Physics Lecture: Understanding Uncertainties in Experiments

Introduction

• Objective: Understand uncertainties in experiments to become "extremely certain about the uncertainties."
• Types of Uncertainties:
  • Absolute Uncertainties
  • Percentage Uncertainties

Absolute Uncertainties

• Definition: The smallest measurement that can be taken by an instrument.
  • Example: A millimeter ruler's absolute uncertainty is 1 mm.
• Digital Instruments: The last digit indicates the absolute uncertainty.
  • Example: For a voltmeter reading of 5.46 volts, the absolute uncertainty is between 5.45 volts and 5.47 volts.

Percentage Uncertainties

• Formula:
  • ( \text{Percentage Uncertainty} = \frac{\text{Absolute Uncertainty}}{\text{Experimental Value}} \times 100 )
• Example Calculation:
  • Absolute Uncertainty: 0.01
  • Experimental Value: 5.46
  • Calculation: ( \frac{0.01}{5.46} \times 100 = 0.18% )

Converting Between Uncertainties

• Example:
  • Reading: 50 volts with ±5% uncertainty
  • Absolute Uncertainty: 5% of 50 volts = 2.5 volts
  • Expression: 50 volts ± 2.5 volts

Combining Uncertainties

Adding or Subtracting Quantities

• Rule: Add absolute uncertainties.
• Example:
  • V1: 5.0 ± 0.1 volts
  • V2: 4.0 ± 0.2 volts
  • Total Voltage: 9.0 volts ± 0.3 volts
  • Percentage Uncertainty: ( \frac{0.3}{9.0} \times 100 = 3.3% )

Multiplying or Dividing Quantities

• Rule: Add percentage uncertainties.
• Example:
  • Voltage: 5.0 ± 0.1 volts
  • Current: 1.1 ± 0.1 amp
  • Resistance: ( R = \frac{V}{I} )
  • Percentage Uncertainty in R: 11%

Raising to a Power

• Rule: Multiply the percentage uncertainty by the power.
• Example:
  • Quantity: Side of a cube, 4.0 ± 0.1 meters
  • Volume: ( 4^3 = 64 \text{ cubic meters} )
  • Volume's Percentage Uncertainty: 7.5%
  • Expression: 64 cubic meters ± 7.5%

Summary

• Addition/Subtraction: Add absolute uncertainties.
• Multiplication/Division: Add percentage uncertainties.
• Power Rule: Multiply percentage uncertainty by the power.

Additional Resources

• Next Topic: Finding uncertainty from a graph.
• Link: Provided in the video description for further revision.

Thank you for engaging with the lecture. Questions are welcomed through the video comments section.