# Introduction

In this lab we focused on analyzing data from a circuit consisting of a capictor and 2 resistors. The circuit was set up to allow voltage to flow through and emit enough to light the LED light. The voltage drop was then recorded and from that, we were able to conclude our analysis by seeing the difference in voltage before and after the resistors. Voltage vs. Time is the main theme of this analysis due to our understanding of how a capacitor works. We know that a capacitor acts very similar to a battery in regard to how it charges. It is expected that as data of time vs volatege is analyzed and graphed that there will be a linear relationship at first, which should be evident on the graphs initial plots. But as the voltage reaches a longer time, the rate at which the capacitor is chagring should decrease thus giving us a exponential graph of data.

# Data

The data collected as part of anaylsis includes the voltage output and the PWM reading. The data presented time in miliseconds and the measure of voltage before and after to allow us to analyze the difference in voltage levels and its behavior over time. Using the Arduino IDE and our microcontroller that provided a steady voltage, we were able to collect 52 rows of data. Rows 0 through 30 (A portion of total data) are depicted below and show the corresponding voltage and PWM level. To anaylze, all data was considered relevant and used in graphs and charts. This is very important as we are able to see when the capacitor is fully charged, which actually turns out to be slightly below the 200 PWM level.

# Shockley Equation

The Shockley diode equation or the diode law, gives the I–V (current-voltage) characteristic of an idealized diode. Graphing this equation results in an exponential graph and because of our use of a diode in our lab, we expected this conclusion. In the equation, the parameters consist of V for voltage, T for time, and I for current; all parameters used in our lab. After deriving this equation, you get a linear model which is why our data is closely related to a linear relationship but this model is not perfect which explains why it wouldn't completely represent our data and graph accurately but gives us a good idea about the characteristics of a diode.

# Analysis

The outcome from the data collected compares well to what was expected. We expected an initial linear relationship between time and voltage and through analysis we can see this is exactly what has happened. As time goes on, the voltage increases at a steady rate until it nears the time when the LED is lit at which point its rate then decreases. This forms the overall exponential graph shown. It is also apparent that when the data reaches a certain time, the voltage begins to decrease to a lower slope and this is because of the data recorded for when the LED light is lit and the voltage is lowered due to the circuit and the flow through the resistors. Whenever the voltage reaches its maximum, the graph then levels out and also contributes to the fit of an exponential conclusion.

Slope = 4.235

# Exercise 1

DALO-3

Without using calculus, I estimate that there is about a *16%* chance that a random number drawn out of this range will be above 35. I did this estimation simply by estimating the columns up to around 35 and adding them. This came to be 20,900 so I then subtracted 20,900 from the total of 25,000 and got 4,100. Which I then divided by 25,00 to obtain 16.4%. In a practical sense, say there were a random group of 25,000 people of various ages from 0 to 50 and just one was selected. There would be a 16% chance that this person would be over the age of 35.

# Exercise 2

DALO-1