Question

Example 2: The length of a conducting
wire is 50 cm and its radius is 0.5 mm. If its
resistance is 30 92, what is the resistivity of
its material?​

Answer 1

Answer:

The resistivity of the material is 0.48513 ohm-m.

Answer 2

Question

The length of a conducting wire is 50 cm and it's radius is 0.5 mm. If it's resistance is 30 , What is the resistivity of its material.

Given

• Length of conducting wire is 50 cm.
• Radius is 0.5 mm.
• Resistance is 30

Required to find

Resistivity of its material

Solution

$\sf \: </strong><strong>L</strong><strong> </strong><strong>= 50cm = 50 \times {10}^{ - 2}m$

$\sf \: r = 0.5mm = 0.5 \times {10}^{ - 3 } m$

$\sf \: 5 \times {10}^{ - 4}m \: and \: </strong><strong>R</strong><strong> = 30</strong><strong>Ω</strong><strong>$

$\sf \: resitivity \: p = \dfrac{</strong><strong>RA</strong><strong>}{</strong><strong>L</strong><strong>} \: and \: \: a = \pi {r}^{2}$

$\sf \: p = R \: \dfrac{\pi {r}^{2} }{L}$

$\sf \implies \: \dfrac{30 \times 3.14 \times (5 \times {10}^{ - 4} {)}^{2} }{50 \times {10}^{ - 2} }$

$\sf \implies \: \dfrac{30 \times 3.14 \times 25 \times {10}^{ - 8} }{50 \times {10}^{ - 2} }$

$\sf \implies \: 47.1 \times {10}^{ - 4} \times 25 \times {10}^{ - 8} m$

$\sf \implies \: 4.71 \times {10}^{ - 5} m$

$\sf \: hence \: resistivity \: of \: the \: wire \: 4.71 \times {10}^{ - 5}Ωm$