Calculating Uncertainties

The resistance R of a resistor is determined by measuring the potential difference V across it and the current I in it. The value of R is then calculated using the equation

 $R=\frac{V}{I}$  .
The values measured are V = 1.00 ± 0.05 V and I = 0.50 ± 0.01 A. What is the % uncertainty in the value of R?

• 2.5 %

• 3.0 %

• 7.0 %

• 10.0 %

In an experiment, a radio-controlled car takes 2.50 ± 0.05 s to travel 40.0 ± 0.1 m.

What is the car’s average speed and the uncertainty in this value?

• 16 ± 1m s^-1

• 16.0 ± 0.2 m s^-1

• 16.0 ± 0.4 m s^-1

• 16.00 ± 0.36 m s^-1

In an experiment to determine the acceleration of free fall g, the period of oscillation T and length l of a simple pendulum were measured. The uncertainty in the measurement of l is estimated to be 4%, and the uncertainty in the measurement of T is estimated to be 1%. 

The value of g is determined using the formula  $g=\frac{4\pi^2l}{T^2}$  

What is the uncertainty in the calculated value for g?

• 2 %

• 3 %

• 5 %

• 6 %

An experiment is carried out to measure the resistance of a wire.

The current in the wire is (1.0 ± 0.2) A and the potential difference across the wire is (8.0 ± 0.4) V.

What is the resistance of the wire and its uncertainty?

• (8.0 ± 0.2) Ω

• (8.0 ± 0.6) Ω

• (8 ± 1) Ω

• (8 ± 2) Ω

A thermometer can be read to an accuracy of ±0.5 °C. This thermometer is used to measure a temperature rise from 40 °C to 100 °C.

What is the percentage uncertainty in the measurement of the temperature rise?

• 0.5 %

• 0.8 %

• 1.3 %

• 1.7 %

A digital caliper is used to measure the 28.50 mm width of a plastic ruler. The digital caliper reads to the nearest 0.01 mm.

What is the correct way to record this reading?

• 0.02850 ± 0.01 m

• 0.0285 ± 0.001 m

• (2.850 ± 0.001) × 10^-2 m

• (2.850 ± 0.001) × 10^-3 m

A student determines the density ρ of steel by taking measurements from a steel wire. 

mass m = 6.2 ± 0.1 g 
length l = 25.0 ± 0.1cm 
diameter d = 2.00 ± 0.01mm 

He uses the equation  $\rho=\frac{4m}{\pi d^2l}$  .
What is the percentage uncertainty in his calculated value of density?

• 1.1 %

• 1.8 %

• 2.5 %

• 3.0 %

A quantity x is to be determined from the equation

x = P-Q.

P is measured as 1.27 ± 0.02 m and Q is measured as 0.83 ± 0.01 m.

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

• 0.4 %

• 2 %

• 3 %

• 7 %

A micrometer screw gauge is used to measure the diameter of a small uniform steel sphere. The micrometer reading is 5.00mm ± 0.01mm.

What will be the percentage uncertainty in a calculation of the volume of the sphere, using these values?

• 0.2 %

• 0.4 %

• 0.6 %

• 1.2 %

The power loss P in a resistor is usually calculated using the formula  $P=\frac{V^2}{R}$  
The percentage uncertainty in the potential difference V is 3 % and the percentage uncertainty in the resistance R is 2 %. What is the percentage uncertainty in P?

• 4 %

• 7 %

• 8 %

• 11 %