The limiting error is an important concept in measurement systems that indicates the maximum possible error in a measurement. It helps define the accuracy and reliability of an instrument.
Table of Contents
Definition of Limiting Error
The limiting error is defined as the maximum deviation of the measured value from the true value that an instrument can have under specified conditions. It is usually expressed as a percentage of full-scale reading or percentage of true value.
Expression of Limiting Error
If the accuracy of an instrument is given as ±(\(x\%\)), then the limiting error is:
\[
\text{Limiting Error} = \pm x\% \text{ of full-scale value}
\]
Absolute Limiting Error
\[
\text{Absolute Error} = \pm \frac{x}{100} \times \text{Full Scale Reading}
\]
Relative Limiting Error
\[
\text{Relative Error} = \frac{\text{Absolute Error}}{\text{Measured Value}}
\]
Percentage Limiting Error
\[
\%\text{ Error} = \frac{\text{Absolute Error}}{\text{Measured Value}} \times 100
\]
Important Concept
Even though limiting error is specified with respect to full-scale value, the percentage error increases as the measured value decreases.
Example
An ammeter has:
- Full-scale reading = 100 A
- Accuracy = ±1%
Absolute Error
\[
\text{Error} = \pm 1\% \times 100 = \pm 1 \text{ A}
\]
Case 1: Reading = 100 A
\[
\%\text{ Error} = \frac{1}{100} \times 100 = 1\%
\]
Case 2: Reading = 50 A
\[
\%\text{ Error} = \frac{1}{50} \times 100 = 2\%
\]
Thus, percentage error increases at lower readings.
Types of Errors Related to Limiting Error
- Absolute Error – difference between true and measured value
- Relative Error – ratio of absolute error to true value
- Percentage Error – relative error in percentage
Importance of Limiting Error
- Determines accuracy of instruments
- Helps in instrument selection
- Important for precision measurements
- Used in error analysis
Practical Implications
- Instruments should be used near full-scale reading for better accuracy
- Avoid taking measurements at very low values on high-range instruments