Understanding Voltmeter Error Calculation

This problem involves calculating the error in a voltmeter reading based on its accuracy specification. Voltmeter accuracy is often stated as a percentage of the full-scale reading, which represents the maximum possible value the instrument can measure.

Information Provided

• Voltmeter Full-Scale Range (FSR): 0-200 V. This means the maximum value the voltmeter can display is 200 V.
• Accuracy Specification: 0.75% of the full-scale reading.
• Measured Voltage: 100 V.

Calculating the Absolute Error

The accuracy specification tells us the maximum possible deviation from the true value. Since it's given as a percentage of the full-scale reading, we first calculate the absolute error in volts:

Absolute Error = Accuracy Percentage $\times$ Full-Scale Reading

Using the given values:

Absolute Error = $0.75\% \times 200 \, \text{V}$

To calculate this, we convert the percentage to a decimal:

Absolute Error = $\frac{0.75}{100} \times 200 \, \text{V}$

Absolute Error = $0.0075 \times 200 \, \text{V}$

Absolute Error = $1.5 \, \text{V}$

So, the maximum possible error for this voltmeter, regardless of the actual reading, is 1.5 Volts.

Expressing Error as a Percentage of Measured Value

The options provided are percentages. Typically, when asked for the error in this format, it refers to the percentage error relative to the *actual measured value*. Let's calculate this:

Percentage Error = $\frac{\text{Absolute Error}}{\text{Measured Voltage}} \times 100\%$

Using the calculated absolute error and the measured voltage:

Percentage Error = $\frac{1.5 \, \text{V}}{100 \, \text{V}} \times 100\%$

Percentage Error = $0.015 \times 100\%$

Percentage Error = $1.5\%$

Conclusion

The calculated error, expressed as a percentage of the measured voltage (100 V), is 1.5%. This matches one of the options.