Question

A silver wire has a diameter 0.4mm and restivity 1.6*10^-8 ohm-m,how much length of thiswire is required to make 1 ohm coil?

Answer 1

$\huge\mathbb{QUESTION-}$

A silver wire has a diameter 0.4mm and restivity $\sf{1.6×10^{-8}}$ ohm-m,how much length of thiswire is required to make 1 ohm coil?

$\huge\mathbb{SOLUTION-}$

$\large\underline{\underline{\sf Given:}}$

• Diameter (d) = 0.4 mm

in metre $\sf{0.4×10^{-3}}$ m

• ⛬ Radius (r) = d/2

$\sf{r = 2×10^{-4}m}$

• Resistance (R) = 1 Ω

$\large\underline{\underline{\sf To\:Find:}}$

• How much lenght of wire required (l)

$\large\underline{\underline{\sf Formula\:Used:}}$

$\large{\boxed{\sf R=\dfrac{\rho l}{A} }}$

A = Area of wire = πr²

$\implies{\sf 1=\dfrac{1.6×10^{-8}×l}{π×(2×10^{-4})^2}}$

$\implies{\sf l =\dfrac{3.14×4×10^{-8}}{1.6×10^{-8}}}$

$\implies{\sf l=\dfrac{12.56}{1.6}}$

$\implies{\bf \red{ l=7.85\:m}}$

$\huge\mathbb{ANSWER-}$

Lenght of wire is ${\bf \red{7.85\:m}}$