This document discusses different types of errors that can arise in measurement in physics experiments. It describes systematic errors, which are consistent biases in measurements, and random errors, which cause scattered readings. Systematic errors cannot be reduced by taking multiple readings, but may be reduced by improving techniques. Random errors can be decreased by taking the average of several readings. The document provides examples of different systematic and random errors and how to combine the uncertainties from multiple measurements to determine the total uncertainty.

1. Physics topic for senior secondary or
A-Level Physics

2. How do errors arise?
 Two causes of error in measurement:
 Choice of instrument
 Techniques of measurement
 It is held that one’s experimental technique must
reduce the uncertainties to the minimum possible
 The technique caused uncertainties are two kinds
 Systematic errors
 Random errors

3. Systematic error
 A systematic error occurs when readings are...
 Above or below the true value by fixed amount
 Error being in the same direction
 Features
 Systematic error can not be removed by taking a few
readings and taking mean value
 It can be reduced by improving experimental technique

4. Three types of systematic error
Type Main points
Instrumental
zero error
-Scale or it’s pointer not at zero before
the measurement starts
Scale graduated or
calibrated wrongly
-Calibrations are marked wrongly at the
instrument manufacturing site
-Check for reading with other
instruments
Experimentalist’s reaction time -When the instruments are operated
manually different people may report
different readings with the same
instruments

5. Random error
 It occurs when readings are scattered around the
accepted value
 It affects the precision of the instrument
 To reduce the random error
 Take a few readings
 Find the mean or average value of readings
 In graphs to reduce random error:
 Draw the best fit line

6. Some examples of random errors
 Judgement or interpolation in rounding up the scale
reading
 Timing without a reference marker
 While attempting to take reading of two variables at
the same time
 Parallax error due to reading of scale from different
angles of line of sight

7. Combining uncertainties
 In indirect measurement, often for a derived physical
quantity, to get the value of a physical quantity, a few
other quantities are measured with each of them having
their own uncertainties
 Combine or add up all certainties to determine the value of
uncertainty of the physical quantity being measured (for a
= b + c or b – c combination error equation is Δa = Δb +
Δc)
 Combine or add up all fractional uncertainties to
determine the value of uncertainty of the physical quantity
(for a = Kbc or Kb/c combination error equation is Δa =
Δb/b + Δc/c)

8. Two simple rule statements for
combining uncertainties
 Rule 1
 For the physical quantities which are added or
subtracted to give final results, add up absolute
uncertainties
 For For the physical quantities which are either
multiplied or divided, add up the fractional
uncertainties