On Kirchoff's Rules and Capacitors

This meeting was quite hectic because two activities were scheduled to be done by 4 pm so that we wouldn't have to perform any experiment next meeting, and we could just review for our long exam in 102, which I consider my impending doom.

Anyway, the lab meeting started with a lecture on Kirchoff's rules and Capacitors, two very new concepts for me. Because of the possible lack of time, the quiz on these topics was postponed to next next week (yey!).

So, the first topic for the lecture was Kirchoff's rules, which are basically two rules on how to simplify measuring current and voltage in a DC circuit.

The first rule, the junction rule, states that "the algebraic sum of the currents at any branch point or junction in a circuit is zero." This rule fortunately conforms to common sense, so "getting" it isn't really that hard. For example, in the situation where a junction connects three branches and two currents (I1 and I2) are flowing into the junction, th

e current flowing out of the junction is I1+I2. Basically, the junction rules says that the sum of the directed currents in a junction is equal to 0. It is, in disguise, the Law of Conservation of Charge.

The second rule, the loop rule states that "the algebraic sum of the potential differences around any complete loop in the network is zero." This is a bit more difficult to grasp qualitatively than the junction rule, nevertheless, it's still a lot easier to understand than the things we learn about in 102 and 111. To put it simply, the voltage input and output must equal zero for any loop in the circuit. After reading a bit about it in University Physics, using the loop rule seems a bit complicated when the loop involves a lot of circuit elements.

The second part of the lecture was about capacitors and capacitance, a new addition to 102.1's ever growing collection of circuit elements.

The marking C is the capacitor in the circuit, and the unit of capacitance is farads. Before going in deeper on capacitors, let me first define it. Capacitors are devices which can store charge, and capacitance is just the measure of how much charge a capacitor can store. The amount of charge stored is determined by

Q=CV

where Q=charge, C=capacitance, V=voltage

The capacitance C is given by another formula:

C=EA/d

where E=permitivity of free space, A=area of the plate of capacitor, d= distance between capacitor plates

When there is an insulator between the plates of the capacitor, the capacitance C becomes:

C=kEA/d

where k is a constant of the insulator that is very much greater than 1

We, then, described the effective capacitance in series and parallel circuits. For series, the capacitance formula is equivalent to that of the resistance formula for parallel circuits. For parallel, the formula is equivalent to that of the resistance formula for series.

The charge obtained by the capacitor and circuit current, as functions of time, was derived via integration. The formulas are:

q(t)=CV(1-1/e^(t/RC)) ----> charging (charge)

i(t)=V/(Re^(t/RC)) ----> charging (current)

q(t)=Q/e^(t/RC) ----> discharging (charge)

i(t)= -Q/RCe^(t/RC) -----> discharging (current)

Wow, those were a lot of formulas.:o

Anyway, we started doing the experiments after the lecture. The first we performed was the experiment on Capacitors. The first thing that popped into my mind when I saw the capacitors was that they seemed awfully familiar. I remember very vaguely that we handled capacitors in HS, but I do not know what we did with them.

The experiment on Capacitors was basically a string of activities that, in one way or another, displayed the wonders of capacitors. I do not want to go much into detail but as an outline, what we did are as follows:

• dissected a capacitor (which was quite difficult)
• measured the capacitor's capacitance (with the ever-powerful multimeter)
• measured the capacitance for series and parallel combinations
• made an experiment that proved the equation Q=CV
• energized a capacitor and connected it to a voltmeter that was connected to a computer and by using labpro (which was cool), graphed the time vs voltage plot

There was a lot of sources of confusion for this experiment. One of which is our lack of knowledge on capacitors. I, for one, do not know a great deal about capacitors, and I consider myself an amateur when it comes to circuits. The last mini activity was confusing because there was a lot of things involved, and the procedure stated in the activity sheet didn't really go much into detail of what we were supposed to do. Thank God Sir was there, kind enough to help us out.

Lab Pro was really cool because it not only allowed us to get the graph of time vs voltage, but it also allowed us to get a best fit curve of the graph. For the first part of the graph (charging up until the capacitor was fully charged), the graph resembled an inverse exponential function. For the second part of the graph (after turning off the power supply/ discharging the capacitor), the graph resembled a natural exponential function.

By 3:40, we were done with the Capacitor experiment. With only a few minutes left until 4:00, we had to rush the Kirchoff's Rules experiment.

Around this time, too, I saw who I thought was Mikaela Fudolig entering the room looking for our instructor. I was :O and very starstruck (Mac was too) because Mikaela Fudolig is amazing. Having that high of a graduating GWA (1.099) at a young age (16), with her course being Physics to boot, I consider her very inspiring and cool.

I digressed. So, back to the experiment. It was quite a short experiment. We just set up a circuit given a diagram and just measured the voltage, current and resistance. By using Kirchoff's rules, we then solved for the current passing through each element... actually, we didn't do the last step there because it was already past 4. So, we just did it at home.

These two quickfire experiments were quite difficult for me because it required of us to be fast workers, so that we would finish by 4. Knowing myself, my motto in these kinds of experiments is 'work slowly, but surely'. Needing to finish 2 experiments in a span of 2 hours, my motto was thrown out of the window.

It's nice to have groupmates that are very much knowledgeable on circuits. After class, I can ask things that I did not understand during the course of the meeting. For example, using the breadboard was still quite vague to me. I can ask help from Mac after class and after that, I'm enlightened quite a bit.

So, I plan to read on the topics that we have discussed and will discuss, and hopefully by next next week, I will be a master of circuits. :D