Error Analysis and Measurements Chapter 1.pptx

Important to start Class 11 Physics as per NCERT syllabus

1. Units and Measurements Error Analysis

2. Theory of Errors Measurements refers to the comparison of an unknown quantity with some known standard of same kind. i.e. measurement of length of a rod when compared with known standard of 1 cm on a scale. L= 3 inches L= 16 cm The resolution of a measurement depends on the least count of the instrument. i.e. Least count of one of the scale in figure is 1 cm. So, the measurement of L=16 cm can have uncertainty of 1 cm. This is referred as tolerance in measurement.

3. If the same length is measured as 16.1 cm then uncertainty in the measurement is 0.1 cm. If taken as 16.12 cm then uncertainty is 0.01 cm. Thus, as the precision of the reading increases uncertainty in measurement decreases. So, the uncertainty in a measurement is called error. Error can be reduced by taking readings with high precision. Any measurement is not perfect. It always has certain error or tolerance. Theory of Errors (continued)

4. Types of errors Systematic Error Random Error Always produce errors of same signs. Either positive or negative. Causes Instrumental error Technical error Personal error Can be corrected by finding the source of error and the rule governing this error. Can be of any type. Positive or negative. Causes Unknown reasons Chance errors Can’t be rectified. Can be reduced by taking as many readings as possible. (principle of probability)

5. Mean Absolute Error, Relative Error, Percentage Error

6. Calculations of Errors Absolute Error: It is the difference between measured value and true value of a physical quantity. Relative Error: It is the ratio of the absolute error to the true value. Percentage Error: The relative error expressed as percentage is called percentage error. percentage 100 So, any physical quantity is represented as   Mean value Absolute error