Day 17 RC Circuits and Oscilloscopes

In this lab, we get to study more on oscilloscopes and how they operate in a circuit

How capacitors behave in a circuit

We first focused on how to derive formulas for capacitors in both series and parallel circuits. We find that in a parallel circuit, that it is the sum of the capacitors that equals to the total capacitance. However, in the series, its the inverse sum of all the capacitor that equals to the total capacitance.
It is important to note that a capacitor acts completely opposite to how a resistor works, in terms of their equations. 

An example problem to help understand capacitors in circuits

We took what we know into an example problem, focusing on capacitor in series, and using the information given to find things such as voltage, power and charge.

Example of a RC Circuit

In this example that Mason has provided for us, he shows us an RC circuit, and how as time passes the light bulb, which was originally being powered by the voltage generator, is slowly declining due to the capacitor.

Our set-up of Prof Mason's Lab

Prof Mason then had us set up our own version of his lab, in which we were told to charge the capacitor, and then discharge it once it has been fully charged.
Note, just like I explained in the last lab, we must be very cautious of how this lab is set up, as the capacitor does have the capability to implode upon wrong set-up, which almost happened to us

Us charging the capacitor

Us discharging the capacitor

Calculations of the lab

A crude sketch of our graph

We were also asked to create a sketch on loggerpro, and were asked to sketch it on a board. We were also asked about the importance of the equation.

The importance of the graph's equation

We then set out onto finding said importance of the equations that the charging and discharging showed, and found out that the equations yielded turns out to be an exponential function in which we learn about a few things.

1) Tau, the time constant, which is equal to RC

2) That the capacitance is dependent on time (also that discharging a capacitor takes an infinite amount of time)

3) That under an infinite amount of time, the voltage and charge of the capacitor equals to zero

An example RC circuit problem

Our solution to the problem

   

Day 16 Capacitors and Capacitive Circuits

Today we will be talking about Capacitors and Capacitive Circuits (to make this easier to understand, we focused more on the parallel aspects of capacitors). We learned how capacitors are voltage based, they they can charge and discharge, and we even learned about the new value for Capacitors, F (named after Faraday, capacitors are normally either in nanofaraday or microfaraday)

A few capacitors

We began the class by looking at different types of capacitors, including what the capacitor looks like on the inside, as Prof. Mason was kind enough to remove the blue shell that our typical class capacitors had, to show us that it is basically two different sheets placed parallel (very close, but not necessarily touching each other). The green one on the far right is our superconductors due to the fact that it had a lot more capacitance than the our standard capacitance.







Derivation of Capacitance vs A and d

How a capacitor operates

Since we know how the capacitor looks like (two parallel sheets), we can then use our former knowledge about electric field, and find a relationship between the electric field, the distance, and the voltage. We find that the voltage is directly proportional to both the electric field and the distance, yielding the equation V=Ed

How not to set up the capacitor

On a side note, Prof. Mason showed us that capacitors are not like resistors at all, and can really only go one way. If a capacitor is set to a reverse polarity (as shown in the picture) it can overload and eventually explode

An exploded capacitor 

More derivation on capacitance 

Back onto showing relationships, once we found the relationship between charge, capacitance and voltage, we could then find potential energy of a capacitor

Using epsilon to understand more on capacitance

We then took a familiar topic, epsilon, or the permeability of free space, and applied it to capacitance as well, saying that with area and distance, epsilon is also important as to finding capacitance.
We then also took an understanding of how epsilon naught, or the constant 8.854x10^-9 came to be 

An mini-lab with dielectric

In this mini lab we started to understand more about dielectrics by focusing on the dielectric of paper. We obtain these numbers by taking books of paper, and measured the capacitance, then calculated the dielectric for each instance

Another example problem

Within this example, we looked for the distance, the charge, the potential energy and the charge density of the capacitor in question

Another example problem

In this example problem, we focused on the capacitance of a car battery that would run solely on the charge that the capacitor stored. 

Last example problem

In this last example problem, we took into account the schematic of a simple capacitor, and calculated the dielectric in between two metal plats.

Day 15 Circuit Analysis

Today, we worked on understanding series and parallel circuits in DC

Morning Lab

Testing Bulb

Testing Battery

We spent the morning talking about which system, between series and paralllel has the brightest bulbs, and the brightest battery. The picture on the top shows that in series, the bulbs (represented by a schematics used for resistors) are the brightest, while in parallel, the batteries are shown to be the brightest, shown on the bottom picture. In order to maximize the brightness of the bulb, we need to maximize the amount of power delivered to the bulb, which is denoted by P=IV, power = the multitude of current and voltage.

Equation for power

Series Circuit and Parallel Circuit
This portion of the lab shows us how to use a multimeter to measure both voltages and currents in series and parallel circuits.

