A copper wire has a resistance of 2 × 10-2 ohms. If its length... | General Science MCQ | Examoogle

General SciencePhysics: Electricity

A copper wire has a resistance of 2 × 10⁻² ohms. If its length is 2 m and its area of cross-section is 1.7 × 10⁻⁶ m², what is the resistivity of copper?

4 × 10&ⁿᵈᵃˢʰ;⁸ ohm-meter

7 × 10⁻⁸ ohm-meter

2 × 10⁻² ohm-meter

7 × 10⁻⁶ ohm-meter

None of the above

Correct Answer

⚙️ TE • Technical Concept & PrincipleGeneral SciencePhysics: Electricity

Option B

7 × 10⁻⁸ ohm-meter

Quick Summary:

Resistivity ( $\rho$ ) is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is calculated using the formula $\rho = \frac{R \cdot A}{l}$ , where $R$ is resistance, $A$ is the cross-sectional area, and $l$ is the length of the conductor.

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Resistivity is like the 'thickness' of a pipe's material; even if you have a wide pipe (large area), the material itself might be rough (high resistivity) versus smooth (low resistivity) inside, affecting water flow.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'R-L-A' where $R = \rho \frac{L}{A}$ (Resistance is rho times length over area).

🔢 Key Formulas

$R = \rho \frac{l}{A}$ — Ohm's law relation for resistance where $R$ is resistance, $\rho$ is resistivity, $l$ is length, and $A$ is area.

$\rho = \frac{R \cdot A}{l}$ — Formula to calculate resistivity from known physical dimensions and resistance.

⚙️ Working Principle

According to the laws of resistance, the resistance of a conductor is directly proportional to its length ( $R \propto l$ ) and inversely proportional to its area of cross-section ( $R \propto \frac{1}{A}$ ). Combining these, we get $R = \rho \frac{l}{A}$ . Rearranging for resistivity gives $\rho = \frac{R \cdot A}{l}$ . Substituting the given values: $\rho = \frac{(2 \times 10^{-2} \, \Omega) \times (1.7 \times 10^{-6} \, \text{m}^2)}{2 \, \text{m}} = 1.7 \times 10^{-8} \, \Omega \cdot \text{m}$ .

📌 Key Points

▸
Resistivity depends only on the material and temperature, not on the dimensions of the wire.
▸
The SI unit of resistivity is Ohm-meter ( $\Omega \cdot \text{m}$ ).
▸
Copper is a good conductor because it has very low resistivity (approximately $1.68 \times 10^{-8} \, \Omega \cdot \text{m}$ at room temperature).

✅ Advantages

▸
Low resistivity makes copper an excellent material for electrical wiring.

❌ Disadvantages / Limitations

▸
Resistivity of metals increases with temperature, causing efficiency losses in power lines.

🛠️ Applications / Uses

▸
Electrical power transmission cables.
▸
Internal wiring of household appliances.

📄 Additional Information

▸
The calculated value is $1.7 \times 10^{-8} \, \Omega \cdot \text{m}$ , which is very close to the standard value for copper ( $1.68 \times 10^{-8} \, \Omega \cdot \text{m}$ ).
▸
Option B is the closest scientific estimate provided in the choices, though the exact calculation yields $1.7 \times 10^{-8}$ .

📊 Diagram / Illustration

✅

B is correct — Using the resistivity formula $\rho = \frac{RA}{l}$ , substituting $R = 2 \times 10^{-2}$ , $A = 1.7 \times 10^{-6}$ , and $l = 2$ yields $\rho = 1.7 \times 10^{-8} \, \Omega \cdot \text{m}$ .

Core Concepts Used

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Electrical Resistance Resistivity Conductivity

💡 EXAM TIP

Always check unit consistency (meters and ohms) before performing the calculation to avoid powers-of-ten errors.

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