In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 3

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Question: In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 1 mm²?

Options:

Correct Answer: 0.024 Ω

Solution:

Resistance R = ρ(L/A) = 2 x 10^-8 * (3 / (1 x 10^-6)) = 0.024 Ω.

In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 1 mm²?

In a material with a resistivity of 2 x 10^-8 Ω·m, what is the resistance of a 3 m long wire with a cross-sectional area of 1 mm²?

Step 1: Identify the resistivity (ρ) of the material, which is given as 2 x 10^-8 Ω·m.
Step 2: Identify the length (L) of the wire, which is given as 3 m.
Step 3: Identify the cross-sectional area (A) of the wire, which is given as 1 mm². Convert this to square meters: 1 mm² = 1 x 10^-6 m².
Step 4: Use the formula for resistance: R = ρ(L/A).
Step 5: Substitute the values into the formula: R = (2 x 10^-8) * (3 / (1 x 10^-6)).
Step 6: Calculate the value of (3 / (1 x 10^-6)), which equals 3,000,000.
Step 7: Multiply 2 x 10^-8 by 3,000,000 to find the resistance: R = 2 x 10^-8 * 3,000,000 = 0.024 Ω.

Resistivity and Resistance – The relationship between resistivity, length, and cross-sectional area of a conductor, expressed by the formula R = ρ(L/A).
Unit Conversion – Understanding the conversion of units, particularly from mm² to m² in the context of cross-sectional area.