Q&A

# Post History

75%
+4 −0

posted 12mo ago by Olin Lathrop‭  ·  edited 12mo ago by Olin Lathrop‭

#2: Post edited by Olin Lathrop‭ · 2021-10-03T19:01:14Z (12 months ago)
• You are somewhat misquoting what I said. It would help if you provide a link to the comments you are asking about, but the issue was most likely about lack of units on numeric values, not variables.
• A number is dimensionless unless you explicitly provide units. A variable can be defined to have certain dimension, and possibly specific units. Of course, you then need to define your variables properly.
• For example, Ohm's law can be expressed:
• &nbsp; &nbsp; V = I R
• where V is EMF (the electro-motive force), I is current, and R is resistance. Note that this only specifies the dimension of each variable, not the specific units. If it is clearly understood that the variables represent only the physical properties, not specific units, then I think this is OK. I'm not sure what the "right" procedure is. Others here should know this better than I do.
• If in doubt, you could always write it as:
• &nbsp; &nbsp; V &prop; I R
• Again, I'm not sure if that's generally required by convention or not.
• However, if the variables are defined to have specific units, then you have to write the equation with whatever conversion constant might be required. For example, if V is EMF in Volts, I current in Amperes, and R resistance in Ohms, then
• &nbsp; &nbsp; V = I R
• Is correct in all cases. That is because in this case the proportionality constant happens to be 1.
• Now let's say you have determined the equation and want to solve for the numeric value of a particular case. Let's say you have 25 mA thru a 140 &Omega; resistor. In this case, you <i>must</i> show the units:
• &nbsp; &nbsp; (25 mA)(140 &Omega;) = 3.5 V
• Just writing
• &nbsp; &nbsp; 0.025 &sdot; 140 = 3.5
• is technically correct, but says absolutely nothing about current, resistance, and voltage. The following is just downright wrong:
• &nbsp; &nbsp; 0.025 &sdot; 140 = 3.5 V &nbsp; &nbsp; &nbsp; &nbsp; WRONG!
• This equation is claiming that the product of two dimensionless quantities results in a value in Volts.
• You are somewhat misquoting what I said. It would help if you provide a link to the comments you are asking about, but the issue was most likely about lack of units on numeric values, not variables.
• A number is dimensionless unless you explicitly provide units. A variable can be defined to have certain dimension, and possibly specific units. Of course, you then need to define your variables properly.
• For example, Ohm's law can be expressed:
• &nbsp; &nbsp; V = I R
• where V is EMF (the electro-motive force), I is current, and R is resistance. Note that this only specifies the dimension of each variable, not the specific units. If it is clearly understood that the variables represent only the physical properties, not specific units, then I think this is OK. I'm not sure what the "right" procedure is. Others here should know this better than I do.
• If in doubt, you could always write it as:
• &nbsp; &nbsp; V &prop; I R
• Again, I'm not sure if that's generally required by convention or not.
• However, if the variables are defined to have specific units, then you have to write the equation with whatever conversion constant might be required. For example, if V is EMF in Volts, I current in Amperes, and R resistance in Ohms, then
• &nbsp; &nbsp; V = I R
• Is correct in all cases. That is because in this case the proportionality constant happens to be 1.
• Now let's say you have determined the equation and want to solve for the numeric value of a particular case. Let's say you have 25 mA thru a 140 &Omega; resistor. In this case, you <i>must</i> show the units:
• &nbsp; &nbsp; (25 mA)(140 &Omega;) = 3.5 V
• Just writing
• &nbsp; &nbsp; 0.025 &sdot; 140 = 3.5
• is technically correct, but says absolutely nothing about current, resistance, and voltage. The following is just downright wrong:
• &nbsp; &nbsp; 0.025 &sdot; 140 = 3.5 V &nbsp; &nbsp; &nbsp; &nbsp; WRONG!
• This equation is claiming that the product of two dimensionless quantities results in a value in Volts.
• <hr>
• I looked thru some comments and found <a href="https://physics.codidact.com/posts/283420/283448#answer-283448">one example</a> you might be referring to. Note that this answer was edited after my comment was written. Originally you wrote:
• &nbsp; &nbsp; m = 20 g<br>
• &nbsp; &nbsp; m = 20 x 10<sup>3</sup>
• Clearly both those two statements are inconsistant with each other. The first says that m has dimension of mass, since it has the value of 20 grams. The second says m is dimensionless since it has the value of just a number (20,000). We don't have to look at the numeric values to see that something is wrong.
#1: Initial revision by Olin Lathrop‭ · 2021-10-03T18:45:33Z (12 months ago)
You are somewhat misquoting what I said.  It would help if you provide a link to the comments you are asking about, but the issue was most likely about lack of units on numeric values, not variables.

A number is dimensionless unless you explicitly provide units.  A variable can be defined to have certain dimension, and possibly specific units.  Of course, you then need to define your variables properly.

For example, Ohm's law can be expressed:

&nbsp; &nbsp; V = I R

where V is EMF (the electro-motive force), I is current, and R is resistance.  Note that this only specifies the dimension of each variable, not the specific units.  If it is clearly understood that the variables represent only the physical properties, not specific units, then I think this is OK.  I'm not sure what the "right" procedure is.  Others here should know this better than I do.

If in doubt, you could always write it as:

&nbsp; &nbsp; V &prop; I R

Again, I'm not sure if that's generally required by convention or not.

However, if the variables are defined to have specific units, then you have to write the equation with whatever conversion constant might be required.  For example, if V is EMF in Volts, I current in Amperes, and R resistance in Ohms, then

&nbsp; &nbsp; V = I R

Is correct in all cases.  That is because in this case the proportionality constant happens to be 1.

Now let's say you have determined the equation and want to solve for the numeric value of a particular case.  Let's say you have 25 mA thru a 140 &Omega; resistor.  In this case, you <i>must</i> show the units:

&nbsp; &nbsp; (25 mA)(140 &Omega;) = 3.5 V

Just writing

&nbsp; &nbsp; 0.025 &sdot; 140 = 3.5

is technically correct, but says absolutely nothing about current, resistance, and voltage.  The following is just downright wrong:

&nbsp; &nbsp; 0.025 &sdot; 140 = 3.5 V &nbsp; &nbsp; &nbsp; &nbsp; WRONG!

This equation is claiming that the product of two dimensionless quantities results in a value in Volts.

I suspect that the comments you mention in your question were about this last case.