Why was this equation required to be in metres before resolving?

[chopnhack]

I used Resistance = Resistivity * Length/Area, but used millimetres. Resistivity will equal P for simplicity in writing out the equations online.

R=P*(5mm/pi*0.25)

R=P*5mm/0.785

R=P*6.36943

1 ohm = P*6.36943 divide out the 6.36943 to get resistivity of material is 0.156999 for that size resistor at 1 ohm

10M ohm = P*6.36943 yields 1.5699 x 10^5

I noticed that my figures where off by the magnitude difference of the conversion of mm to metre, but didn't understand why they used metres and how would I have known to have done so!

 

[(*steve*)]

In general, I would convert to metres before I performed the calculation otherwise the results may be in different units than you expect.

 

[Arouse1973]

View attachment 14369

I used Resistance = Resistivity * Length/Area, but used millimeters. Resistivity will equal P for simplicity in writing out the equations online.

R=P*(5mm/pi*0.25)

R=P*5mm/0.785

R=P*6.36943

1 ohm = P*6.36943 divide out the 6.36943 to get resistivity of material is 0.156999 for that size resistor at 1 ohm

10M ohm = P*6.36943 yields 1.5699 x 10^5

I noticed that my figures where off by the magnitude difference of the conversion of mm to meter, but didn't understand why they used meters and how would I have known to have done so!

Hi Chopnhack

The SI unit for length is the metre which is probably why they used metres. They have complicated things by writing 1mm instead of 1*10^-3 m. So it quite easy for someone to enter this as just 1 and not 1*10^-3. I always use the *10^x button on my calculator so enter the figures as written and remember if it's written as mm then it's ^-3.

You will always see these type of thing abbreviated to say uA, mA, pA you just have to get your head around it, it will soon become very natural and you will enter the numbers correctly with out even noticing. The one thing that still catches me out is when you say you want to convert from mA into nA or uA into nA etc. It all depends on how much you use all of this stuff. I suppose we may have became lazy because of calculators.
Adam

 

[Merlin3189]

Chopnhack, what struck me about your post was the comment,
"... to get resistivity of material is 0.156999 for that size resistor at 1 ohm..."
But resistivity is not a pure number - it has units. Just like speed, time, weight, density, area and most of the quantities you come across.
You would not say your speed was 35, because people would have to guess whether you meant 35mph, 35 kmph, 35fps, 35m/sec or whatever. They might guess from the context, just as you did when you noticed the discrepancy in your result, but to avoid errors (as with the Mars lander *) you should always be aware of what units you are using and make it absolutely clear to anyone else.
Your answer was not wrong! If you had put your units, 1.59 x10^5 Ohm mm, you would have had the same answer as given, 1.6x10^2 Ohm m. That answer in Ohm mm is perfectly acceptable, because it IS correct.
The reason they used metres is simply, that many people prefer to work with SI units for consistency with their colleagues who also prefer SI. I grew up before SI, when FPS, CGS and MKS were all common. Most people didn't worry overmuch about which one you used, but we all knew it was absolutely essential to say which units we were using. That's all you need to do now.

* http://mars.jpl.nasa.gov/msp98/news/mco990930.html

 

[Gryd3]

Arouse1973 has mentioned SI units in his post, this is the main reason.
Every formula I am familiar with uses Standard Units.
Take a look at: http://en.wikipedia.org/wiki/International_System_of_Units

It would be very difficult to try to remembers what 'magnitude' each value should be when using the vast collection of formulas out there, so they all use the base format. Not milli, mega, or any other prefix you can think of.

(Perhaps someone can find a formula to disprove this)

 

[(*steve*)]

The issue that can arise is that if you're working in units of mm and your result unit (let's call it X) has units containing metres^1 then you'll get a result in mX. However if it has units in m^2, you'll get results in μX, and for m^3 in pX.

If you don't know the fundamental nature of your unit (1Ω, for example = 1 (m².kg)/(s.C²)) you might not know if your answer needs to be multiplied (or divided) by 1, 1000, 1,000,000, or 1,000,000,000.

If working in mm means that you automatically enter the figure as 0.001, then you're working in metres and you won't fall for this common problem.

 

[chopnhack]

The issue that can arise is that if you're working in units of mm and your result unit (let's call it X) has units containing metres^1 then you'll get a result in mX. However if it has units in m^2, you'll get results in μX, and for m^3 in pX.

If you don't know the fundamental nature of your unit (1Ω, for example = 1 (m².kg)/(s.C²)) you might not know if your answer needs to be multiplied (or divided) by 1, 1000, 1,000,000, or 1,000,000,000.

If working in mm means that you automatically enter the figure as 0.001, then you're working in metres and you won't fall for this common problem.

And therein lies the rub! The text did not cover resistivity or define it, but now I understand the why.

As Merlin points out, resistivity has units - Ω/m and that is why I was off by an order of 3. I saw that I had the same number, just the wrong decimal point. Key to remember is keep track of your units!

Thanks all!

 

[Merlin3189]

... As Merlin points out, resistivity has units - Ω/m ...

Just to be clear, the units are Ω x m not Ω / m
The defining equation for resistivity is
resistivity = Resistance x Area / Length , units Ohm x m x m / m or Ohm x m

See http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

(Apologies that I haven't worked out how to write equations properly in this editor yet.)

 

[Arouse1973]

Hey dont worry. They thought Einstein was simple when he was at school. He was just bored

Adam

 

[chopnhack]

Thanks Merlin, I didn't catch that.