Question

a wire is 1.0 m long, 0.2mm in diameter and has a resistance of 10 ohm. calculate the resistivity of material.​

Answer 1

Answer:

Length of the wire = 1.0 m

Diameter of the wire = 0.2 mm = 0.2×10⁻³ m

Radius of the wire = 0.1×10⁻³ m

Resistance of the wire = 10 ohm

$R = \rho \frac{l}{A} \: \: \: ....ohm \\ \\ \rho = \frac{RA}{l} \: \: \: ....ohm \: m \\ \rho = \frac{R \times \pi {r}^{2} }{l} \: \: \: ....ohm \: m \\ \rho= \frac{10 \times \pi \times {(0.1 \times {10}^{ - 3} )}^{2} }{1} \\ = \frac{10\pi \times 0.01 \times {10}^{ - 6} }{1 } \\ = 3.14 \times 10 \times 0.01 \times {10}^{ - 6} \\ = 3.14 \times 0.1 \times {10}^{ - 6} \\ = 3.14 \times {10}^{ - 7} ohm \: m$

Therefore, the resistivity of the wire is 3.14×10⁻⁷ ohm m.

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