Question

An analog instrument has a specified accuracy of \(\pm 1%\) of full-scale reading. If its full-scale value is 300 V and it reads 120 V, the maximum percentage error with respect to the indicated reading is

• A. \(1%\)
• B. \(1.5%\)
• C. \(2.5%\)
• D. \(5%\)

Hint:

The absolute error remains constant at 3 V across the entire scale. As the measured voltage reading decreases, this fixed 3 V uncertainty becomes a larger percentage of the reading: \(\frac{3}{120} \times 100 = 2.5%\).

Answer 1

The Correct Option is C

Concept: The static error limit of an instrument is often specified as a percentage of its Full-Scale Deflection (FSD) value. This fixed error value remains constant across the entire measurement range of the instrument scale: \[ \text{Absolute Limiting Error } (\delta V) = \pm (\text{Accuracy Grade}) \times (\text{Full-Scale Value}) \] When evaluating accuracy at an intermediate measurement point (the indicated reading), the relative limiting percentage error increases and is calculated as: \[ % \text{ Relative Limiting Error} = \frac{\text{Absolute Limiting Error } (\delta V)}{\text{Actual Indicated Reading } (V_{\text{actual}})} \times 100% \]

Step 1: Calculate the absolute limiting error value from the full-scale specifications. Given parameters:
• Full-scale range value = 300 V
• Base full-scale accuracy limit error = \(\pm 1%\) \[ \delta V = \frac{1}{100} \times 300\text{ V} = 3\text{ V} \] This means any reading taken on this scale has an inherent absolute uncertainty limit of \(\pm 3\text{ V}\).

Step 2: Calculate the relative percentage error at the indicated value. The instrument displays an indicated reading value of 120 V. Using our relative limiting error formula: \[ % \text{ Error at 120 V} = \frac{\delta V}{V_{\text{indicated}}} \times 100% = \frac{3}{120} \times 100% \] Simplifying the fraction: \[ \frac{3}{120} = \frac{1}{40} \] Now substitute this value back into the percentage equation: \[ % \text{ Error} = \frac{1}{40} \times 100% = \frac{10}{4}% = 2.5% \] Thus, the maximum relative percentage error at the indicated reading is \(2.5%\), matching option (C).