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Calculate the resistance of a constantan wire of length $2 m$ and radius $0.1 mm$ . Given that resistivity of constantan is $49 \times 10^{- 8} Ωm$ .

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31.8 Ω

32.1 Ω

20 Ω

31.1 Ω

answer is D.

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Detailed Solution

The resistance of a constantan wire is

31.1 Ω

.
Given data in the problem,
Length of wire,

l = 2 m

Radius of wire,

r = 0.1 mm

Resistivity of constantan,

ρ = 49 \times 10^{- 8} Ωm

Area of wire,

A = π r^{2}

\Rightarrow A = 3.14 {\times 0.1}^{2}

By using the formula,
Resistance

R = ρ \cdot \frac{L}{A}

\Rightarrow R = 49 \times 10^{- 8} \times \frac{2}{3.4 * {0.1}^{2}}

\Rightarrow R = 31.1 ohm

So, the resistance of constantan is

31.1 ohm

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