UNCERTAINTY ANALYSIS

A digital balance is used to weigh ingredients in a laboratory. When a weight is applied to the digital balance, an electronic circuit generates a current which is then converted into a digital readout on the display.

The electronic circuit gives a current of 2.0mA when a weight of 30N is applied, and a current of 0.5 mA when a weight of 5 N is applied.

Which calibration curve could represent this circuit?

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Four students measure a time interval that is known to be 1.734 s.The measurement recorded by each student is shown.Which measurement is the most accurate?

• 1 s

• 1.7 s

• 1.83 s

• 1.604 s

The power P dissipated in a resistor of resistance R is calculated using the expression P = V²/R

where V is the potential difference (p.d.) across the resistor. The percentage uncertainty in V is 5% and in R is 2%.

What is the percentage uncertainty in P ?

• 3%

• 7%

• 8%

• 12%

Which experimental technique reduces the systematic error of the quantity being investigated?

• adjusting an ammeter to remove its zero error before measuring a current

• measuring several internodal distances on a standing wave to find the mean internodal distance

• measuring the diameter of a wire repeatedly and calculating the average

• timing a large number of oscillations to find a period

A student makes measurements from which she calculates the speed of sound as 327.66 m s–1.

She estimates that her result is accurate to ±3 %.

Which of the following gives her result expressed to the appropriate number of significant figures?

• 327.7 m s^–1

• 328 m s^–1

• 330 m s^–1

• 300 m s^–1

In a simple electrical circuit, the current in a resistor is measured as (2.50 ± 0.05) mA. The resistor is marked as having a value of 4.7Ω ± 2 %.

If these values were used to calculate the power dissipated in the resistor, what would be the percentage uncertainty in the value obtained?

• 2 %

• 4 %

• 6 %

• 8 %

A student uses a digital ammeter to measure a current. The reading of the ammeter is found to fluctuate between 1.98A and 2.02A.

The manufacturer of the ammeter states that any reading has a systematic uncertainty of ±1%.

Which value of current should be quoted by the student?

• (2.00 ± 0.01)A

• (2.00 ± 0.02)A

• (2.00 ± 0.03)A

• (2.00 ± 0.04)A

A calibration graph is produced for a faulty ammeter.

Which ammeter reading will be nearest to the correct value?

• 0.2A

• 0.4A

• 0.6A

• 0.8A

A quantity x is to be determined from the equation x = P – Q.

P is measured as 1.27 ± 0.02m.

Q is measured as 0.83 ± 0.01m.

What is the percentage uncertainty in x to one significant figure?

• 0.4 %

• 2 %

• 3 %

• 7 %

Which type of the error can be avoided and corrected?

• Systematic

• Random