Question

A metal wire has diameter of 0.25 mm and electrical resistivity of 0.8×10^-8 ohm-m​.

(i) what will be the length of this way to make a resistance 5 Ohm?

(ii) how much will the resistance change, if the diameter of the wire is doubled?

Answer 1

Answer:

See the attachment.

Thanks for asking.

Answer 2

(A) L = 30.67 m

(B) R = 5 ohms

Explanation:

Given that,

Diameter of the metal wire, d = 0.25 mm

Radius of the wire, r = 0.125 mm

Electrical resistivity of the metal wire, $\rho=0.8\times 10^{-8}\ \Omega-m$

(i) Here, we need to find the length of the wire. The formula of the resistivity of the wire is given by :

$R=\rho \dfrac{l}{A}\\\\l=\dfrac{RA}{\rho}\\\\l=\dfrac{5\times \pi (0.125\times 10^{-3})^2}{0.8\times 10^{-8}}\\\\l=30.67\ m$

(ii) If diameter is doubled, d = 0.25 mm × 2 = 0.5 mm

Radius, r = 0.25 mm

So, if the diameter of wire is doubled, the resistance will not change.

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