Physics 1.4 Errors Practice Flashcards

Flashcards covering the definitions of measurement errors, the categories of systematic and random errors, and the mathematical steps for error estimation including absolute, relative, and percentage errors.

Error

A fault which may occur even in the most careful observation, a deviation of measurement from standard value, or an uncertainty in a given measurement.

Instrumental error (Constant error)

An error caused due to faulty instrument because of faulty construction or faulty calibration, resulting in a constant amount of difference from the true value across all observations.

Systematic error (Persistent error)

Error caused due to defective setting of instrument, defective adjustment, or unsystematicness of the experimentor, which exists due to known causes.

Personal error

A systematic error due to restlessness or fault of an observer while taking readings, such as failing to ensure eye sight is exactly perpendicular to the display to remove parallax.

Error because of external causes

Errors arising due to changes in environmental conditions, such as change in temperature, humidity, or pressure.

Error due to defect in the system

Error resulting from a defective or imperfect experimental setup, such as improper thermal contact between a thermometer and a metal rod.

Random errors

Errors caused due to experimental conditions and human limitations, such as voltage fluctuations during electrical experiments or variations in stopwatch timing.

Methods to minimize errors

Taking large magnitude of the physical quantity to be measured, taking a large number of readings, and using an instrument with a smaller least count.

Estimation of errors

A process used to minimize error, understand accuracy and precision, calibrate instruments, and determine if a job meets tolerance levels in quality control.

Corrected reading

The adjustment of a reading based on a constant error, calculated as $\text{reading} \pm \text{zero error}$ where a $+ve$ zero error requires a $-ve$ correction.

Mean (average) reading ($x_m$)

The sum of all corrected readings divided by the total number of readings, also referred to as the most probable value.

Absolute error ($\delta x$)

The difference between an individual corrected reading and the mean (average) reading, calculated as $\delta x = |x_c - x_m|$.

Average (mean) absolute error ($\delta x_{avg}$)

The average of all individual absolute errors, calculated as $\delta x_{avg} = \frac{\delta x_1 + \delta x_2 + \delta x_3}{3}$ in a three-reading set.

Relative error

The ratio of average absolute error to the mean (average) reading, expressed as $\frac{\delta x_{avg}}{x_m}$.

Percentage error

A way of expressing a relative error as a fraction of $100$, calculated as $\text{Relative error} \times 100$.