Short Answer:

Percentage error is the measure of how much a measured value differs from the true or actual value, expressed as a percentage of the true value. It helps us understand the size of the error in comparison to the actual quantity being measured.

To calculate percentage error, subtract the true value from the measured value, take the absolute value of the result, divide it by the true value, and multiply by 100. This gives a clear idea of how accurate or inaccurate the measurement is in percentage terms.

Detailed Explanation:

Percentage Error 

In electrical engineering and science, measurements are rarely perfect. There is always some difference between the measured value and the actual or true value. This difference is known as an error. Percentage error is a simple and effective way to express this error in a clear and understandable form. It shows how big the error is in comparison to the true value, and it is expressed in percentage.

Meaning of Percentage Error

Percentage error tells us how much the measured value deviates from the true value in terms of percentage. It shows the accuracy of the measurement. A small percentage error means the measurement is close to the actual value, while a large percentage error shows the measurement is less accurate.

It is helpful in comparing different measurements or results taken using different instruments or methods.

Formula for Percentage Error

The percentage error is calculated using the following formula:

Percentage Error (%) = (|Measured Value − True Value| / True Value) × 100

Explanation of Terms:

• Measured Value: The value you get from your instrument.
• True Value: The actual or correct value of the quantity.
• | |: The absolute value (always take the positive value of the difference).

Example:

If the true value of voltage is 100V and the measured value is 95V:

Percentage Error = (|95 − 100| / 100) × 100
= (5 / 100) × 100 = 5%

This means the measurement has a 5% error from the actual value.

Importance of Percentage Error

1. Shows Accuracy Clearly
   By converting the error into a percentage, it becomes easier to understand how accurate a measurement is.
2. Useful for Comparisons
   It allows comparison between errors in different types of measurements regardless of their units.
3. Guides Instrument Selection
   Helps in deciding which instrument gives more accurate results based on lower percentage error.
4. Helps in Calibration
   Identifying high percentage error tells us when calibration is needed.

Applications in Electrical Engineering

• In voltage and current measurements using voltmeters or ammeters.
• In resistance measurement using ohmmeters or multimeters.
• In testing sensors and circuit components for design and quality checks.
• In comparing theoretical and experimental results in lab experiments.

How to Reduce Percentage Error

1. Use better quality instruments.
2. Calibrate the instruments regularly.
3. Avoid parallax and manual reading mistakes.
4. Take multiple readings and use average.
5. Control external factors like temperature, vibration, and noise.

Conclusion

Percentage error is a simple but powerful way to express how far a measured value is from the actual value. It helps in understanding the quality of measurements in electrical engineering and other technical fields. By calculating and minimizing percentage error, we can improve the reliability and accuracy of instruments and systems, leading to better performance and safer operations.