Question

A Voltmeter with a range of 0 to 30 V has an accuracy of +/- 2% of full scale deflection. What would be the range of reading, if the true voltage is 25 V?

• A. 23 V to 27 V
• B. 24.8 V to 25.2 V
• C. 24.4 V to 25.6 V
• D. 24.4 V to 30.0 V

Hint:

Instrument Accuracy Calculation: Error = $\pm 2\% \times 30\text{ V} = \pm 0.6\text{ V}$. Reading Range = $25 \pm 0.6 = \mathbf{24.4\text{ V to } 25.6\text{ V}}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Measurement error analysis and full-scale instrument accuracy: the limiting absolute error is calculated as a percentage of the Full Scale Deflection (FSD), remaining constant across the entire measurement range.
Key Formula or Approach:
\[ \text{Full Scale Value (FSD)} = 30\text{ V} \]
\[ \text{Absolute Limiting Error } (\delta V) = \pm 2\% \times \text{FSD} = \pm \frac{2}{100} \times 30\text{ V} = \mathbf{\pm 0.6 \text{ V}} \]
\[ \text{Range of Reading} = V_{\text{true}} \pm \delta V = 25\text{ V} \pm 0.6\text{ V} = \mathbf{24.4 \text{ V to } 25.6 \text{ V}} \]

Step 2: Detailed Explanation:
Step-by-step mathematical calculation of voltmeter measurement range:
1. Full Scale Deflection (FSD):
\[ V_{\text{FSD}} = 30\text{ V} \]
2. Maximum Absolute Limiting Error ($\delta V$):
\[ \delta V = \pm 2\% \times 30\text{ V} = \pm 0.02 \times 30 = \mathbf{\pm 0.60\text{ V}} \]
3. Range of Expected Instrument Reading for True Value $V_{\text{true = 25\text{ V}$:}
- Minimum Reading: $25 - 0.6 = \mathbf{24.4\text{ V}}$
- Maximum Reading: $25 + 0.6 = \mathbf{25.6\text{ V}}$
\[ \text{Range of Reading} = \mathbf{24.4\text{ V to } 25.6\text{ V}} \]

Step 3: Final Answer:
Therefore, the range of reading is 24.4 V to 25.6 V, corresponding to option (C).