Voltmeter Reading Range Calculation

Understanding the range of readings for a voltmeter is crucial when dealing with instrument errors. This problem involves a voltmeter with a specified full-scale deflection (FSD) and a percentage error based on that FSD. We need to determine the possible range of readings when a specific true voltage is applied.

Voltmeter Specifications

• Full Scale Deflection (FSD): The maximum voltage the voltmeter can measure, which is given as 300 V.
• Error Percentage: The instrument has an error of 2% of the full scale deflection.
• True Voltage: The actual voltage being measured is 30 V.

Calculating the Absolute Error

The first step is to calculate the absolute error in volts, based on the given percentage of the full scale deflection. The error is not a percentage of the true voltage, but rather a fixed value derived from the instrument's maximum capability.

Formula for Absolute Error:

$$ \text{Absolute Error} = \text{Error Percentage} \times \text{Full Scale Deflection (FSD)} $$

Calculation:

Given:

• Error Percentage = 2%
• FSD = 300 V

$$ \text{Absolute Error} = \frac{2}{100} \times 300 \text{ V} $$

$$ \text{Absolute Error} = 0.02 \times 300 \text{ V} $$

$$ \text{Absolute Error} = 6 \text{ V} $$

So, the voltmeter has an absolute error of ±6 V.

Determining the Reading Range

Once the absolute error is known, we can determine the range of possible readings. The measured voltage can be anywhere from the true voltage minus the absolute error to the true voltage plus the absolute error.

Formula for Reading Range:

• Minimum Reading: True Voltage - Absolute Error
• Maximum Reading: True Voltage + Absolute Error

Calculation:

Given:

• True Voltage = 30 V
• Absolute Error = 6 V

Minimum Reading:

$$ \text{Minimum Reading} = 30 \text{ V} - 6 \text{ V} $$

$$ \text{Minimum Reading} = 24 \text{ V} $$

Maximum Reading:

$$ \text{Maximum Reading} = 30 \text{ V} + 6 \text{ V} $$

$$ \text{Maximum Reading} = 36 \text{ V} $$

Therefore, the range of readings on this voltmeter would be 24 V to 36 V.

Summary of Voltmeter Readings

The calculation demonstrates how the fixed error, based on the full scale, affects the accuracy of readings even for smaller true voltage values.