Calculating R_L(max) and R_L(min) Using Significant Figures

In summary: The significant figure would be 1. In summary, the conversation was about finding the external load resistance of an open collector of standard TTL using a given formula. The values of R_L(max) and R_L(min) were calculated to be 0.0022 [ohm] and 0.3 [ohm] respectively, but there were doubts about their accuracy. The use of significant figures to estimate uncertainty was discussed and it was recommended to use actual uncertainties for a proper analysis. The significance of the source voltage value of 5 in the formula was also mentioned, with a suggestion to assume an uncertainty of ~1 if no other information is known. Therefore, the significant figure for the final answer would be 1.
  • #1
aruwin
208
0
Can you give me the answer to the right significant number please?
I got R_L(max) = 0.0022 [ohm] and R_L(min) = 0.3 [ohm] but I have a feeling that they're not correct. Someone please check.

R_L(max) = |(5 - 2.4)/(3*(-400) + 40))|

R_L(min) = (5 - 0.4)/(16 - (-1.6))
 
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  • #2
Assuming 5 and 16 are fixed constants without uncertainty, you could quote R_L(min) as 0.26, as 5-0.4=4.6 and 16+1.6 = 17.6.

R_L(max) looks fine.
 
  • #3
mfb said:
Assuming 5 and 16 are fixed constants without uncertainty, you could quote R_L(min) as 0.26, as 5-0.4=4.6 and 16+1.6 = 17.6.

R_L(max) looks fine.

Actually this is the actual question. It's about finding the external load resistance of an open collector of standard TTL.

Here's the picture so you can everything clearly. So can you check if I am doing it right?
 

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  • #4
Actually this is the actual question.
You cannot answer this based on your equations.

Significant figures can be a handy tool to estimate the uncertainty of a result. If you need a proper analysis, use actual uncertainties and not significant figures.
 
  • #5
mfb said:
You cannot answer this based on your equations.

Significant figures can be a handy tool to estimate the uncertainty of a result. If you need a proper analysis, use actual uncertainties and not significant figures.

But that's the formula given to find the max/min resistance. So how am I supposed to calculate them?
 
  • #6
As you did, with the improvement given in post 2 if you know that 5 and 16 are exact. If you do not know that, 0.3 is fine as result.
 
  • #7
mfb said:
As you did, with the improvement given in post 2 if you know that 5 and 16 are exact. If you do not know that, 0.3 is fine as result.

Did I get the significant figure right?


I know that when we take account of the significant figures, 5-2.4 would be 3 because there is no decimal value after five so it becomes unknown and we can't just make it 0 and minus 4. But I am not sure about this calculation though, because I don't know if I have to calculate everything normally first and then think about the s.g. when I get the final answer OR taking in account of the s.g. for every step of the calculation. I hope I am clear with my doubts here.
 
  • #8
But I am not sure about this calculation though, because I don't know if I have to calculate everything normally first and then think about the s.g. when I get the final answer OR taking in account of the s.g. for every step of the calculation.
The second method is better, the first can lead to problems in some types of calculations.
 
  • #9
mfb said:
The second method is better, the first can lead to problems in some types of calculations.

So I would have to calculate 5-2.4 as 3??Then that means my final answer would only have 1 significant figure. So do I have to do that?
 
  • #10
If that value 5 is known to one significant figure only, yes.
 
  • #11
mfb said:
If that value 5 is known to one significant figure only, yes.

As you can see in the formula, that value of 5 is the source voltage. 5 is obviously one significant figure, right?
 
  • #12
Probably, and if you don't know anything else about it, just assume that it is 5 with an uncertainty of ~1.
 
  • #13
mfb said:
Probably, and if you don't know anything else about it, just assume that it is 5 with an uncertainty of ~1.

So that would mean the significant figure is 1. Correct?
 
  • #14
As I said before, yes.
 

FAQ: Calculating R_L(max) and R_L(min) Using Significant Figures

What is the purpose of calculating RL(max) and RL(min) using significant figures?

The purpose of calculating RL(max) and RL(min) using significant figures is to accurately represent the range of values for the resistance of a given component or circuit. This can help in determining the precision and accuracy of measurements, as well as in making proper calculations and predictions.

How do you calculate RL(max) and RL(min) using significant figures?

To calculate RL(max) and RL(min) using significant figures, you must first determine the uncertainty of the measurement by identifying the last significant digit in the measurement. Then, use the rules of significant figures to round the measurement and determine the maximum and minimum values for RL based on the uncertainty.

What are the rules for significant figures when calculating RL(max) and RL(min)?

The rules for significant figures when calculating RL(max) and RL(min) are:

  • If the last significant digit is greater than or equal to 5, round up the preceding digit.
  • If the last significant digit is less than 5, round down the preceding digit.
  • If the last significant digit is 5 and followed by non-zero digits, round up the preceding digit.
  • If the last significant digit is 5 and not followed by any digits, round up the preceding digit if it is odd, and round down if it is even.

Can you provide an example of calculating RL(max) and RL(min) using significant figures?

Yes, for example, if the measured value of resistance is 125.67 ohms with an uncertainty of 0.05 ohms, the maximum value for RL would be 125.72 ohms (rounding up the last significant digit), and the minimum value would be 125.62 ohms (rounding down the last significant digit).

How do you determine the number of significant figures in a measurement?

The number of significant figures in a measurement is determined by counting all digits from the first non-zero digit on the left to the last significant digit on the right. Trailing zeros after a decimal point are also significant, but leading zeros before a decimal point are not significant. Zeros between non-zero digits are also significant. Scientific notation can also be used to indicate significant figures, with all digits (including zeros) before the exponent being significant.

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