ISC PV Cell Question (Isolating a variable)
- Thread starter Ryaner
- Start date
Bachelor of Engineering (Honours)(2.1)
Bachelor of Technology (Ordinary)(2.1)
As with most engineer I know. It is not the complex maths that cause the issue it is the simple stuff.
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I'm pretty sure that there is no way I am ever going to convince you that it is worth your time and effort to track units, despte the fact that doing so would have screamed out to you the mistake you made in your last line.
Check the units:
Isc = (e^ Voc /0.0257)*Io-1
The Voc/0.0257V (I've added the proper unit back in, again) is dimensionless. This is good because the exponential function requires a dimensionless argument.
The (e^ Voc /0.0257V) is dimensionless because the exponential function produces a dimentionless result.
The (e^ Voc /0.0257)*Io has units of current.
The (e^ Voc /0.0257)*Io-1 can't be done because you can't add a current to a dimensionless quantity. So you KNOW it is wrong.
So take a step back to the previous line:
Isc/Io +1= e^ Voc /0.0257V (again, I added the V)
This is dimensionally consistent. Now, that doesn't mean that it is correct. But it at least has a chance. The fact that it is consistent while the next line isn't also means that there is an error in going from one to the other.
With that in mind, see if you can fix it.
What does 2.1 mean? I've never seen that notation before.
It most certainly does have something to do with voltage. It has to. Otherwise the equation you are starting from is fundamentally wrong and useless.
If you look carefully, you will find that those two values you refer to have units and that the units that survive when you divide one by the other has units of voltage.
In fact, even without you indicating where that constant comes from or me not knowing a damn thing about solar cells, I can all but guarantee you what that constant is. It is the thermal voltage given by;
\(
V_T = \frac{kT}{q}
\)
where:
k is boltzmann's constant
T is the temperature
q is the magnitude of the electron charge
\(
k = 1.3806488 \times 10^{-23} \frac{m^2 kg}{s^2 K}
T = 298.15K \ (i.e., \ 25^o C)
q = 1.60217657 \times 10^{-19} C
\)
So, plugging in these values:
\(
V_T \; = \; \frac{1.3806488 \times 10^{-23} \. \frac{m^2 kg}{s^2 K} \. \cdot \. 298.15K }{1.60217657 \times 10^{-19} C}
\
V_T \; = \; 0.025693 \. \frac{m^2 kg K }{s^2 K C} \; = \; 0.025693 \. \frac{m^2 kg }{s^2 C}
\)
Now,
1 newton is one kilogram-meter per second-squared
1 joule is one newton-meter
1 volt is one joule per coulomb
\(
V_T \; = \; 0.025693 \. \frac{m^2 kg }{s^2 C} \.\cdot\. \frac{1N}{\frac{kg m}{s^2}} \.\cdot\. \frac{1J}{Nm} \.\cdot\. \frac{1V}{\frac{J}{C}}\; = \; 0.025693 V\; = \; 25.7mV
\)
If you look carefully, you will find that those two values you refer to have units and that the units that survive when you divide one by the other has units of voltage.
In fact, even without you indicating where that constant comes from or me not knowing a damn thing about solar cells, I can all but guarantee you what that constant is. It is the thermal voltage given by;
\(
V_T = \frac{kT}{q}
\)
where:
k is boltzmann's constant
T is the temperature
q is the magnitude of the electron charge
\(
k = 1.3806488 \times 10^{-23} \frac{m^2 kg}{s^2 K}
T = 298.15K \ (i.e., \ 25^o C)
q = 1.60217657 \times 10^{-19} C
\)
So, plugging in these values:
\(
V_T \; = \; \frac{1.3806488 \times 10^{-23} \. \frac{m^2 kg}{s^2 K} \. \cdot \. 298.15K }{1.60217657 \times 10^{-19} C}
\
V_T \; = \; 0.025693 \. \frac{m^2 kg K }{s^2 K C} \; = \; 0.025693 \. \frac{m^2 kg }{s^2 C}
\)
Now,
1 newton is one kilogram-meter per second-squared
1 joule is one newton-meter
1 volt is one joule per coulomb
\(
V_T \; = \; 0.025693 \. \frac{m^2 kg }{s^2 C} \.\cdot\. \frac{1N}{\frac{kg m}{s^2}} \.\cdot\. \frac{1J}{Nm} \.\cdot\. \frac{1V}{\frac{J}{C}}\; = \; 0.025693 V\; = \; 25.7mV
\)
The answer for Isc is 4, see if it works out for you.
We know everything except Isc.
Voc = 0.63
Io = 10^-10
We are trying to find a current. Not voltage, the measurement has no impact on the calculation.
Why is the V so important ?
Vt = kT/q is indeed what the constant that is used. Sadly my book stops at that formula.
We know everything except Isc.
Voc = 0.63
Io = 10^-10
We are trying to find a current. Not voltage, the measurement has no impact on the calculation.
Why is the V so important ?
Vt = kT/q is indeed what the constant that is used. Sadly my book stops at that formula.
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I should already be obvious why tracking units is important and useful because I've already pointed out that your failure to do so resulted in you missing an error in your result in post #24. But clearly you just went, "Oh well. So what?" and moved on. You would have happily used that result as your answer and/or in further computation and been blissfully unware that everything you did was flat wrong. And you wouldn't have cared a bit.
