Question

Choose the correct alternative.

The wire of length L and resistance R is stretched so that its radius of cross-section is halved. What is its new resistance?

Options

• 5R

• 8R

• 4R

• 16R

Answer 1

16R

Explanation:

let r, and l, be their initial radius of the wire and r₂ and l₂ be their final radius of the wire.
∴ Initial volume = Final volume
`π"r"_1^2  "l"_1=π"r"_2^2  "l"^2`

∴ `"l"_1/"l"_2=(("r"_2)/("r"_1))^2`

Since r₂ = `"r"_1/2`

∴ `"r"_2/"r"_1=1/2` ....(i)

∴ `"l"_1/"l"_2=1/4` ....(ii)

∴ Resistance, R = `(ρ"l")/"A"=(ρ"l")/(π"r"^2)`

∴ `"R"_1/"R"_2=((ρ"l"_1)/(π"r"_1^2))/((ρ"l"_2)/(π"r"_2^2))="l"_1/"l"_2xx(("r"_2)/"r"_1)^2`

= `1/4xx(1/2)^2=1/16`

∴ R₂ = 16 R₁