Units and Measurements — Part 2: Errors and dimensional analysis: visual lesson, CBSE Class 11 Physics

Lesson

Errors and dimensions

Part 2 — no measurement is exact, so how far can a result be trusted? And how can dimensions alone expose a wrong equation?

In this lesson you will

Find absolute, relative and percentage error and combine errors in calculations
Write dimensional formulae and check whether an equation is consistent
Deduce relations by dimensional analysis and state its limitations

Concept

Accuracy, precision and kinds of error

Accuracy is how close a result is to the true value. Precision is how closely repeated readings agree with each other. A set of readings can be precise but inaccurate.

Table comparing systematic errors, random errors and least-count error: causes, effects and remedies
Kind of error	Cause	Effect and remedy
systematic	zero error, faulty calibration, a wrong method, a habit of the observer	shifts every reading the same way; correct it or change the method
random	unpredictable small changes in reaction time, temperature, draughts	scatter both ways; reduce by taking many readings and averaging
least count	the smallest division the instrument can show	a fixed limit on any single reading; use a finer instrument

Diagram

Repeated readings, mean and error

Several students time the same event. Each reading differs from the mean by an absolute error.

The mean is the best estimate of the true value.
The mean absolute error is the average of the absolute errors; it describes the spread.

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