It is important for several reasons.
Consider an analogy. Your wife goes to the doctor and get a diagnosis that calls for a certain drug. The dosage of the drug is listed as 10mg/kg of body mass and he writes that down on her chart for his assistant to prepare the prescription. The assistant then looks at your chart where the nurse wrote down her weight and sees "100" written there. So she multiplies the two together and prepares a prescription containing 1000mg of the drug. Your wife dutifully takes her medication and a week later dies. The autopsy reveals that she overdosed on that drug and the investigation reveals that the "100" written on the chart was in "pounds" but the assistant assumed it was in "kilograms" because that is what the office scale reads out in. But the nurse had to use a backup scale because the usual scale was broke and the old scale read out in pounds.
The assistant says, "I'd never seen the woman before, so how was I supposed to know that she was rail-thin instead of morbidly obese? We have plenty of patients who are either. I just applied the formula to the data. I was trying to calculate a dosage, not a weight. The measurement has no impact on the calculation."
The nurse says, "I fail to see why putting 'lb' was so important."
Who is to blame? Who should be held accountable for the death of your wife? Are you going to be satisfied with the conclusion that it was just an unfortunate miscommunication? Even after you find out that it is the third time that something like this has happened in the last year?
Or are you going to contend that the nurse failing to note the proper units on the chart and the assistant failing to insist that the units be there prior to preparing the prescription both amount to extreme negligence and malpractice? Would part of your argument be that people in the medical profession has a particular responsibility to make sure that their calculations are error free since mistakes can cost lives?
Now consider that, in general, health professionals are limited to killing people one at a time whereas engineers kill people in job lots.
Tracking and checking units is perhaps the single most powerful error detection tool available to the engineer. Most (not all) mistakes will mess up the units and the error can be detected, tracked down, and corrected efficiently. But that only works if the units are properly tracked and checked.
Would you really like to be the defendent in a criminal negligence case where the prosecutor's closing argument goes something like, "Ladies and gentlemen of the jury, those three hundred people are dead for just one reason: the defedendent couldn't be bothered to track his units. As a result, he was completely oblivious to the fact that the point at which he multiplied by 2.54 to convert from inches to centimeters he actually should have multiplied by 2.54^2 because the number he was multiplying was the area of the failed connecting pin in square inches and not the diameter in inches. As a consequence, a pin that was intended to have a design safety factor of two was actually more than twenty percent smaller than required to handle its rated load."
What would you expect your lawyer to say in their closing remarks? That it is unreasonable to expect an engineer to utilize such a powerful error detecting tool?
It is important for several reasons.
Consider an analogy. Your wife goes to the doctor and get a diagnosis that calls for a certain drug. The dosage of the drug is listed as 10mg/kg of body mass and he writes that down on her chart for his assistant to prepare the prescription. The assistant then looks at your chart where the nurse wrote down her weight and sees "100" written there. So she multiplies the two together and prepares a prescription containing 1000mg of the drug. Your wife dutifully takes her medication and a week later dies. The autopsy reveals that she overdosed on that drug and the investigation reveals that the "100" written on the chart was in "pounds" but the assistant assumed it was in "kilograms" because that is what the office scale reads out in. But the nurse had to use a backup scale because the usual scale was broke and the old scale read out in pounds.
The assistant says, "I'd never seen the woman before, so how was I supposed to know that she was rail-thin instead of morbidly obese? We have plenty of patients who are either. I just applied the formula to the data. I was trying to calculate a dosage, not a weight. The measurement has no impact on the calculation."
The nurse says, "I fail to see why putting 'lb' was so important."
Who is to blame? Who should be held accountable for the death of your wife? Are you going to be satisfied with the conclusion that it was just an unfortunate miscommunication? Even after you find out that it is the third time that something like this has happened in the last year?
Or are you going to contend that the nurse failing to note the proper units on the chart and the assistant failing to insist that the units be there prior to preparing the prescription both amount to extreme negligence and malpractice? Would part of your argument be that people in the medical profession has a particular responsibility to make sure that their calculations are error free since mistakes can cost lives?
Now consider that, in general, health professionals are limited to killing people one at a time whereas engineers kill people in job lots.
Tracking and checking units is perhaps the single most powerful error detection tool available to the engineer. Most (not all) mistakes will mess up the units and the error can be detected, tracked down, and corrected efficiently. But that only works if the units are properly tracked and checked.
Would you really like to be the defendent in a criminal negligence case where the prosecutor's closing argument goes something like, "Ladies and gentlemen of the jury, those three hundred people are dead for just one reason: the defedendent couldn't be bothered to track his units. As a result, he was completely oblivious to the fact that the point at which he multiplied by 2.54 to convert from inches to centimeters he actually should have multiplied by 2.54^2 because the number he was multiplying was the area of the failed connecting pin in square inches and not the diameter in inches. As a consequence, a pin that was intended to have a design safety factor of two was actually more than twenty percent smaller than required to handle its rated load."
What would you expect your lawyer to say in their closing remarks? That it is unreasonable to expect an engineer to utilize such a powerful error detecting tool?
Oh, and it should be
Io = 10^-10 A
They way you have it written, you are saying that the magnitude is 10 and that the units are 1/(A^10).
What you need to do is think of units pretty much like any other factor and use the same rules of math on it as you would a variable.
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