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?
0.5 mm²
1 mm²
2 mm²
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.
