Resistivity Formula Quiz: Test Your Knowledge Of Material Physics

Grade 10th

Reviewed by Ekaterina Yukhnovich

Ekaterina Yukhnovich, PhD |

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Ekaterina V. is a physicist and mathematics expert with a PhD in Physics and Mathematics and extensive experience working with advanced secondary and undergraduate-level content. She specializes in combinatorics, applied mathematics, and scientific writing, with a strong focus on accuracy and academic rigor.

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| Questions: 20 | Updated: Mar 13, 2026

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1. Which change decreases resistance the most (same material)?

Doubling length

Halving area

Halving length

Using the same wire unchanged

Concept: direction of changes. Resistance is proportional to length and inversely proportional to area. Reducing length decreases resistance, while halving area increases it.

Explanation

Concept: direction of changes. Resistance is proportional to length and inversely proportional to area. Reducing length decreases resistance, while halving area increases it.

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About This Quiz

Resistivity Formula Quiz: Test Your Knowledge Of Material Physics - Quiz

This assessment focuses on the resistivity formula and its application in material physics. It evaluates your understanding of key concepts like electrical resistance, conductivity, and the relationships between material properties. Engaging with this content is essential for anyone looking to deepen their knowledge in physics, particularly in understanding how different... see morematerials behave under electrical stress. see less

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2. The formula (r=\rho l/a) assumes a uniform material and constant cross-section along the wire.

True

False

Concept: model assumptions. If the wire’s thickness or material changes along its length, resistance must be treated piecewise. The simple formula works for uniform wires.

Explanation

Concept: model assumptions. If the wire’s thickness or material changes along its length, resistance must be treated piecewise. The simple formula works for uniform wires.

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3. A wire is stretched to twice its length. If its volume stays roughly constant, its cross-sectional area becomes smaller, so resistance:

Definitely decreases

Increases by more than a factor of 2

Stays the same

Becomes zero

Concept: stretching changes both l and a. Stretching increases (l) and reduces (a), and both changes increase (r). So the resistance increases more than just doubling.

Explanation

Concept: stretching changes both l and a. Stretching increases (l) and reduces (a), and both changes increase (r). So the resistance increases more than just doubling.

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4. If the area increases by 4× (same (l,\rho)), resistance decreases by 4×.

True

False

Concept: inverse relationship. Because (r\propto 1/a), multiplying (a) by 4 divides (r) by 4. This is a common scaling result.

Explanation

Concept: inverse relationship. Because (r\propto 1/a), multiplying (a) by 4 divides (r) by 4. This is a common scaling result.

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5. If a wire’s radius doubles (same length/material), its area increases by a factor of:

Concept: area scales with radius squared. Cross-sectional area (a=\pi r^2). Doubling (r) multiplies (a) by (2^2=4), which reduces resistance by 4.

Explanation

Concept: area scales with radius squared. Cross-sectional area (a=\pi r^2). Doubling (r) multiplies (a) by (2^2=4), which reduces resistance by 4.

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6. For a uniform wire, resistance is proportional to (l) and inversely proportional to ______.

Concept: proportionality summary. Longer wires resist current more. Wider wires resist less because the current has more cross-section to travel through.

Explanation

Concept: proportionality summary. Longer wires resist current more. Wider wires resist less because the current has more cross-section to travel through.

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7. Making a wire thicker changes resistance but does not change resistivity.

True

False

Concept: geometry vs material. Thickness changes cross-sectional area, affecting resistance. Resistivity remains a material property (at fixed temperature).

Explanation

Concept: geometry vs material. Thickness changes cross-sectional area, affecting resistance. Resistivity remains a material property (at fixed temperature).

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8. A common engineering reason to choose low-resistivity materials for wiring is to:

Increase heating

Reduce power loss as heat

Increase voltage

Increase charge creation

Concept: resistive heating losses. Power loss in wires is linked to resistance. Lower resistivity lowers resistance and reduces wasted energy.

Explanation

Concept: resistive heating losses. Power loss in wires is linked to resistance. Lower resistivity lowers resistance and reduces wasted energy.

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9. Two wires have the same (l) and (a), but wire x has higher resistivity than wire y. Wire x will have:

Lower resistance

Higher resistance

The same resistance

Zero resistance

Concept: (r\propto \rho). Higher resistivity means stronger opposition to charge flow. So resistance increases if (\rho) is larger.

Explanation

Concept: (r\propto \rho). Higher resistivity means stronger opposition to charge flow. So resistance increases if (\rho) is larger.

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10. If you know (\rho), (l), and (a), you can estimate a wire’s resistance without measuring current.

True

False

Concept: predicting resistance from geometry. The formula links resistance to physical dimensions and material. This is useful in design and engineering.

Explanation

Concept: predicting resistance from geometry. The formula links resistance to physical dimensions and material. This is useful in design and engineering.

