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In the unit of work done, $Nm$, $N $ stands for the force applied and $m$ stands for the length of displacement, by taking their product we get work done or $Nm$.

But in the case of electrical resistivity, $ohm-meter$, I know that $ohm$ stands for resistance of wire which is not defined for a given resistivity, and $metre$ stands for something i don't understand.

1.What is the meaning of ohm-meter?

2.Also tell me what is electrical resistivity? (not asking its derivation in this question)

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  • $\begingroup$ Ohmmeter is the name of a device measuring resistance, where meter means measurement (rather than teh unit of the same name). Not sure whether thsi answers your question - just to make sure that it is properly understood. $\endgroup$
    – Roger V.
    Jan 22, 2022 at 14:06
  • $\begingroup$ Sorry i was talking about metre a unit of length $\endgroup$ Jan 22, 2022 at 17:23

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"Metre" is the side length of a cube of the material that you are testing.

To find the resistivity of a substance you can make a cube of the substance, with side length $x$ metres and measure the resistance to electricity $r$ Ohms, then the resistivity is $r\times x$ and units are Ohm-metres.

This is useful because at a standard temperature, this is a constant that depends only on the substance under test.

You can observe that the resistance is proportional to the length of the resister, and inversely proportional to the cross-sectional area of the resistor. or $r.\Omega \propto x.\text{m} \times (A.\mathrm{m}^2)^{-1}$.

If the constant of proportionality is $\rho$ the electrical resistivity. You might write $\rho = r\times A \times x^{-1}.\Omega\,\mathrm{m}^2\,\mathrm{m}^{-1}$

Or resistivity has units of Ohm metre-square per metre.

But as units are simplified, Ohm metre-square per metre is simplified to Ohm-metres.

(Not to be confused with Ohmmeters which are different altogether.)

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  • $\begingroup$ Is it in the definition? Making a cube? $\endgroup$ Jan 22, 2022 at 17:25
  • $\begingroup$ Yes, but in practice you don't use a cube. While the resistivity is equal the resistance of a metre-cube of the substance you don't need an actual block to do the measurement. You can measure the resistance of a small prism of the substance, and use the proportionalities to work out the resistance that a metre cube would have. $\endgroup$
    – James K
    Jan 22, 2022 at 17:32
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Electrical resistivity is a property of a material. The units for resistivity $\rho$ in ohm-meters comes from the equation for the resistance of a conductor,

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

where $L$ is the length of the conductor in meters, $A$ the cross sectional area in square meters and $R$ the resistance in ohms.

The SI units for the Ohm are

$$\Omega = \frac{\rm kg\,m^2}{\rm s^{3}\,A^2},$$

where $\rm A$ is the ampere and $\rm s$ the second. This comes from the equation for Ohm's law,

$$R=\frac{V}{I},$$

where the SI units for the voltage $V$ are

$$\rm V = \frac{\rm kg\,m^2}{\rm s^{3}\,A}$$

and the SI unit for current $I$ is the ampere $\rm A$.

Substituting the SI units for resistance in the first equation gives the SI units for resistivity $\rho$ of

$$\frac{\rm kg\,m^3}{\rm s^{3}\,A^2} = \rm \Omega\,m$$

Hope this helps.

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  • $\begingroup$ Can you explain the meaning of expression? The expression at last ${kg} m^3/ {s^3A^2}$ $\endgroup$ Jan 22, 2022 at 17:22
  • $\begingroup$ It's not an "expression". It's simply the SI units for electrical resistivity that are the equivalent of $\Omega.m$. Just like the SI units for Newtons is $kg m/s^2$. $\endgroup$
    – Bob D
    Jan 22, 2022 at 18:23
  • $\begingroup$ Can you give a meaning to it for example Nm in work done means Newtons of force applied for a given metre of distance. $\endgroup$ Jan 22, 2022 at 19:26
  • $\begingroup$ Nm doesn’t necessarily mean work. It’s also the unit of torque. So even though the units are the same as energy Nm doesn’t necessarily mean energy. The same applies to PV. So one last time, units don’t always refer to the same thing. $\endgroup$
    – Bob D
    Jan 22, 2022 at 19:34
  • $\begingroup$ Ok thanks for help $\endgroup$ Jan 22, 2022 at 19:37

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