Question

Calculate the resistance of 1 km long copper wire of radius 1 mm.

(specific resistance of copper is 1.72 * 10^-8 ohm meter) ​

Answer 1

given:

Length, l=1 km=1000 m

Radius, r=1 mm=10^−3 m

to find:

the resistance.

solution:

Specific resistance of copper:

ρ=1.72×10^−8

Area of cross-section:

A=π×r2=3.14×10^−6 m^2

Let the resistance be R.

As we know, R=ρ l/A

On substituting values:

R=1.72×10^−8×10^3/3.14×10^−6

=5.5 ohm

⇒ Resistance of the copper wire, is 5.5 ohm.

Answer 2

5.5 Ω

Step-by-step explanation:

Given : l = 1 km = 1000 m, r = 1 mm = 10^-3 m,

`a = \pi {r}^(2)`

`= > 3.14 * ( {10}^( - 3) )^(2) \\ = > 3.14 * {10}^( - 6) \: {m}^(2) .`

`specific \: \: resistance \: \: ρ \: \\ = > 1.72 * {10}^( - 8) Ω \: m`

Resistance (R) :-

`R \: = ρ * (l)/(a) \\ \\ = > \frac{(1.72 * {10}^( - 8) ) * 1000}{3.14 * {10}^( - 6) } \\ \\ = > 5.5 \: Ω`

Hope it helps you!!