Short Answer:

Absolute error is the difference between the measured value and the true or actual value of a quantity. It tells how much the measurement has deviated from the correct value, usually expressed in the same unit as the measurement.

Relative error is the ratio of absolute error to the true value. It shows how significant the error is in comparison to the actual value, and it is usually expressed as a percentage. While absolute error gives the size of the mistake, relative error gives an idea of its importance.

Detailed Explanation:

Absolute Error and Relative Error in Measurement

In electrical and scientific measurements, accuracy and precision are very important. However, no measurement is ever perfectly accurate due to limitations in instruments, human judgment, and external conditions. To understand how much error is present in a measurement, we use terms like absolute error and relative error. These terms help in evaluating how good or bad a measurement is.

Absolute Error

Definition:
Absolute error is the numerical difference between the measured value and the actual or true value of the quantity being measured.

Formula:
Absolute Error = |Measured Value − True Value|

Example:
If the true voltage is 100V and the measured voltage is 98V, then:
Absolute Error = |98 − 100| = 2V

Importance:

It tells the exact size of the mistake.
It is expressed in the same unit as the measurement (like volts, ohms, etc.).
It helps in understanding how far off the reading is from the correct value.

Limitations:

It does not give any idea about how serious the error is in comparison to the true value. For large values, a 2V error may be small, but for small values, it may be large. That’s where relative error helps.

Relative Error

Definition:
Relative error is the ratio of the absolute error to the true value. It shows how large the error is in comparison to the actual value.

Formula:
Relative Error = (Absolute Error / True Value)
Often expressed as a percentage:
Relative Error (%) = (Absolute Error / True Value) × 100

Example:
If the absolute error is 2V and the true value is 100V:
Relative Error = 2 / 100 = 0.02 or 2%

Importance:

It gives a better idea of the significance of the error.
It allows comparison of errors across different measurement scales.
It is especially useful when dealing with large or small values.

Why Both Are Important

Absolute error is useful when we need to know how much the measured value has shifted from the correct value.
Relative error is useful when comparing errors in different measurements or understanding the seriousness of an error in context.

Instruments and Measurement Systems:

Engineers and technicians use both errors to test and calibrate instruments.
In research and industry, keeping both absolute and relative error low ensures reliability and trust in the measurements.

How to Reduce These Errors

Use well-calibrated instruments.
Avoid parallax and human reading mistakes.
Take multiple readings and use average value.
Avoid environmental interference like temperature and vibration.
Use instruments within their accurate measuring range.

Conclusion

Absolute error tells the amount of deviation in measurement, while relative error tells how serious that deviation is compared to the true value. Both are important in analyzing the accuracy and quality of any measurement in electrical engineering. By understanding and reducing these errors, we can ensure better results and more reliable instrument readings in all types of applications.