A copper wire has a resistivity of 1.68 x 10^-8 Ω·m. What is the resistance of a

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Question: A copper wire has a resistivity of 1.68 x 10^-8 Ω·m. What is the resistance of a 100 m long wire with a cross-sectional area of 1 mm²?

Options:

Correct Answer: 1.68 Ω

Solution:

Resistance (R) = ρ * (L / A) = 1.68 x 10^-8 * (100 / 1 x 10^-6) = 1.68 Ω.

A copper wire has a resistivity of 1.68 x 10^-8 Ω·m. What is the resistance of a 100 m long wire with a cross-sectional area of 1 mm²?

A copper wire has a resistivity of 1.68 x 10^-8 Ω·m. What is the resistance of a 100 m long wire with a cross-sectional area of 1 mm²?

Correct Answer: 1.68 Ω

Step 1: Identify the formula for resistance (R) which is R = ρ * (L / A).
Step 2: Write down the values given in the question: resistivity (ρ) = 1.68 x 10^-8 Ω·m, length (L) = 100 m, and cross-sectional area (A) = 1 mm².
Step 3: Convert the cross-sectional area from mm² to m². Since 1 mm² = 1 x 10^-6 m², we have A = 1 x 10^-6 m².
Step 4: Substitute the values into the formula: R = 1.68 x 10^-8 * (100 / (1 x 10^-6)).
Step 5: Calculate the value inside the parentheses: 100 / (1 x 10^-6) = 100000000.
Step 6: Now multiply: R = 1.68 x 10^-8 * 100000000.
Step 7: Perform the multiplication: R = 1.68 Ω.

Resistance Calculation – The question tests the ability to calculate the resistance of a wire using the formula R = ρ * (L / A), where ρ is resistivity, L is length, and A is cross-sectional area.
Unit Conversion – The question requires understanding of unit conversion, particularly converting mm² to m² for the cross-sectional area.