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A wire made of material A has a resistivity of 1.5 x 10^-8 Ω·m, while material B

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Question: A wire made of material A has a resistivity of 1.5 x 10^-8 Ω·m, while material B has a resistivity of 3.0 x 10^-8 Ω·m. If both wires have the same dimensions, which wire will have a higher resistance?

Options:

  1. Wire A
  2. Wire B
  3. Both have the same resistance
  4. Cannot be determined

Correct Answer: Wire B

Solution: 

Resistance is directly proportional to resistivity; hence, wire B with higher resistivity will have higher resistance.

A wire made of material A has a resistivity of 1.5 x 10^-8 Ω·m, while material B

Practice Questions

Q1
A wire made of material A has a resistivity of 1.5 x 10^-8 Ω·m, while material B has a resistivity of 3.0 x 10^-8 Ω·m. If both wires have the same dimensions, which wire will have a higher resistance?
  1. Wire A
  2. Wire B
  3. Both have the same resistance
  4. Cannot be determined

Questions & Step-by-Step Solutions

A wire made of material A has a resistivity of 1.5 x 10^-8 Ω·m, while material B has a resistivity of 3.0 x 10^-8 Ω·m. If both wires have the same dimensions, which wire will have a higher resistance?
Correct Answer: Wire B
  • Step 1: Understand what resistivity means. It is a property of a material that affects how much it resists the flow of electric current.
  • Step 2: Note the resistivity values given: Material A has a resistivity of 1.5 x 10^-8 Ω·m and Material B has a resistivity of 3.0 x 10^-8 Ω·m.
  • Step 3: Recognize that higher resistivity means higher resistance when the dimensions (length and cross-sectional area) of the wires are the same.
  • Step 4: Compare the resistivity values. Since 3.0 x 10^-8 is greater than 1.5 x 10^-8, Material B has higher resistivity than Material A.
  • Step 5: Conclude that since Material B has higher resistivity, it will also have higher resistance than Material A.
  • Resistivity and Resistance – Resistance of a wire is directly proportional to its resistivity and length, and inversely proportional to its cross-sectional area.
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