Question

A 1.3 digit digital voltmeter has a specified accuracy of \( \pm (0.5% \, {of reading} + 1 \, {digit}) \). If it is used to measure a 10 V DC voltage, the error in the measurement would be:

• A. \( \pm 0.4% \)
• B. \( \pm 1.5% \)
• C. \( \pm 0.6% \)
• D. \( \pm 1% \)

Hint:

For digital voltmeters with specified accuracy, the error is the sum of the percentage of the reading and the error due to 1 digit. Ensure to calculate both components.

Answer 1

The Correct Option is C

Step 1: Understanding the accuracy formula.
The accuracy of the digital voltmeter is given by the formula: \[ \pm ({accuracy percentage of the reading} + {1 digit}) \] In this case, the accuracy percentage is \( 0.5\% \) of the reading, and the additional error is 1 digit.
Step 2: Calculate the error due to the accuracy percentage.
The reading is \( 10\, {V} \), so the error due to the accuracy percentage is: \[ {Error from percentage} = 0.5\% \times 10 = 0.05\, {V} \]
Step 3: Determine the value of 1 digit.
The digital voltmeter has a 1.3 digit display. This means the last digit can either be \( 1 \) or \( 0 \). Thus, 1 digit is equivalent to \( 0.1 \, {V} \).
Step 4: Calculate the total error.
The total error is the sum of the error from the percentage of the reading and the error due to 1 digit: \[ {Total error} = 0.05\, {V} + 0.1\, {V} = 0.15\, {V} \]
Step 5: Calculate the percentage error.
The percentage error relative to the measured value of \( 10\, {V} \) is: \[ {Percentage error} = \left( \frac{0.15}{10} \right) \times 100 = 1.5\% \]
Step 6: Final Answer.
Thus, the total error in the measurement is \( \pm 1.5\% \), and the correct answer is: \[ \boxed{B} \, \pm 1.5\% \]