Question

What is the resistance of a silver wire 25 m long at 20 °C and whose diameter is 0.00095 cm? the of silver is at 20 °C is 1.6 x 10-8Ω.m.

Answer 1

We solve the problem using the formula

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

We have the parameters:

Length of wire, $l$ =$25m$

diameter of wire, $d=0.00095cm$

Resistivity, $\rho=1.6\times10^{-8} Ωm$

We convert diameter from $cm$ to $m$ and then divide the results by 2 to get our $radius$

$d=\frac{0.00095}{100}m=0.0000095m$

Radius, $r=\frac{0.0000095}{2}=4.75\times10^{-6}m$

Therefore, we get the value for $Area$ by the formula

$A=\pi\times r²$

$A=\frac{22}{7}\times[4.75\times10^-{6}]²$

$A=\frac{22}{7}\times2.256\times10^{-11}$

$A=7.09\times10^{-11}m²$

Now, we have the necessary parameters to work with which are, $Length (m)$ ,$Resistivity,(\rho)$ and $Area(m²)$

We then get the resistance of the wire using the formula

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

$R=\frac{1.6\times10^{-8}\times25}{7.09\times10^{-11}}$

$R=\frac{4\times10^{-7}}{7.09\times10^{-11}}$

$R=5.64\times10^{-19}Ω$

Therefore, the resistance of the silver wire is

$5.64\times10^{-19}Ω$