A copper wire has length 5 m and cross‑sectional area 2.5×10^-6 m^2. Given the resistivity of copper is 1.68×10^-8 Ω · m, calculate the resistance of the wire.

A copper wire has length $5 m$ and cross‑sectional area $2.5 \times 1 0^{- 6} m^{2}$ . Given the resistivity of copper is $1.68 \times 1 0^{- 8} Ω \cdot m$ , calculate the resistance of the wire.

medium 3 marks Class 10 · Science · Electricity

Answer

0.034 Ω

(approximately).

The correct answer is $0.034 Ω$ (approximately). — Round to two significant figures: $R \approx 0.034 Ω$ .

Use the formula $R = ρ \frac{L}{A}$ where $ρ$ is resistivity, $L$ is length and $A$ is cross‑sectional area.
Substitute the values: $R = (1.68 \times 1 0^{- 8}) \times \frac{5}{2.5 \times 1 0 ^{- 6}}$ .
Calculate the fraction: $\frac{5}{2.5 \times 1 0 ^{- 6}} = 2.0 \times 1 0^{6}$ .
Multiply: $R = 1.68 \times 1 0^{- 8} \times 2.0 \times 1 0^{6} = 3.36 \times 1 0^{- 2} Ω$ .
Round to two significant figures: $R \approx 0.034 Ω$ .

Common mistake: Forgetting to convert the area to square metres or mixing up the numerator and denominator in

R = ρ L / A

Concept tested: Resistance from resistivity