Question

What will be the length of a nichrome wire resistance 5.0Ω, if the length of similar wire of 120 cm has resistance of 2.5 Ω? Why?

Answer 1

Here,

I₂ = 120cm = 1.20m 

R₁ = 5.0Ω 

R₂ = 2.5Ω 

Now,

R₁ = \(\frac{ρ\,\times\,I_1}{A}\)

And,

R₂ = \(\frac{ρ\,\times\,I_2}{A}\)

(Here, resistivity ρ and the area A remain same as the wires are similar.)

∴ \(\frac{R_1}{R_2} = \frac{ρ\,\times\,\frac{I_1}{A}}{ρ\,\times\,\frac{I_2}{A}}\)

\(\frac{R_1}{R_2} = \frac{I_1}{I_2}=\frac{I_1}{120\,\times10^{-2}}\)

Now,

\( \frac{5.0}{2.5}=\frac{I_1}{120\,\times10^{-2}}\)

l₁ = 2×120×10-2 m 

l₁ = 24×10-1 m 

∴ l₁ = 240 cm