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A wire has a resistance of 12 Ω and is made of a material with a resistivity of

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Question: A wire has a resistance of 12 Ω and is made of a material with a resistivity of 3 x 10^-6 Ω·m. If the length of the wire is 4 m, what is its cross-sectional area?

Options:

  1. 0.5 mm²
  2. 1 mm²
  3. 2 mm²
  4. 3 mm²

Correct Answer: 1 mm²

Solution: 

A = ρ * (L / R) = 3 x 10^-6 * (4 / 12) = 1 mm².

A wire has a resistance of 12 Ω and is made of a material with a resistivity of

Practice Questions

Q1
A wire has a resistance of 12 Ω and is made of a material with a resistivity of 3 x 10^-6 Ω·m. If the length of the wire is 4 m, what is its cross-sectional area?
  1. 0.5 mm²
  2. 1 mm²
  3. 2 mm²
  4. 3 mm²

Questions & Step-by-Step Solutions

A wire has a resistance of 12 Ω and is made of a material with a resistivity of 3 x 10^-6 Ω·m. If the length of the wire is 4 m, what is its cross-sectional area?
  • Step 1: Identify the given values: resistance (R) = 12 Ω, resistivity (ρ) = 3 x 10^-6 Ω·m, and length (L) = 4 m.
  • Step 2: Use the formula for cross-sectional area (A): A = ρ * (L / R).
  • Step 3: Substitute the values into the formula: A = 3 x 10^-6 * (4 / 12).
  • Step 4: Calculate the value of (4 / 12), which is 1/3 or approximately 0.3333.
  • Step 5: Multiply 3 x 10^-6 by 0.3333 to get A = 1 x 10^-6 m².
  • Step 6: Convert the area from m² to mm² by multiplying by 1,000,000 (since 1 m² = 1,000,000 mm²).
  • Step 7: The final result is A = 1 mm².
  • Resistance and Resistivity – Understanding the relationship between resistance, resistivity, length, and cross-sectional area of a wire.
  • Formula Application – Applying the formula A = ρ * (L / R) correctly to find the cross-sectional area.
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