Question

A tungsten wire has a radius of 0.070 mm.When 108 V is applied across the ends of the hot wire, a current of 3.80 A is produced. How long is the wire? (The resistivity of tungsten is Ωm)

Answer 1

Answer:

$l=7.8126\ m$

Explanation:

Given:

• radius of the tungsten wire, $r=0.07\ mm$

• electric potential applied across the ends, $V=108\ V$

• current through the wire, $i=3.8\ A$

• we have the resistivity of the wire, $\rho=5.6\times 10^{-8}$

Using Ohm's law:

$V=R.I$

$108=R\times 3.8$

$R=28.421\ \Omega$

The mathematical expression for the resistivity is given as:

$R=\rho.\frac{l}{a}$

where;

$l=$ length of wire

$a=$ cross sectional area of wire

$28.421=5.6\times 10^{-8}\times \frac{l}{\pi\times (7\times 10^{-5})^2 }$

$l=7.8126\ m$