Question

What is the diameter of a 1.00-m length of tungsten wire whose resistance is 0.10 Ω ?

Answer 1

Length of the wire, L= 1.0m

Resistance of wire, $R= 0.10 \Omega$

Resistivity of tungsten, $\rho= 5.6 \times 10^{-8} \Omega m$

Let "d" is the diameter of the wire and "r" is the radius of the wire, then we can write Area of wire as

$A= \pi r^2= \pi \frac{d^2}{4}$

Now using the formula of resistance,

$R= \frac{\rho L}{A}$

using all given values in above,

  $0.1= \frac{5.6 \times 10^{-8} \times 1.0 }{\pi \times \frac{d^2}{4}}$

  $d^2= \frac{5.6 \times 10^{-8} \times 1.0 }{3.14 \times 0.1 \times 0.25}$

$d= \sqrt{0.7133 \times 10^{-6}}=0.844 \times 10^{-3}m= 0.844mm$(ANS)