Experiment 9

Simple Circuit Experiment Setup

  • Components Used:

    • Series circuit consisting of:
    • Coil (indicated by a curly symbol)
    • Resistor (2 kΩ)

  • Arduino Pin Setup:

    • 3.3 volts applied to the coil from the Arduino's 3.3V pin.
    • Connection of the coil to the resistor leading to ground.
    • Midpoint Measurement:
    • The voltage is measured at the junction between the coil and the resistor using the Arduino.

Theory of Operation

  • The Arduino can measure voltage from 0 volts to 5 volts.
  • Using 3.3 volts as the input to the coil serves as a baseline; any induced voltage due to a change in magnetic field will fluctuate above or below this.
  • Since the resistance of the coil is low (approximately 1-2 Ω), the voltage drop across the coil is negligible.

Voltage Measurement

  • Expected midpoint voltage at the junction just after applying 3.3 volts will be close to 3.3 volts (possibly around 3.2 volts).
  • As a magnet traverses through the coil, it induces voltage variances that can be both positive and negative.

Experimental Setup Procedure

  1. Setting up the components on a breadboard:

    • Connect the 3.3V pin of the Arduino to the coil using a red alligator clip.
    • Connect the coil to one side of the resistor and then connect the other side of the resistor to ground.

  2. Data Collection Settings:

    • Utilize a baud rate of 230,400 for high-speed data capture as the magnet moves rapidly through the coil.
    • Ensuring that the data is collected within a time frame of less than 3000 milliseconds (3 seconds).
    • Analog reading will be performed on pin 0 to capture the voltage at the midpoint.
    • Convert the data for display, which can then be printed in the Serial Monitor of the Arduino IDE.

  3. Data capture procedure:

    • After setting everything, reset the Arduino, and be prepared to drop the magnet to start data collection.
    • Start the collection as numbers appear in the Serial Monitor.

Data Analysis and Expected Observations

  • Waveform of Voltage:
    • The expected graph should show a baseline voltage followed by spikes in either direction when the magnet is introduced and retrieved from the coil.
    • Magnets have a north pole and south pole, which will affect the direction of electrical current induced when either pole moves through the coil.
    • Depending on whether the north or south pole is first introduced to the coil, the induced voltage will be flipped in corresponding direction.

Faraday's Law

  • The experiment aims to validate Faraday's Law which states:
    • The induced voltage ( = - rac{d ext{flux}}{dt})
    • Voltage induced in a coil is linearly proportional to the rate of change of the magnetic flux through that coil.

Experimental Variations

  • Changing the height from which the magnet is dropped will alter the magnet's speed as it moves through the coil:
    • Starting at 43 centimeters, change in increments of 10 centimeters (between 20 cm and 80 cm) will yield different speeds.
    • Height affects gravitational potential energy, converting to kinetic energy:
    • Kinetic Energy = Potential Energy, or mgh = rac{1}{2}mv^2 which reduces to:
    • v = ext{sqrt(2gh)} with gravitational constant g = 9.8 ext{ m/s}^2.

Data Collection Approach

  • Measure voltage change (delta voltage) relative to baseline voltage:
    • This voltage change will be plotted against the speed of the magnet.
    • Example of the equation for delta velocity is based on gravitational potential energy, reiterated:
    • ext{delta } v = ext{base height} - 3.3
  • The first peak observed (either positive or negative) is recommended for data collection, as the second peak may represent interference while the magnet exits the coil.

Capacities in Data Analysis:

  • Data Collection Guidance:
    • Utilize Excel to input and plot data points collected.
    • The relationship between voltage change (delta v) and velocity (v) should demonstrate linear correlation consistent with Faraday's Law under ideal conditions.

Voltage Calculation Example

  • As noted in the discussion:
    • If the data reads 670 bits, the approximate conversion back to volts remains anchored to the baseline voltage of 3.3 volts.

Conclusion

  • The experiment is aimed at solidifying the concept behind electromagnetic induction while verifying Faraday’s Law through practical measurement and visualization of voltage changes across various heights and speeds of a magnetic drop.
  • Issues encountered related to Arduino data handling and data plotting were discussed, emphasizing the need for consistency in data input for accurate results.

Disclaimer: Ensure to verify the connection setup and coding fiascos are debugged to ensure clean data collection.