Due 08/01/20

Voltage Drop for a Discharging Capacitor

# loading the data set

volts<- read.csv("Volts.csv")

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals. Capacitors typically discharge slowly when a resistor is connected to each leg. The resistor must be rated for the same or higher voltage than the capacitor can store for this method of discharge in order to work safely. Let’s take a look at the summary of the Voltage Drop for a Discharging Capacitor:

summary(volts)

##        X            Voltage           Time      
##  Min.   : 1.00   Min.   :1.240   Min.   :0.000  
##  1st Qu.:13.25   1st Qu.:1.956   1st Qu.:0.245  
##  Median :25.50   Median :3.199   Median :0.490  
##  Mean   :25.50   Mean   :3.873   Mean   :0.490  
##  3rd Qu.:37.75   3rd Qu.:5.381   3rd Qu.:0.735  
##  Max.   :50.00   Max.   :9.213   Max.   :0.980

View(volts)

Upon reviewing the .csv file, one can see that as time progresses, the voltage drop decreases. Based on the file, is there a correlation between average rate of voltage decay for capacitors over time?

Let’s analyze the original volt.csv file.

#mean

mean(volts$X, na.rm = TRUE)

## [1] 25.5

mean(volts$Voltage, na.rm = TRUE)

## [1] 3.873356

mean(volts$Time, ra.rm = TRUE)

## [1] 0.49

#median

median(volts$X, na.rm = TRUE)

## [1] 25.5

median(volts$Voltage, ra.rm = TRUE)

## [1] 3.1986

median(volts$Time, ra.rm = TRUE)

## [1] 0.49

I will compare the voltage decay by creating two new data frames with a subset of the columns and rows.

halfvolts<-subset(volts[c(1:25),c("X","Voltage","Time")])
View(halfvolts)

secondhalfvolts<-subset(volts[c(26:50),c("X","Voltage","Time")])
View(secondhalfvolts)

summary(halfvolts)

##        X         Voltage           Time     
##  Min.   : 1   Min.   :3.268   Min.   :0.00  
##  1st Qu.: 7   1st Qu.:4.203   1st Qu.:0.12  
##  Median :13   Median :5.435   Median :0.24  
##  Mean   :13   Mean   :5.723   Mean   :0.24  
##  3rd Qu.:19   3rd Qu.:7.066   3rd Qu.:0.36  
##  Max.   :25   Max.   :9.213   Max.   :0.48

#mean

mean(halfvolts$X, na.rm = TRUE)

## [1] 13

mean(halfvolts$Voltage, na.rm = TRUE)

## [1] 5.723144

mean(halfvolts$Time, ra.rm = TRUE)

## [1] 0.24

#median

median(halfvolts$X, na.rm = TRUE)

## [1] 13

median(halfvolts$Voltage, na.rm = TRUE)

## [1] 5.4353

median(halfvolts$Time, ra.rm = TRUE)

## [1] 0.24

summary(secondhalfvolts)

##        X         Voltage           Time     
##  Min.   :26   Min.   :1.240   Min.   :0.50  
##  1st Qu.:32   1st Qu.:1.538   1st Qu.:0.62  
##  Median :38   Median :1.936   Median :0.74  
##  Mean   :38   Mean   :2.024   Mean   :0.74  
##  3rd Qu.:44   3rd Qu.:2.453   3rd Qu.:0.86  
##  Max.   :50   Max.   :3.129   Max.   :0.98

#mean

mean(secondhalfvolts$X, na.rm = TRUE)

## [1] 38

mean(secondhalfvolts$Voltage, na.rm = TRUE)

## [1] 2.023568

mean(secondhalfvolts$Time, ra.rm = TRUE)

## [1] 0.74

#median

median(secondhalfvolts$X, na.rm = TRUE)

## [1] 38

median(secondhalfvolts$Voltage, na.rm = TRUE)

## [1] 1.9361

median(secondhalfvolts$Time, ra.rm = TRUE)

## [1] 0.74

#Scatter plot of volts

plot(volts$Time, volts$Voltage,xlab = 'Time', ylab = 'Voltage', main = 'Volts', ylim = c(0,10), pch = 20 , col='blue')

#Scatter plot of half volts


plot(halfvolts$Time, halfvolts$Voltage, xlab = 'Time', ylab = 'Voltage', main = 'Half Volts', ylim = c(0,10), pch = 20 , col='red')

#Scatter plot of second half volts

plot(secondhalfvolts$Time, secondhalfvolts$Voltage, xlab = 'Time', ylab = 'Voltage', main = 'Second Half Volts', ylim = c(0,10), pch = 20 , col='green')

# Box plot of volts

boxplot(volts, col="blue")

#Box plot of half volts

boxplot(halfvolts,col="red")

#Box plot of second half volts

boxplot(secondhalfvolts,col="green")

#Histogram of volts in respect to time

hist(volts$Time, xlab = 'Time', ylab = 'Voltage', main = 'Volts', ylim = c(0,10), pch = 20 , col='blue')

#Histogram of volts in respect to Voltage

hist(volts$Voltage, xlab = 'Time', ylab = 'Voltage', main = 'Volts', ylim = c(0,10), pch = 20 , col='blue')

#Histogram of half volts in respect to time

hist(halfvolts$Time, xlab = 'Time', ylab = 'Voltage', main = 'Volts', ylim = c(0,10), pch = 20 , col='red')

#Histogram of half volts in respect to voltage

hist(halfvolts$Voltage, xlab = 'Time', ylab = 'Voltage', main = 'Volts', ylim = c(0,10), pch = 20 , col='red')

#Histogram of second half volts in respect to time

hist(secondhalfvolts$Time, xlab = 'Time', ylab = 'Voltage', main = 'Volts', ylim = c(0,10), pch = 20 , col='green')

#Histogram of second half volts in respect to voltage

hist(secondhalfvolts$Voltage, xlab = 'Time', ylab = 'Voltage', main = 'Volts', ylim = c(0,10), pch = 20 , col='green')

Based on the data provided, the mean voltage drop of the original .csv is 3.87V with an average time of 0.49 seconds. The initial voltage drop of at t = 0 is 9.2128V. Half volts had an average voltage drop of 5.723V with an average time of 0.24 seconds. Second half volts had an average voltage drop of 2.024V with an average time of 0.74 seconds. The capacitor discharge equation is V = Voe-(t/RC).When t = RC, V = Vo/e = 0.37 Vo and the product RC is known as the time constant for the circuit. The bigger the value of RC, the slower the rate at which the capacitor discharges. The average rate of voltage drop is dependent in respect to time.

#BONUS

volts<- read.csv("https://raw.githubusercontent.com/sagreen131/R-Week-3/master/Volts.csv")

Shana Green

R Bridge

Final Project

Due 08/01/20