Devices

Voltage



      /*
        AnalogReadSerial

        Reads an analog input on pin 0, prints the result to the Serial Monitor.
        Graphical representation is available using Serial Plotter (Tools > Serial Plotter menu).
        Attach the center pin of a potentiometer to pin A0, and the outside pins to +5V and ground.

        This example code is in the public domain.

        https://www.arduino.cc/en/Tutorial/BuiltInExamples/AnalogReadSerial
      */

      // the setup routine runs once when you press reset:
      void setup() {
        // initialize serial communication at 9600 bits per second:
        Serial.begin(9600);
      }

      // the loop routine runs over and over again forever:
      void loop() {
        // read the input on analog pin 0:
        int sensorValue = analogRead(A0);
        // print out the value you read:
        Serial.println(sensorValue);
        delay(1);        // delay in between reads for stability
      }

The voltage divider

The Voltage Divider circuit is the easiest way to measure an unknown resistance. It has some limitations, but will essentially work for many applications $$ V_{\mathrm {out} }={\frac {R_{ref}}{R_{unknown}+R_{ref}}}\cdot V_{\mathrm {in} }$$

$R_?$

Let's consider the ways we can affect $R_?$.

The first equation you saw that even mentioned $R$ was probably Ohm's law. $$ R = \frac{V}{I} $$

Deeper look at $R$.

Consider the resistivity instead: $$ \rho = \frac{E}{J} $$

A little substitution leads to $$R = \rho \frac{L}{A}$$

A little more leads to a relation between resistivity and some of the properties of a particular material. $$ \rho = \frac{m}{e^2 n \tau}$$ ($m$ is the mass of an electron, $e$ its charge, $n$ is the electron density (i.e. carriers per volume), and $\tau$ is the mean free time (i.e. time between collisions) )

$R$ as a function of Temperature

One of the first discoveries is that the resistivity will change due to temperature. $$ \rho - \rho_0 = \rho_0 \alpha \left( T - T_0\right) $$

This relation is a linear approximation and is not sufficient for many situations. Though, for most metals within certain T ranges, it suffices.

Python code snippit to make the above plot:


import numpy as np
import matplotlib.pyplot as plt

temp = np.linspace(0, 500, 500)
T_0 = 293
alpha = .00386
rho_0 = 1.72E-8
rho = rho_0*(1+alpha*(temp-T_0))

fig, ax = plt.subplots(figsize=(7, 5))

ax.plot(temp, rho)
ax.set_xlabel('Temp [K]')
ax.set_ylabel('Resistivity [$\\Omega \cdot$ m]')
ax.set_title('Resistivity vs. Temperature for Copper')
ax.plot(temp[293], rho[293],'o', color = 'tab:blue')
ax.grid()
plt.annotate("Room Temperature", # this is the text
                 xy=(temp[293], rho[293]), # these are the coordinates to position the label
                 textcoords="offset points", # how to position the text
                 xytext=(-40,40), # distance from text to points (x,y)
                 ha='center',
                 va='bottom',
                 bbox=dict(boxstyle='round,pad=0.5', fc='white', alpha=0.2),
                 arrowprops=dict(arrowstyle = '-|>', connectionstyle='arc3, rad=0')) 
plt.show()

Other materials/situations

Resistivity vs. Temperature for an intrinsic semiconductor)

Very Low temperatures: superconductivity

Semiconductors, different relationship: $$\rho = \rho_0 e^{-a T}$$ (Note the log scale)

The Thermistor

These devices are designed to have resistance values that are very dependent on temperature. They are semi-conductors and can be custom made for specific temperature ranges.

The Steinhart–Hart equation approximates their temperature/resistance dependance. $$ \frac{1}{T}=A+B\ln R+C(\ln R)^{3} $$ where, $A$, $B$, and $C$ are constants specific to the actual device. (Note: there are several other forms of this equation. Use the product data sheet when you do your lab.)

Two kinds: NTC (Negative Temperature Coefficient) and PTC (Positive Temperature Coefficient)

Found in kitchens, living rooms, hospitals, labs, etc...

Calibration tool (online at https://www.vishay.com/en/thermistors/ntc-rt-calculator/

Measuring T with arduino

It's not much different than what we did before, except now we have a time variable to record also.

The Arduino Programming Referencehttps://www.arduino.cc/reference/en/

The language reference is something to get used to working with.

For example, we need to find some way to record the time:

millis()

This function just returns the number of milliseconds since the sketch started running. Learn how to use it here:

https://www.arduino.cc/reference/en/language/functions/time/millis/



void setup() {  
  Serial.begin(9600);
}

void loop() {
  
  int sensorValue = analogRead(A0);

  // Add time to the serial out put.
    
  Serial.print(millis());
  Serial.print(',');
  Serial.println(sensorValue);
  
  delay(10);
}

Here is our familiar analog read sketch. We just added some more stuff to send to the console.

Serial.print() vs. Serial.println()

Data Format

A very common data format is the csv (comma separated values)


DataColumn1, DataColumn2
0.0,432
0.1,433
0.2,436
...