Question

What length of copper wire of resistivity 1.7 × 10^-8 Ω m and radius 1 mm is required so that its resistance is 2Ω? 

Answer 1

Resistance (R) = 2 ohm

Resistivity (ρ) = 1.7 × 10^-8 ohm metre

Radius (r) = 1 mm = 10^-3 m

Length (l) = ? 

`R=ρ l/A`  

`ρ=l/(pir^2)` 

Substituting the values in the formula above we get,

`2 = 1.7xx10^-8l/(pi(10^-3)^2)`

`2 = 1.7xx10^-8l/(3.14xx(10^-3)^2)`

`2=(1.7xx10^-2xxl)/3.14`

`2 =(1.7xxl)/314`

⇒ l = `(314xx2)/1.7` 

⇒ l = 369.4 m

Hence, the length of the copper wire = 369.4 m.