OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(ii) techniques and procedures used to determine the resistivity of a metal.
Full specification wording
Resistivity: (ii) techniques and procedures used to determine the resistivity of a metal.
To find the resistivity of a metal you measure R, L and A for a wire and use ρ = RA/L. Measure the diameter d with a micrometer at several places and orientations, then average; A = πd²/4.
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- Point 2 of 4
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
To find the resistivity of a metal you measure R, L and A for a wire and use ρ = RA/L. Measure the diameter d with a micrometer at several places and orientations, then average; A = πd²/4. Measure L with a metre rule between the contact points. Measure R by passing a current and finding V and I, using R = V/I; a voltmeter in parallel with the wire and an ammeter in series avoids contact resistance. Take several readings of V and I, plot V against I and use the gradient to reduce random error. Then ρ = RA/L. A typical metal gives ρ of order 10⁻⁸ to 10⁻⁶ Ω m. In multiple-choice questions you may be asked which instrument suits which quantity, or how to reduce uncertainty.
What earns the marks
- Measure the diameter d with a micrometer screw gauge at several positions and orientations, then average.
- Calculate the cross-sectional area from A = πd²/4, converting d to metres.
- Measure the length L of the wire between the contact points with a metre rule.
- Measure current I with an ammeter in series and potential difference V with a voltmeter in parallel with the wire.
- Calculate resistance from R = V/I, or better, plot V against I and use the gradient.
- Substitute into ρ = RA/L and give the unit as Ω m.
Common mistakes and how to put them right
Measuring the diameter once only.
Put it right: Take several readings at different places and orientations and average them, because the wire may not be uniform.
Using A = πd² instead of A = πd²/4.
Put it right: d is the diameter, so the radius is d/2 and A = π(d/2)² = πd²/4.
Connecting the voltmeter in series or the ammeter in parallel.
Put it right: Voltmeter in parallel with the wire, ammeter in series with it.
Forgetting to convert the diameter from mm to m before calculating A. Correction: divide mm by 1000 to get m, then square.
Exam tips
- List the measurements in the order you would take them: d, L, I, V, then calculate.
- State that the micrometer is used because the diameter is small and needs precision.
- Mention taking repeat readings and averaging to reduce random error.
- Use the gradient of a V–I graph rather than a single pair of readings for a more reliable R.
Try the lesson
The start of the Resistivity: (ii) techniques and procedures used to determine the resistivity of a metal. lesson, made from checked teaching notes for this specification point.
Listen
To find the resistivity of a metal you measure R, L and A for a wire and use ρ = RA/L. Measure the diameter d with a micrometer at several places and orientations, then average; A = πd²/4. Measure L with a metre rule between the contact points. Measure R by passing a current and finding V and I, using R = V/I; a voltmeter in parallel with the wire and an ammeter in series avoids contact resistance. Take several readings of V and I, plot V against I and use the gradient to reduce random error. Then ρ = RA/L. A typical metal gives ρ of order 10⁻⁸ to 10⁻⁶ Ω m. In multiple-choice questions you may be asked which instrument suits which quantity, or how to reduce uncertainty. A strong answer earns marks for these points. Measure the diameter d with a micrometer screw gauge at several positions and orientations, then average. Calculate the cross-sectional area from A = πd²/4, converting d to metres. Measure the length L of the wire between the contact points with a metre rule. Measure current I with an ammeter in series and potential difference V with a voltmeter in parallel with the wire. A common slip: Measuring the diameter once only. Instead, take several readings at different places and orientations and average them, because the wire may not be uniform. Exam tip: List the measurements in the order you would take them: d, L, I, V, then calculate.
See it
Put it in order
Put these steps in the order they happen.
- 1. Voltmeter in parallel with wire to measure V
- 2. Substitute into ρ = RA/L and give unit as Ω m
- 3. Take several readings of V and I
- 4. Measure diameter d with micrometer at several positions and orientations, then average
- 5. Calculate A = πd²/4, converting d to metres
- 6. Plot V against I and use gradient to find R
- 7. Measure length L between contact points with metre rule
- 8. Ammeter in series to measure current I
Key words
Say what each word means before you turn the card.
Experimental determination of resistivity
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Choice of measuring instruments
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Graphical analysis of V and I
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See every definition
- Experimental determination of resistivity
- Measure R, L and A for a wire and use ρ = RA/L to find the resistivity of a metal.
- Choice of measuring instruments
- A micrometer measures the diameter d, a metre rule measures L, an ammeter in series measures I and a voltmeter in parallel measures V.
- Graphical analysis of V and I
- Plot V against I and use the gradient to give a more reliable R than a single pair of readings.
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