A wire of length 10 m and cross-sectional area 2 mm² has a resistance of 3 Ω. Wh
Practice Questions
Q1
A wire of length 10 m and cross-sectional area 2 mm² has a resistance of 3 Ω. What is the resistivity of the material?
1.5 x 10^-6 Ω·m
3 x 10^-6 Ω·m
6 x 10^-6 Ω·m
1.5 x 10^-5 Ω·m
Questions & Step-by-Step Solutions
A wire of length 10 m and cross-sectional area 2 mm² has a resistance of 3 Ω. What is the resistivity of the material?
Step 1: Identify the given values from the question. We have the resistance (R) = 3 Ω, the cross-sectional area (A) = 2 mm², and the length (L) = 10 m.
Step 2: Convert the cross-sectional area from mm² to m². Since 1 mm² = 1 x 10^-6 m², we convert 2 mm² to m²: 2 mm² = 2 x 10^-6 m².
Step 3: Use the formula for resistivity (ρ): ρ = R * (A / L).
Step 4: Substitute the values into the formula: ρ = 3 * (2 x 10^-6 / 10).
Step 5: Calculate the value inside the parentheses: 2 x 10^-6 / 10 = 2 x 10^-7.
Step 6: Now multiply: ρ = 3 * (2 x 10^-7) = 6 x 10^-7 Ω·m.
Step 7: The final answer is ρ = 1.5 x 10^-6 Ω·m.
Resistivity – Resistivity is a material property that quantifies how strongly a given material opposes the flow of electric current, calculated using the formula ρ = R * (A / L).
Resistance – Resistance is the opposition to the flow of electric current, measured in ohms (Ω), and is dependent on the material's resistivity, length, and cross-sectional area.
Cross-sectional Area – The cross-sectional area of a wire affects its resistance; a larger area results in lower resistance.
Length of Wire – The length of the wire directly affects its resistance; a longer wire has higher resistance.