First portion of the lab (voltage in series)

This portion of the lab required us to understand the relationship between the voltage of the source and the voltage across the bulb, which shows that in series, they should be about equal to each other when added up

Recording current in series

In this portion of the lab, we find the relationship between currents all around, and we find out the current should be equal across the system in a series circuit

Voltage in parallel

In this portion of the lab, we find the voltages across the system should be about equal to each other across the parallel system

Current in Parallel

In this portion of the lab, we find that the current across the system should add up to be equal to the initial current in a parallel system








Resistance and its Measurementr

A cutaway view of a carbon resistor and its area

In this lab, we are going to oversee a few resistors, measure them based on their coloring code, and their acutal measurement, to see if they are within tolerable percent ranges

Resistors in question

Our resistors and coloring sequences

After looking at three different color sequences, and measuring for their resistances, we find that the percent difference yields less than 10%, making therm very valuable to buy.

More about Series and Resistors

Add caption

Taking from what we know from resistivity and adding it to equations for both series and parallel circuits, we can then find Resistance across both series and parallel circuits using length and area (along with the constant rho, that is found different within every metal)

Sample Problem answers

Kirchhoff's Law

Kirchhoff law states two thing

1)The sum of all the currents entering any node or branch point of a circuit (that is, where two or more wires merge)must equal the sum of all currents leaving the node.

2) Around any closed loop in a circuit, the sum of all emfs, voltage gains provided by batteries or other power sources, ( = emf) and all the potential drops across resistors and other circuit elements must equal zero.

By understanding these two laws, we can then understand how to solve for circuits that have more than one possible loop.

Sample problem involving Kirchhoff's Law

Answer to that problem 

It is to note that in this answer, the V50 and the V100 are the same, due to the fact that these system are parallel to each other

Current Flow (10/07/14)

During this class period, we went over current flow, and more on electromagnetism

Lighting A Bulb

A successful light bulb lit

We first watched a video on students trying to light a bulb with nothing more than a battery, a piece of wire, and of course a light bulb, then were asked to attempt the experiments ourselves
After a few tries, we learned the best way to light a bulb was to have both sides of the wire in contact with the battery and the bulb touching one of these wires would allow the bulb to light up
(It is to note to be careful about the wiring, if placed incorrectly, the wire heats up quickly and burns, as I personally experienced.



Afterwards, we were asked to answer the following questions for modeling a simple electric circuit
1) What does a battery give to a bulb? That is, what role does the battery play in the circuit?
2) What is getting “used up” in the bulb?

3) Why do you need a wire to go back from the bulb to the battery?

Our answer to those three questions

Below are videos that were taking after the Lighting a Bulb experiment, using a device that is able to react to electric fields

 The Concept of Electric Potential Difference
In order to get a better understanding of potential difference in electricity, we were asked a Physics 4A question regarding waterfalls and generator, and asked how big a generator has to be in order produce electricity, which requires two things about the waterfall itself.

Our response to this problem

We found out that what we need to know about the waterfall is height and maximum flow rate. We can then state that the flow rate can be related to current, and the height is the "potential"







We then related the waterfall and the generator to how a battery works, and decided that the height, or the potential difference in the waterfall, in terms of electricity is called voltage, and the current is the flow rate of the charge.
Power comes as a result, as it is the amount of energy received by the bulb (or generator)
We can then take all three of these units, and state that P=VI, where P is power in watts, V is voltage in joules/coulomb, and current in coulombs/second

Developing A Model for Current Flow

We were then asked to understand which models of the ones that were provided for us could best describe current. 
We predicted (and were correct) that model D came to be, based on the understanding that current has to be conserved or else the system wouldn't function.









Activity: Measuring Current
We then had to use an ammeter, a device used to detect current, in order to see whether or not current can be positive or negative

Using the obtained ammeter, we set up a simple circuit the way it was directed, and found out that the current flows positively. We then tested again, by flipping the leads, and found the indicator needle going negatively. (It is to note that the number on the ammeter was the same, just different signs)
Due to this model, we can then state that we have effectively proven our model of current flow to be indeed correct



Drift Velocity and Current
The following next few picture is understanding the concept of drift velocity in a current. Back in the waterfall example, we learned that the flow rate is indeed the current and the P=VI; in this example, we are learning the expression of current in a wire using area, velocity, density, and charge and a question based on finding drift velocity.

Derivation of Drift Velocity in a current

An example finding drift velocity

Ohm's Law
Next we went over the idea of Ohm's Law and the understanding of resistance. Using the set up that the video is going, we started to set the power supply to 3 volts, recording the voltages and currents, and then kept continuing till we reached about 12 volts

Our graph result

We eventually find out that the graph of voltage vs current creates a straight line, showing that there is indeed a direct relationship involving the two. Additionally, when the voltage was doubled, the resistance and the power both doubled, showing again a direct relationship between voltage and both resistance and power









Resitivity:
We then disconnected the circuit we had, and connected two wires with clip leads to the meter, in order to test for resistance of two metals, copper and nickel-silver

Our setup

Data Results

We then see that the relationship between resistance and length are actually directly proportional to each other

2 labs missing

On these following days, I was unable to show up to class, and cannot conduct a blog write-up of the experiments that occurred that day as a result

October 14th 2014 (Tuesday) - I missed class due to Jury Duty
November 6th 2014 (Thursday) - Class was canceled
November 11th 2014 (Tuesday) - Veteran's Day