Question

Determine the resistance, in milliOhms, of a metal rod 1.78 m long, 0.58cm diameter and composed of aluminum of resistivity 2.8 x 10-8 Ωm .

Answer 1

Given:

The length of the metal rod is,

`l=1.78\text{ m}`

The diameter of the aluminum rod is,

`\begin{gathered} d=0.58\text{ cm} \\ =0.58*10^(-2)\text{ m} \end{gathered}`

The resistivity of aluminum is,

`\rho=2.8*10^(-8)\text{ ohm.m}`

To find:

The resistance

Step-by-step explanation:

The resistance of the material is,

`\begin{gathered} R=(\rho l)/(A) \\ Here,\text{ A=}(\pi d^2)/(4) \\ R=(\rho l)/((\pi d^2)/(4)) \\ R=(4\rho l)/(\pi d^2) \end{gathered}`

Substituting the values we get,

`\begin{gathered} R=(4*2.8*10^(-8)*1.78)/(\pi*(0.58*10^(-2))^2) \\ =1.88*10^(-3)\text{ ohm} \\ =1.88\text{ mOhm} \end{gathered}`

Hence, the resistance is 1.88 mOhm.