[TowerTalk] Fwd: Tower base/Ufer ground

[Jim Lux]

On 5/18/14, 2:17 AM, Roger (K8RI) on TT wrote:
> On 5/18/2014 12:44 AM, Jim Lux wrote:
>> On 5/17/14, 9:13 PM, Roger (K8RI) on TT wrote:
>>> On 5/17/2014 11:27 PM, Jim Lux wrote:
>>>> On 5/17/14, 6:11 PM, Drax Felton wrote:
>>>>> What is the conductance per inch of concrete in mho's ?
>>>>>
>>>>>
>>>> http://www.k1ttt.net/technote/concrete.html
>>>> 10-50 mS/m
>>>
>>> Shouldn't the medium be in cubic units?
>>
>>
>> No.. it works out right if you do the dimensional analysis..
>
> Not if you do the math right.
>
>>
>> Resistivity is in ohm-m, conductivity in 1/(ohm-m) or S/m  (since S is
>> 1/ohms)
> Resistivity is not ohms per m, it's usually given as ohms per cubic
> centimeter.
>
> Resistance usually is dimensionless, unless it's bulk and then it's so
> many ohms per unit length


Resistance isn't actually dimensionless, but we can consider it so here.

Resitivity (rho in most equations)
The SI unit of electrical resistivity is the ohm⋅metre (Ω⋅m)

So, to compute the resistance of a bar of material that has length L (in 
meters) and cross sectional area A (in square meters), you'd calculate as:

R = rho (ohm * meters) * L (meters) / A (meters*meters)

reducing units, you see that you wind up with (ohms * meters * 
meters)/(meters * meters), so the result is in ohms, which is what you 
would expect.

Conductivity  (sigma) is in Siemens per meter (S/m).  Just as for 
resistance, to calculate the conductance you follow a similar equation.
Doubling the length halves the conductance; doubling the area doubles 
the conductance so

G = sigma (Siemens/meter) * Area (meters * meters) / Length (meters)

Again, the length units cancel, so we're left with G in Siemens


>
> You are confusing resistance with resistivity. You are losing a unit
> somewhere because resistivity is ohms per cubic meter or more often ohms
> per cubic centimeter.  Look up the dictionary definition. Resistance is
> between two points. Resistivity takes into account the volume as the
> units are .
> Resistivity is in ohms per cubic centimeter. I worked with developing
> standards for liquids and circular solids With a Silicon production
> company for many years.
>   The dictionary definition: for resistivity takes into account both
> area and length. IE: volume as in resistivity ohms ^3 cm.  Had a devil
> of a time getting the techs to stop confusing the two.  The easiest was
> to give them a probe consisting of 2, 1cm square plates, 1 cm apart,
> then thy had no conversions.
>
>
>
>> Resistance = Length * resistivity/cross sectional area.
>
> No. Again that is resistivity

Not according to the SI definition.. Resistance is measured in ohms, etc.

I think you might be conflating "how it's measured" vs "how it's defined".

If I take a bar of material, and connect my resistance meter to the ends 
(assuming I can contact the entire end simultaneously, e.g. if I had a 
bar of carbon with silver plated ends) then everything works out.




>
>> so to get ohms as resistance, you need resistivity to be ohms * length
>> (because Length/area is 1/length)
>>
>> Likewise, conductivity is = Area * conductivity/length, so it needs to
>> be Siemens/meter
>>
>>
>
> Conductivity is the reciprocal of resistivity, not resistance. Please
> stop working the formulas and just look up the definitions
>



http://en.wikipedia.org/wiki/Electrical_conductivity
Electrical resistivity (also known as resistivity, specific electrical 
resistance, or volume resistivity) quantifies how strongly a given 
material opposes the flow of electric current. A low resistivity 
indicates a material that readily allows the movement of electric 
charge. Resistivity is commonly represented by the Greek letter ρ (rho). 
The SI unit of electrical resistivity is the ohm⋅metre (Ω⋅m)[1][2][3] 
although other units like ohm⋅centimetre (Ω⋅cm) are also in use. As an 
example, if a 1 m × 1 m × 1 m solid cube of material has sheet contacts 
on two opposite faces, and the resistance between these contacts is 1 Ω, 
then the resistivity of the material is 1 Ω⋅m.

Electrical conductivity or specific conductance is the reciprocal of 
electrical resistivity, and measures a material's ability to conduct an 
electric current. It is commonly represented by the Greek letter σ 
(sigma), but κ (kappa) (especially in electrical engineering) or γ 
(gamma) are also occasionally used. Its SI unit is siemens per metre 
(S/m) and CGSE unit is reciprocal second (s−1).


> 73
>
> Roger  (K8RI)
>
>
>
>
> _______________________________________________
>
>
>
> _______________________________________________
> TowerTalk mailing list
> TowerTalk at contesting.com
> http://lists.contesting.com/mailman/listinfo/towertalk
>