A 1‑m long copper wire has resistivity $1.68 \times 1 0^{- 8} Ω m$ . Its cross‑sectional area is $0.5 mm^{2}$ . (i) Find its resistance. (ii) If its length is increased to 1.5 m, what will be the new resistance?

medium 3 marks Class 7 · Science · Electric Current and its Effects

Answer

(i) 0.0336 Ω (ii) 0.0504 Ω

The correct answer is (i) 0.0336 Ω (ii) 0.0504 Ω — For $L = 1.5$  m, keep $ρ$ and $A$ same: $R_{n e w} = \frac{1.68 \times 1 0 ^{- 8} \times 1.5}{5 \times 1 0 ^{- 7}} = 0.0504$  Ω.

Step-by-step solution

Convert area to square metres: $0.5 mm^{2} = 0.5 \times 1 0^{- 6} = 5 \times 1 0^{- 7} m^{2}$ .
Use $R = \frac{ρ L}{A}$ for $L = 1$  m: $R = \frac{1.68 \times 1 0 ^{- 8} \times 1}{5 \times 1 0 ^{- 7}} = 0.0336$  Ω.
For $L = 1.5$  m, keep $ρ$ and $A$ same: $R_{n e w} = \frac{1.68 \times 1 0 ^{- 8} \times 1.5}{5 \times 1 0 ^{- 7}} = 0.0504$  Ω.

Common mistake: Leaving the area in mm² without converting to m².

Concept tested: Resistivity and resistance of a wire

Published 7 October 2026 · How this solution was prepared and checked

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A 1‑m long copper wire has resistivity 1.68×10−8Ωm. Its cross‑sectional area is 0.5mm2. (i) Find its resistance. (ii) If its length is increased to 1.5 m, what will be the new resistance?

Step-by-step solution

A 1‑m long copper wire has resistivity $1.68 \times 1 0^{- 8} Ω m$ . Its cross‑sectional area is $0.5 mm^{2}$ . (i) Find its resistance. (ii) If its length is increased to 1.5 m, what will be the new resistance?