Question

Find the resistance at 50°C of a copper wire 2
mm in diameter and 3 m long.​

Answer 1

Answer:

$\large\bold\red{0.0182\:\Omega}$

Explanation:

Given,

A copper wire having,

• l = 3m
• d = 2mm

Therefore,

• r = d/2= 1mm = 0.001m
• t= 50° C

Also,

We know that,

For copper wire,

• $\rho = 1.6 \times{10}^{-8}$
• $\alpha = 0.0039$

Now,

In order to find resistance at 50 °C,

At first we have to find resistance at 0°C,

And,

We know that

$\large \boxed{\purple{R_{o}= \rho \frac{l}{a}} }$

Where,

• a is the area of cross section of the wire.

Now,

Calculate area, which is equal to:

$= > a = \pi {r}^{2} \\ \\ =>a = 3.14 {r}^{2} \\ \\ </p><p>=>a = (3.14) {(0.001)}^{2} \\ \\ </p><p>=>a = (3.14)(0.000001) \\ \\ </p><p>=>a = 3.14 \times {10}^{ - 6}$

Now putting value of area in above formula:

We get,

$=>R_{o}=(1.6\times{10}^{-8})\frac{(3)}{(3.14\times{10}^{-6})}\\\\=>R_{o}=0.0152\:\Omega$

Also,

We know that:

$\large\boxed{\purple{R_{t}=R_{o}(1+αt)}}\\\\=>R_{t}=(0.0152)(1+(0.0039)(50))\\\\=>R_{t}=(0.0152)(1+0.195)\\\\=>R_{t}=(0.0152)(1.195)\\\\=>R_{t} =0.0182\: \Omega$

Hence,

Resistance of the Copper wire is 0.0182 Ω

Answer 2

Answer:

Explanation:

Find the resistance at 50°C of a copper wire 2 mm in diameter and 3 m long.

[Ans: 0.0184 2]