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11. The relationship between resistance and resistivity for a uniform wire is:

R = \rho a/l

R = \rho l/a

R = \rho la

R = \rho / (la)

Concept: resistivity formula. Resistance increases with length and decreases with cross-sectional area. (r=\rho l/a) captures this geometry dependence for a uniform conductor.

Explanation

Concept: resistivity formula. Resistance increases with length and decreases with cross-sectional area. (r=\rho l/a) captures this geometry dependence for a uniform conductor.

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12. If (a) is measured in m² and (l) in m, then (\rho) must be in ______.

Concept: consistent SI units. Using SI geometry units ensures the resistance comes out in ohms. That requires resistivity in ohm-metres.

Explanation

Concept: consistent SI units. Using SI geometry units ensures the resistance comes out in ohms. That requires resistivity in ohm-metres.

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13. The unit Ω·m is consistent with (r=\rho l/a) because (l/a) has units of 1/m.

True

False

Concept: unit check. (l) is metres and (a) is m², so (l/a) is 1/m. Multiplying Ω·m by 1/m gives Ω, as required.

Explanation

Concept: unit check. (l) is metres and (a) is m², so (l/a) is 1/m. Multiplying Ω·m by 1/m gives Ω, as required.

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14. If a wire’s length is tripled and its area is tripled (same material), its resistance:

Triples

Becomes one-third

Stays the same

Becomes nine times

Concept: ratio (l/a). In (r=\rho l/a), if both (l) and (a) scale by the same factor, their ratio stays constant. So resistance stays unchanged.

Explanation

Concept: ratio (l/a). In (r=\rho l/a), if both (l) and (a) scale by the same factor, their ratio stays constant. So resistance stays unchanged.

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15. A wire’s resistance doubles when you:

Double the area

Double the length

Halve the length

Use a thicker wire

Concept: (r\propto l). With the same area and material, doubling length doubles resistance. Area changes work in the opposite direction.

Explanation

Concept: (r\propto l). With the same area and material, doubling length doubles resistance. Area changes work in the opposite direction.

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16. Resistivity (\rho) is the same for two samples of the same material at the same temperature.

True

False

Concept: intrinsic property. Resistivity does not depend on length or thickness. It can change with temperature or impurities, but not with shape.

Explanation

Concept: intrinsic property. Resistivity does not depend on length or thickness. It can change with temperature or impurities, but not with shape.

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17. Two wires of the same material and same length: wire 1 has area (a), wire 2 has area (2a). Compared to wire 1, wire 2 has resistance:

Twice

Half

The same

Four times

Concept: comparing by area. Resistance is inversely proportional to area. Doubling area reduces resistance by a factor of 2.

Explanation

Concept: comparing by area. Resistance is inversely proportional to area. Doubling area reduces resistance by a factor of 2.

Submit

18. In (r=\rho l/a), (a) stands for cross-sectional ______.

Concept: geometry variable. The area term represents how 'thick' the conductor is. Larger area gives more parallel pathways for electrons.

Explanation

Concept: geometry variable. The area term represents how 'thick' the conductor is. Larger area gives more parallel pathways for electrons.

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19. If a wire’s cross-sectional area doubles (same (\rho) and (l)), resistance becomes:

Double

Half

The same

Four times

Concept: area reduces resistance. Since (r\propto 1/a), doubling area halves resistance. This is why thicker wires carry current more easily.

Explanation

Concept: area reduces resistance. Since (r\propto 1/a), doubling area halves resistance. This is why thicker wires carry current more easily.

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20. If (l) increases and (a) stays the same, (r) increases.

True

False

Concept: length increases resistance. A longer wire provides a longer path with more scattering. This directly raises resistance in the formula.

Explanation

Concept: length increases resistance. A longer wire provides a longer path with more scattering. This directly raises resistance in the formula.

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Which change decreases resistance the most (same material)?

The formula (r=\rho l/a) assumes a uniform material and constant...

A wire is stretched to twice its length. If its volume stays roughly...

If the area increases by 4× (same (l,\rho)), resistance decreases by...

If a wire’s radius doubles (same length/material), its area...

For a uniform wire, resistance is proportional to (l) and inversely...

Making a wire thicker changes resistance but does not change...

A common engineering reason to choose low-resistivity materials for...

Two wires have the same (l) and (a), but wire x has higher resistivity...

If you know (\rho), (l), and (a), you can estimate a wire’s...

The relationship between resistance and resistivity for a uniform wire...

If (a) is measured in m² and (l) in m, then (\rho) must be in ______.

The unit Ω·m is consistent with (r=\rho l/a) because (l/a) has units...

If a wire’s length is tripled and its area is tripled (same...

A wire’s resistance doubles when you:

Resistivity (\rho) is the same for two samples of the same material at...

Two wires of the same material and same length: wire 1 has area (a),...

In (r=\rho l/a), (a) stands for cross-sectional ______.

If a wire’s cross-sectional area doubles (same (\rho) and (l)),...

If (l) increases and (a) stays the same, (r) increases.

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