N a simple electric circuit, Ohm's law states that V=IR, where V is the voltage in Volts, I is the current in Amperes, and R is the resistance in Ohms. Assume that, as the battery wears out, the voltage decreases at 0.02 Volts per second and, as the resistor heats up, the resistance is increasing at 0.04 Ohms per second. When the resistance is 300 Ohms and the current is 0.02 Amperes, at what rate is the current changing?

Given Information:  

Rate of change of Voltage = dV/dt = -0.02 V/s

Rate of change of Resistance = dR/dt = 0.04 Ω /s

Resistance = R = 300 Ω

Current = I = 0.02 A

Required Information:  

Rate of change of current = dI/dt = ?

dI/dt = -6.93x10⁻⁵ A/s

Explanation:  

The Ohm's law is given by

V = IR  eq. 1

Where V is the voltage across Resistance R and I is the current flowing through the Resistance R

Taking derivative of eq. 1 with respect to time t yields

dV/dt = I*dR/dt + dI/dt*R

dI/dt*R = -I*dR/dt + dV/dt

dI/dt = (-I*dR/dt + dV/dt)/R  eq. 2

Now substitute the given values into eq. 2

dI/dt = (-0.02*0.04 + (-0.02))/300

dI/dt = (-0.0008 - 0.02)/300

dI/dt = -0.0208/300

dI/dt = -6.93x10⁻⁵ A/s

Therefore, the current is decreasing at the rate of 6.93x10⁻⁵ A/s

This doesn't work fully, but it's a start. Good Luck

#include <iostream>

#include <fstream>

#include <string>

#include <cstdlib>

using namespace std;

class People

{

private:

const static int SIZE = 30;  

string names[SIZE];  

int birth_years[SIZE];  

int count;  

void sort();  

void display();  

public:

People();

void simulate();

};

People::People()

{

count = 0;

// open both files

ifstream namesFile, birthyearsFile;

namesFile.open("Names.txt");

birthyearsFile.open("BirthYear.txt");

while (!namesFile.eof() && !birthyearsFile.eof() && count < SIZE)

{

 getline(namesFile, names[count]);  

 birthyearsFile >> birth_years[count];  

 count++;  

}

// files open failed, exit the program

if (namesFile.fail() || birthyearsFile.fail())

{

 cout << "Unable to open input file(s). Terminating" << endl;

 exit(1);

}

//close the files

namesFile.close();

birthyearsFile.close();

sort();

display();

}

void People::sort()

{

for (int i = 0; i < count - 1; i++)

{

 for (int j = 0; j < count - 1 - i; j++)

 {

 if (names[j] > names[j + 1])

 {

   string tempName = names[j];

   names[j] = names[j + 1];

   names[j + 1] = tempName;

   int tempYear = birth_years[j];

   birth_years[j] = birth_years[j + 1];

   birth_years[j + 1] = tempYear;

 }

 }

}

}

void People::display()

{

cout << "Alphabetical Roster of Names: " << endl;

for (int i = 0; i < count; i++)

{

 cout << names[i] << "\t" << birth_years[i] << endl;

}

cout << endl;

}

void People::simulate()

{

int year;

cout << endl << "Names by Birth Year" << endl;

// input the birth year

cout << "Please enter the birth year: ";

cin >> year;

// loop that continues until valid input has been read

while (cin.fail() || year < 1995 || year > 2005)

{

 cin.clear();  

 cin.ignore(100, '\n');  

 cout << "Invalid birth year entered, try again: ";  

 cin >> year;

}

bool found = false;  

for (int i = 0; i < count; i++)

{

 if (birth_years[i] == year)  

 {

 if (!found)  

 {

   cout << endl << "For the birth year of " << year << ":" << endl;

   found = true;

 }

 // display the name

 cout << names[i] << endl;

 }

}

// no name with birth year found

if (!found)

 cout << endl << "No names with the birth year " << year << "." << endl;

cout << "End of results" << endl;

}

int main()

{

People people;  

people.simulate();  

return 0;

}

Explanation: