Voltmeter Static Error Calculation

When we use measuring instruments like a voltmeter, it's common for the indicated reading to be slightly different from the actual, true value of the quantity being measured. This difference is known as the static error. Understanding and calculating static error is crucial for accurate measurements in electrical systems.

Understanding Static Error

Static error refers to the difference between the measured value indicated by an instrument and the true value of the quantity being measured. It is a fundamental concept in instrumentation and measurement. A positive static error means the instrument is reading higher than the actual value, while a negative static error means it's reading lower.

The formula for calculating static error is:

$ \text{Static Error (E_S)} = \text{Measured Value (V_M)} - \text{True Value (V_T)} $

Measurement Data Analysis

Let's identify the given values from the question:

• True Value (Line Voltage): The actual line voltage is given as $230 \text{ V}$. This is the correct or expected value.
• Measured Value (Indicated Voltage): The voltmeter indicates a reading of $232 \text{ V}$. This is the value obtained from the instrument.

Calculating Static Error

Now, we will apply the static error formula using the given voltmeter readings.

Given:

• True Value ($V_T$) = $230 \text{ V}$
• Measured Value ($V_M$) = $232 \text{ V}$

Using the formula for static error:

$ E_S = V_M - V_T $

Substitute the values:

$ E_S = 232 \text{ V} - 230 \text{ V} $

$ E_S = 2 \text{ V} $

Therefore, the static error in the voltmeter measurement is $2 \text{ V}$. This positive value indicates that the voltmeter is reading $2 \text{ V}$ higher than the actual line voltage.

Conclusion on Static Error

The calculated static error for the voltmeter measurement is $2 \text{ V}$. This means the instrument shows a reading that is $2 \text{ V}$ higher than the actual line voltage of $230 \text{ V}$. Understanding this error helps in calibrating instruments or accounting for discrepancies in measurements.