# MCQ on Error in Measurement

## MCQ on Error in Measurement

MCQ on Error in Measurement, Error in Measurement MCQ, Measurement of Error MCQ, Multiple Choice Questions of Error Measurement

### Objective Type Questions

1. An 0 – 10 A ammeter has a guaranteed accuracy of 1 percent of full scale deflection. The limiting error while reading 2.5 A is :

• 1%
• 2%
• 4%
• none of the above

2. A 0 – 300 V voltmeter has an error of ± 2% of full scale deflection. What would be the range of readings if true voltage is 30 V ?

• 24 V – 36 V
• 29.4 V – 30.6 V
• 20 V to 40 V
• none of the above

Answer: 24 V – 36 V

3. A wattmeter has a full scale range of 2500 W. It has an error ± 1% of true value. What would be range of reading if true power is 1250 W ?

• 1225 W – 1275 W
• 1245 W – 1255 W
• 1200 W – 1300 W
• 1237.5 W – 1262.50 W

Answer: 1237.5 W – 1262.50 W

4. Power in a d.c. circuit is measured by measuring the voltage across and current through the circuit. The voltage and current measurements are made to an accuracy of ± 2 % and ± 3% respectively. The errors are limiting errors. The error in measurement of power is

• ± 2%
• ± 3%
• ± 6%
• ± 5%

5. The power in a circuit is measured by measuring a current through a resistor. The current is measured with an accuracy of ± 1.5% and the tolerance band of the resistor ± 0.5%. The errors are limiting or Guarantee erross. The accuracy with which power is measured is

• ± 1.125%
• ± 3.5%
• ± 2%
• ± 2.5%

6. In a permanent magnet moving coil ammeter the deflection of the pointer is proportional to product of flux density of magnetic field produced by the permanent magnet and the current in the moving coil. If the strength of the permanent magnet becomes 95% of the original, the meter gives erraneous reading resulting into error. This error can be classified as

• Gross error
• Systematic error
• Random error
• None of the above

7. The voltage of a circuit is measured by a voltmeter having an input impedance comparable with the output impedance of the circuit thereby causing error in voltage measurement. This error may be called

• Gross error
• Random error
• Error caused by misuse of instrument

8. The mean deviation $\bar{D}$ in terms of deviations from the mean value of n readings is

• $\frac{\Sigma |d|}{n}$
• $\frac{\Sigma d}{n}$
• $\frac{\sqrt{\Sigma d^{2}}}{n}$
• $\sqrt{\frac{\Sigma d^{2}}{n}}$

Answer: $\frac{\Sigma |d|}{n}$

9. A set of readings has a wide range and therefore it has

• low precision
• high precision
• low accuracy
• high accuracy

10. The Gaussian distribution can be mathematically expressed as (y = number of readings at a deviation x and h is a precision index):

• $y=\frac{h}{\sqrt{\pi }}\exp (h^{2}x^{2})$
• $y=-\frac{h}{\sqrt{\pi }}\exp (h^{2}x^{2})$
• $y=\frac{h}{\pi}\exp (-h^{2}x^{2})$
• $y=\frac{h}{\sqrt{\pi }}\exp (-h^{2}x^{2})$

Answer: $y=\frac{h}{\sqrt{\pi }}\exp (-h^{2}x^{2})$

11. For a Gaussian distribution, the probable error is r. This means that

• area under the curve between ±r limits is 0.5
• half of the observed values lie between ± r limits
• the chances that an additional observation will lie between ± r limits are 50 percent.
• all of the above

12. Two resistances 100 Ω ± 5 Ω and 150 Ω ± 15 Ω are connected in series. If the deviations are standard deviations, the resultant resistance can be expressed as

• 250 ± 20 Ω
• 250 ± 10 Ω
• 250 ± 15.8 Ω
• 250 ± 10.6 Ω

13. If the result of a measurement is expressed as $\bar{X}\pm 3\sigma$ where $\bar{X}$ = mean value and σ = standard deviation, it means that

• approximately 99 percent of the readings lie between ± 3σ limit
• 26 readings out of 1000 will lie outside ± 3σ limit
• the odds for any reading to lie within ± 3σ limit are 256 to 1
• all of the above

14. A batch of resistors have a mean value of 100.00 Ω and a standard deviation σ = 0.2 Ω. The probability corresponding to 2σ is 0.9546. The value of odds that randomly selected resistor will lie within 100.00 ± 0.40 Ω is

• 1 to 1
• 2.15 to 1
• 21 to 1
• 369 to 1

15. According to Chauvenet’s criterion, a reading out of a set of n readings should be rejected if the probability of obtaining the particular deviation from mean is

• less than 1/2n
• greater than 1/2n
• less than 1/n
• less than 1/n

16. If the confidence level is 0.95, then the values lying outside the confidence interval are

• 1 in 5
• 1 in 20
• 1 in 100
• 1 in 1000