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alewisGB
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If two units have the same dimensions are they always inequivalent? I was thinking, would doing dimensional analysis on units prove they are equivalent or could they have the same units but not be equivalent.
phinds said:what do you mean by equivalent? Are 5 miles and 10 miles equivalent?
alewisGB said:If two units are in SI and you do dimensional analysis on the two different units that come to the same dimensions does that mean the units are equal?
f95toli said:If I understand the question correctly the answer is no.
Example: The dimensions of surface resistance is ohm. but it is a propery of the material (the thin film), it does not become a "real" resistance until you multiply it with a length and divide by the width.
Hush said:Different answers to this question imply the question is not well stated.
mikeph said:If I understand right, in this example the first quantity you describe is resistivity, a material property, with units Ohm*metre; the second quantity is resistance, with units Ohm (resistivity*length/area).
alewisGB said:My question was relating to Units only, If two units are in SI and you do dimensional analysis on the two different units that come to the same dimensions does that mean the units are equal?
e.g Resistance Ω Is equvilant as Inductance H * frequency Hz so, A resistor could be measured as 100 H Hz or 100 Ω
Two units have the same dimensions if they measure the same physical quantity, such as length, mass, or time.
Yes, two units with the same dimensions can have different numerical values. For example, 1 meter and 100 centimeters both measure length, but have different numerical values.
No, units with the same dimensions are not always equivalent. They may have different conversion factors or be used in different systems of measurement.
To determine if two units with the same dimensions are equivalent, you can use a conversion factor or compare their values in a specific system of measurement.
Understanding the difference between equivalent and equivalent units is important in accurately measuring and converting between different units. It also helps prevent errors and confusion when working with measurements and calculations.