Question

The resistance of a metal wire of length 1m is 10 raised to 4 ohm at 20°C. If the diameter of the wire is 0.15mm, find the resistivity of the metal at that temperature.

Answer 1

Answer:

resistivity will be 7.06×10^-4ohm meters

see the attachment for explanation

please mark as brainliest answer

Answer 2

Given that,

Length of metal wire (l) = 1 m

Resistance (R) = 10⁴ Ω

Temperature (T) = 20° C

Also given that, the diameter of the wire is 0.15 mm.

Diameter (d) = 0.15 mm = 1.5 × 10-⁴ m

Radius = Diamter/2 = (1.5 × 10-⁴)/2 = 7.5 × 10^5- m

We have to find the resistivity of the metal at that temperature.

Now,

R = p l/A

Here, R = resistance, p = rho (resistivity), l = length and A = area of cross-section

Also, Area = πr²

So,

R = p l/(πr²)

⇒ 10^4 = p (1)/(22/7 × 7.5 × 10^5- × 7.5 × 10^5-)

⇒ 10^4 = p (1)/(1.76 × 10^8-)

⇒ 10^4 × 1.76 × 10^8 = p

⇒ 1.76 × 10^12 = p

Therefore,

The resistivity of the metal at that temperature is 1.76 × 10^12 Ω m