Question

:. The resistivity of the material of a wire is 6 x 10-5 ohm cm. If the
resistance of the wire is 12 ohms and its diameter is 2.0 mm,
calculate the length of the wire.​

Answer 1

Answer:

35cm

Explanation:

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Answer 2

Given: The resistivity of the material of a wire is 6 x 10⁻⁵ ohm-cm, the resistance of the wire is 12 ohms, and its diameter is 2.0 mm.

To find: The length of the wire.​

Solution:

• The specific resistance or resistivity of a material is equal to the resistance of the wire of that material of specific length and area of cross-section.
• It is given by the formula,

        $\rho = \frac{RA}{l}$

• Here, ρ is the resistivity, R is the resistance of the conductor, A is the area of cross-section and l is the length of the conductor.
• In the question the diametre is given as 2.0 mm, so the radius becomes 0.1 m.
• To find resistivity, the area of the wire (cylinder) is to be found which is calculated as,

        $Area = 2\pi r(l+r)$

                 $= 0.63 (l+r) cm^{2}$

                 $= 0.63 (l+0.1) cm^{2}$

• On replacing the terms with the values given in the question,

        $6*10^{-5} = \frac{12*0.63(l+0.1)}{l}$

        $l = 0.1cm$

Therefore, the length of the wire. is 0.1 cm.