A resistivity is found from a resistance known to 2.0%, a length known to 0.5% and a diameter known to 2.6%. Calculate the percentage uncertainty in the resistivity.

The area depends on the square of the diameter so contributes 2 × 2.6 = 5.2%, and the total is 2.0 + 0.5 + 5.2 = 7.7%, since resistivity is a product and quotient of these quantities.

A resistance is found from a potential difference known to 1.5% and a current known to 2.5%, and comes out as 30 Ω. State the resistance with its absolute uncertainty.

The percentage uncertainty is 1.5 + 2.5 = 4.0%, so the absolute uncertainty is 0.040 × 30 = 1.2 Ω and the resistance is 30 ± 1 Ω, since 1.2 ÷ 30 × 100 returns 4.0%.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

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Practical Skills and Data Analysis

Combining uncertainties and uncertainty on a graph

3 things to know
Units AS 3 and A2 3

Overview

Recall questions on adding absolute uncertainties for a sum or difference and percentage uncertainties for a product or quotient, multiplying by the power for a raised quantity, worked combinations for a resistivity and a pendulum determination, error bars and the worst acceptable line, and rounding a result to match its uncertainty.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the rule for combining uncertainties when two quantities are multiplied or divided.

Key term

State the rule for the uncertainty in a quantity that is raised to a power.

Numbers

The diameter of a wire is known to ±2.0%. Calculate the percentage uncertainty in its cross-sectional area.

Questions from this subtopic

Each one with the model answer underneath.

1
State the rule for combining uncertainties when two quantities are added or subtracted.
Model answer
The absolute uncertainties are added, whether the quantities themselves are being added or subtracted, and the result is quoted with that combined absolute uncertainty.
2
State the rule for combining uncertainties when two quantities are multiplied or divided.
Model answer
The percentage uncertainties are added, and the total is the percentage uncertainty in the product or the quotient.
3
State the rule for the uncertainty in a quantity that is raised to a power.
Model answer
The percentage uncertainty is multiplied by the power, so squaring a quantity doubles its percentage uncertainty and cubing it trebles it.
4
A resistivity is found from a resistance known to 2.0%, a length known to 0.5% and a diameter known to 2.6%. Calculate the percentage uncertainty in the resistivity.
Model answer
The area depends on the square of the diameter so contributes 2 × 2.6 = 5.2%, and the total is 2.0 + 0.5 + 5.2 = 7.7%, since resistivity is a product and quotient of these quantities.
5
A resistance is found from a potential difference known to 1.5% and a current known to 2.5%, and comes out as 30 Ω. State the resistance with its absolute uncertainty.
Model answer
The percentage uncertainty is 1.5 + 2.5 = 4.0%, so the absolute uncertainty is 0.040 × 30 = 1.2 Ω and the resistance is 30 ± 1 Ω, since 1.2 ÷ 30 × 100 returns 4.0%.
6
The diameter of a wire is known to ±2.0%. Calculate the percentage uncertainty in its cross-sectional area.
Model answer
Since A = πd²/4 the diameter is squared, so the percentage uncertainty in the area is 2 × 2.0 = 4.0%; π and 4 are exact and contribute nothing.

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Combining uncertainties and uncertainty on a graph

Overview

What you need to know

State the rule for combining uncertainties when two quantities are multiplied or divided.

State the rule for the uncertainty in a quantity that is raised to a power.

The diameter of a wire is known to ±2.0%. Calculate the percentage uncertainty in its cross-sectional area.

Questions from this subtopic

State the rule for combining uncertainties when two quantities are added or subtracted.

State the rule for combining uncertainties when two quantities are multiplied or divided.

State the rule for the uncertainty in a quantity that is raised to a power.

A resistivity is found from a resistance known to 2.0%, a length known to 0.5% and a diameter known to 2.6%. Calculate the percentage uncertainty in the resistivity.

A resistance is found from a potential difference known to 1.5% and a current known to 2.5%, and comes out as 30 Ω. State the resistance with its absolute uncertainty.

The diameter of a wire is known to ±2.0%. Calculate the percentage uncertainty in its cross-sectional area.

Other ways to work this

What is inside Levo

The 3-step method, run for you

Cram a whole paper in one sitting

Blank Blitz makes facts automatic

Build It gets the exam shape right

Test It catches misconceptions

Brain Breaks between sessions

Every question in Practical Skills and Data Analysis, on a schedule.