Notes from Toppers
Notes for JEE Preparation: Accuracy and Precision in Measuring Instruments
1. Measuring Instruments:
- Vernier calipers:
- NCERT Reference: Physics (Class 11, Chapter 5: Laws of Motion)
- Additional notes:
- Construction and working principle
- How to read Vernier scale
- Precautions while using Vernier calipers
- Sources of error in using Vernier calipers
- Micrometer screw gauge:
- NCERT Reference: Physics (Class 11, Chapter 5: Laws of Motion)
- Additional notes:
- Construction and working principle
- How to read micrometer screw gauge scale
- Precautions while using micrometer screw gauge
- Sources of error in using micrometer screw gauge
- Spherometer:
- NCERT Reference: Physics (Class 12, Chapter 6: Dual Nature of Radiation and Matter)
- Additional notes:
- Construction and working principle
- How to use a spherometer to determine the radius of curvature and focal length of a spherical mirror or lens
- Precautions while using a spherometer
- Sources of error in using a spherometer
- Travelling microscope:
- NCERT Reference: Physics (Class 12, Chapter 9: Ray Optics)
- Additional notes:
- Construction and working principle
- How to use a travelling microscope to determine the focal length of a lens
- Precautions while using a travelling microscope
- Sources of error in using a travelling microscope
- Optical lever:
- NCERT Reference: Physics (Class 12, Chapter 14: Semiconductor Electronics)
- Additional notes:
- Construction and working principle
- Applications of optical lever in measuring small displacements and angular rotations
- Precautions while using an optical lever
- Sources of error in using an optical lever
2. Accuracy:
- Definition and significance:
- Accuracy refers to the closeness of a measurement to the actual value.
- It is important in scientific experiments and measurements to obtain reliable and meaningful results.
- Factors affecting accuracy:
- Accuracy is affected by various factors, including:
- Instrument’s precision
- Environmental conditions (temperature, pressure, humidity)
- Human errors
- Limitations of measurement techniques
3. Precision:
- Definition and significance:
- Precision refers to the degree of agreement between repeated measurements of the same quantity.
- It is important to ensure precision in measurements to obtain consistent and repeatable results.
- Factors affecting precision:
- Precision is affected by factors such as:
- Quality and calibration of measuring instruments
- Experimental conditions
- Observer’s skill and training
4. Least Count:
- Definition and calculation:
- Least count is the smallest value that can be measured or detected by a measuring instrument.
- It is calculated by dividing the smallest division on the measuring scale by the number of divisions on the scale.
- Relationship between least count and precision:
- Precision is inversely proportional to least count.
- A smaller least count indicates higher precision, meaning that the instrument can measure smaller changes in the quantity being measured.
5. Errors in Measurements:
- Types of errors (random and systematic):
- Random errors are caused by unpredictable factors and can be minimized but not completely eliminated.
- Systematic errors are consistent errors that occur due to a flaw in the measurement system or procedure.
- Sources of errors (instrumental, environmental, personal):
- Instrumental errors are caused by limitations or defects in the measuring instrument.
- Environmental errors are caused by factors such as temperature, humidity, and vibrations.
- Personal errors are caused by the observer’s limitations or mistakes.
- Minimization of errors:
- Errors in measurements can be minimized by:
- Using accurate and precise instruments
- Controlling environmental conditions
- Careful observation and data recording
- Proper calibration of instruments
- Taking multiple measurements and calculating the mean
6. Significant Figures:
- Definition and concept:
- Significant figures are the digits in a measurement that are considered reliable and meaningful.
- They include all the digits that are known with certainty, plus one estimated digit.
- Rules for determining significant figures:
- The number of significant figures in a measurement is determined by the following rules:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros (zeros before the first non-zero digit) are not significant.
- Trailing zeros (zeros after the decimal point) are significant if the decimal point is specified; otherwise, they are not significant.
- Rounding off numbers:
- Numbers are rounded off to a certain number of significant figures by dropping the digits beyond the desired number of significant figures and adjusting the last significant figure if necessary.
7. Uncertainty in Measurements:
- Definition and concept:
- Uncertainty in measurement refers to the doubt or lack of precision associated with a measurement.
- It is expressed as a range of values within which the true value of the measurement is likely to lie.
- Propagation of uncertainty:
- When multiple measurements with uncertainties are combined in calculations, the uncertainty of the final result depends on the uncertainties of the individual measurements.
- Expression of uncertainty in calculations:
- Uncertainty is expressed in calculations by using the concept of standard deviation or standard error of the mean.
- It is represented as a ± sign followed by the uncertainty value.
8. Precision and Accuracy in Experiments:
- Planning experiments for precise and accurate results:
- To obtain precise and accurate results in experiments, it is important to plan carefully by:
- Selecting appropriate measuring instruments
- Controlling experimental conditions
- Repeating measurements and calculating the mean
- Using statistical analysis to assess precision and accuracy
- Analysis of experimental data to assess accuracy and precision:
- Experimental data is analyzed to determine precision and accuracy by calculating:
- Mean and standard deviation
- Percentage error or relative error
- Correlation coefficient (for determining the relationship between variables)
By mastering these concepts and applying them effectively, students can significantly improve their understanding and problem-solving abilities related to accuracy and precision in measuring instruments, which is essential for success in the JEE exam and beyond.