Question

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

Answer 1

r = 1 mm = `1/1000`m

R = 1Ω

ρ = 1.7 × 10^-8 Ω

l = ?

R = `"ρ"l/a`

`l = "Ra"/"ρ"`

= `("R"pir^2)/"ρ"`

= `(2 xx 3.142 xx 1/1000 xx 1/1000)/(1.7 xx 10^-8)`

= `((2 xx 3142 xx 10)/(17 xx 1000)) xx 10^8/10^6`

= `6284/17 xx 10^(8+1-6-3)`

= 369.4 × 10⁰

= 369.4 × 1

l = 369.4 m