Circuiti RC

A carica completata, il bilancio energetico impone che l'energia erogata dalla batteria durante la carica $\Delta U_B$ sia uguale all'energia immagazzinata dal condensatore $\Delta U_C$ più quella $\Delta U_R$ dissipata sul resistore $R$
Verifichiamo questo assunto:

Immagine da: https://ludusrusso.cc/

                int tau;
int R;

int experiment_counter;
void setup() {
  // put your setup code here, to run once:
  tau = 1; // tau = 1 second
  R = 1e6; // R = 1e6 ohm
  experiment_counter = 0;
  int bps = 9600; // velocità, espressa in bps (boud rate per secondo).
  Serial.begin(bps);
  pinMode(2,OUTPUT); // set pin mode of second pin to OUTPUT

  //make sure there is no tension in the capacitor at the beginning of experiment
  digitalWrite(2, LOW); // turn OFF battery
  delay(6*1000); // wait 6 seconds

}

void charge(){
  digitalWrite(2, HIGH); //// turn ON battery
  Serial.print("Experiment n. ");
  Serial.print(experiment_counter);
  Serial.print("\n");
  unsigned long startChargingTime = millis();
  unsigned long chargeTime = startChargingTime;
  int seconds = 6;
  while(chargeTime < startChargingTime+seconds*1000){
     int sensorValue = analogRead(A0); //read tension
     float voltage = sensorValue * (5.0 / 1023.0); // Convert the analog reading (which goes from 0 – 1023) to a voltage (0 – 5V)
     chargeTime = millis(); //get current time
     Serial.print(chargeTime-startChargingTime); // print charging time
     Serial.print(" ");
     Serial.print(voltage); //print voltage
     Serial.print("\n");
     delay(100); //wait 100ms
  }

}

void discharge(){
  digitalWrite(2, LOW); // turn OFF battery
  int seconds = 6;
  Serial.println("Discharging...");
  unsigned long startDischargingTime = millis();
  unsigned long dischargeTime = startDischargingTime;
  while(dischargeTime < startDischargingTime+seconds*1000){
    int sensorValue = analogRead(A0); //read tension
    float voltage = sensorValue * (5.0 / 1023.0); // Convert the analog reading (which goes from 0 – 1023) to a voltage (0 – 5V)
    dischargeTime = millis();
    Serial.print(dischargeTime-startDischargingTime); // print charging time
     Serial.print(" ");
     Serial.print(voltage); //print voltage
     Serial.print("\n");
     delay(100); //wait 100ms
  }

}

void stop(){
  Serial.println("Stopping sketch");
  while(1);
}

void loop() {
  // put your main code here, to run repeatedly:
  charge();
  discharge();
  experiment_counter++;
  if(experiment_counter==50){
    stop();
  }
}
                
              

                #include < iostream >
#include < fstream >
#include < string >

#define N_DATA 61 // data gathered during charging/discharging
#define N_EXPERIMENTS 50 // numbers of time the experiment wasrepeted

struct CapacitorData // structure containing data to be plotted
{
    Double_t avg_voltages[N_DATA]; // Y axis
    Double_t avg_times[N_DATA]; // X axis
    int experiment_counter = 0;
};

void readData(std::ifstream &f,CapacitorData &c){
    Double_t time, voltage;
    std::string line;
    for(int i=0;i< N_DATA; i++){
        std::getline(f, line);
        std::istringstream iss(line);
        iss >> time >> voltage;
        c.avg_times[i] = ((c.avg_times[i]*c.experiment_counter) + time/1000)/(c.experiment_counter+1);
        c.avg_voltages[i] = ((c.avg_voltages[i]*c.experiment_counter)+ voltage)/(c.experiment_counter+1);
    }
    c.experiment_counter++;
}
void readFile(string fileName, CapacitorData &c, CapacitorData &d){    
    std::ifstream dataFile;
    string line;
    dataFile.open(fileName);
    if(!dataFile){
        std::cerr<< "Unable to open file: "<< fileName << std::endl;
        exit(1);    
    }
    for(int i=0;i < 2; i++){
        std::getline(dataFile, line); // read "Experiment n. #"
        readData(dataFile, c);
        std::getline(dataFile, line); // read "Discharging..."
        readData(dataFile, d);    
    }   
}

void analysis() {
    CapacitorData charging;
    CapacitorData discharging;
    readFile("capacitor_data.txt", charging, discharging); // read data and fill charging/discharging structures
    TCanvas *c = new TCanvas("c", "Capacitor D.D.P. over time", 200, 200, 950,700); // create canvas
    TGraph *graphFromData = new TGraph(N_DATA,charging.avg_times,charging.avg_voltages);
    graphFromData->Draw();  // draw graph of charging
    TF1 *expectedGraph = new TF1("expectedGraph","5*(1-e^(-x/1))",0,6);
    expectedGraph->Draw("same"); //draw expected graph
    TLegend *legend = new TLegend(.1,.7,.3,.9);     //adding legend
    legend->AddEntry(graphFromData,"d.d.p over time","l");
    legend->AddEntry(expectedGraph,"Expected result","l");
    legend->Draw();
    graphFromData->GetYaxis()->SetTitle("D.D.P. [V]"); // set axis name
    graphFromData->GetXaxis()->SetTitle("Time [s]"); // set axis name}
}