Lecture Summary

Introduction to Errors and Measurements in Physics

Physical Quantities: Quantities that can be measured and explained using the laws of physics. Examples: length, mass, temperature, speed, force, electric current.
MKS and SI Systems: MKS (Meter-Kilogram-Second) is a subset of the SI (International System) that includes additional quantities like the ampere for electric current.
Fundamental Quantities: Quantities not dependent on other quantities. Examples: length (meter), mass (kilogram), time (second), temperature (kelvin), electric current (ampere), luminous intensity (candela), amount of substance (mole).
Derived Quantities: These depend on fundamental quantities. Examples: area (length²), volume (length³), density (mass/volume).
Dimensional Analysis: Represents physical quantities in terms of fundamental quantities. Used for converting units, checking equation correctness, and deriving relationships.

Types of Errors:
- Constant Error: Same error in all measurements.
- Systematic Error: Consistent error in one direction (positive or negative). Includes instrumental errors, imperfections in experimental techniques, and personal errors.
- Random Error: Irregular and varying errors due to unpredictable factors.
- Least Count Error: Error due to the resolution of the measuring instrument.
- Gross Error: Large mistakes due to human errors or equipment failures.

Absolute Error: Difference between true value and measured value.
Mean Absolute Error: Arithmetic mean of absolute errors from multiple measurements.
Relative Error: Absolute error divided by true value.
Percentage Error: Relative error multiplied by 100.

Addition/Subtraction:
- Absolute error in sum/difference is the sum of absolute errors of individual quantities.
Multiplication/Division:
- Relative error in product/quotient is the sum of relative errors of individual quantities.

Various examples illustrating how to derive dimensional formulas for different physical quantities using fundamental quantities.

Significant Figures: Digits in a measurement known with certainty plus one uncertain digit.
Rules for Significant Figures:
- Non-zero digits are always significant.
- Zeros between significant digits are significant.
- Leading zeros are not significant.
- Trailing zeros in a decimal number are significant.
Rounding Off Rules:
- Greater than 5: Increase by one.
- Less than 5: Leave unchanged.
- Equal to 5: Make the previous digit even.

Calculating errors in various practical scenarios including the measurement of physical constants, combination of resistances, and periods of oscillations.