CLASS 10 SCIENCE · ELECTRICITY

Resistance of a wire (resistivity)

R = ρl/A. Resistance increases with length, decreases with cross-sectional area, and depends on the material (ρ). Stretching a wire to n times its length makes R n² times.

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Worked examples

Example 1 · level 1

Find the resistance (in ohm) of a manganin wire 50 m long with cross-sectional area 0.5 mm². Resistivity of manganin = 44 × 10⁻⁸ Ω m. (Correct to 2 decimal places.)

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R = (44 × 10⁻⁸ × 50) ÷ (0.5 × 10⁻⁶)
= 44 × 50 ÷ (0.5 × 100) = 44 Ω.

Answer: 44 ohm

Example 2 · level 2

Find the resistance (in ohm) of a manganin wire 20 m long with cross-sectional area 0.1 mm². Resistivity of manganin = 44 × 10⁻⁸ Ω m. (Correct to 2 decimal places.)

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R = (44 × 10⁻⁸ × 20) ÷ (0.1 × 10⁻⁶)
= 44 × 20 ÷ (0.1 × 100) = 88 Ω.

Answer: 88 ohm

Example 3 · level 3

A uniform wire of resistance 19 Ω is stretched to 3 times its original length (volume unchanged). Find its new resistance (in ohm).

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R′ = ρ(3l)/(A/3) = 9R = 9 × 19 = 171 Ω.

Answer: 171 ohm