Question

Choose the correct alternative.

Masses of three pieces of wires made of the same metal are in the ratio 1:3:5 and their lengths are in the ratio 5:3:1. The ratios of their resistances are

Options

• 1:3:5

• 5:3:1

• 1:15:125

• 125:15:1

Answer 1

125:15:1

Explanation:

R = `(ρ"l")/"A"=(ρ"l"xx"l")/("A"xx"l")=(ρ"l"^2)/"V"`

Since, V = `"m"/"d"`

∴ R = `(ρ"l"^2)/("m"//"d")`

∴ R α `"l"^2/"m"`

∴ R₁:R₂:R₃ = `"l"_1^2/"m"_1:"l"_2^2/"m"_2:"l"_3^2/"m"_3`

= `5^2/1:3^2/3:1^2/5`

= 125:15:1