circuit to light up a light bulb. And as you can see, it worked.

If the following circuit was being closed by a person, the person would feel 1.21 gigawatts! That is some incredible power. The current is shown to be flowing from the positive end of the battery to the negative end which is also charging the capacitor. When the battery is taken out of the circuit, the current will flow in the opposite direction because now, the capacitor acts like the battery.

The next few pictures are of the group measuring the volts within the capacitor.

We found a constant number to be at 3.54 V.

This was how we set the circuit up to charge and measure the capacitor.

This circuit was set up to measure the current and potential change within the capacitor that is connected to a resistor and an external energy source through Logger Pro.

This was the result that we got from the Logger Pro program.

The bubbles displayed the numerical relationship like slope. Through this exercise, we found that this certain equation had a power that is called the time constant: RC.

The highlighted numbers are the time constants.

Using letters A, B, and C to represent a general equation, we found that when the capacitor was charging, the equation is A(1-e^-Ct) and discharging equation is A*e^-Ct. We found the time constant for our lab to be about .37.

The following is a derivation to get the time constant equation. We started with the capacitor equation and the voltage equation, where I was also equal to the derivation of charge, Q. The time constant is also represented with the Greek letter tao.

We were then finally asked to find the current in terms of time with the equation we found through our experimentation.