Calculator gives math error

[henRJ]

I'm attempting to solve an electrical engineering problem. The question was to find the values of x_d, x_a, r_s and g_d in a p-n junction, as such I have completed the first three parts and am now struggling to find the value of the the last part due to my calculator stating a math error when imputing the values into the equation i'm using. The value of g_d is found using the equation g_{d =} I/ nkT and the only value i'm missing is the value for I which when I input i receive my error. With all the correct values inserted, i have put this equation into my calculator. I = 10^-8 * ( e^{(0.5/1.4*1.38x10^-23*300} -1). Any help would be greatly appreciated, thank you.   

[studiot]

I expect your error is that the calculator see the division by 10-23 as division by zero, since it cant hold such a small number.

Have you tried cancelling all the powers of 10 first.

 

[Sensei]

Physical calculators are reporting error when there is e.g. division by 0, or sqrt( negative number ).

 

You can try on-line calculators. Like e.g. Wolfram Alpha:

https://www.wolframalpha.com/

Your equation is missing parenthesis.

 

e can be interpreted as Euler's number https://en.wikipedia.org/wiki/E_(mathematical_constant)

but it also can be interpreted as exponent in IEEE floating-point standard.

 

[Janus]

If I plug the equation into my calculator as written, I get an answer of 0, as 0.5/1.4*1.38e-23*300 = 1.479e-21 and my when my calculator tries to raise e to this power, the answer requires more accuracy than the calculator can handle, so it rounds it down to 1 and then you are subtracting 1 from this.   However, I can get an answer when I use the calculator on my PC, as it carries out answers to many more decimal places.

If However, you meant to write 0.5/(1.4*1.38e23*300), then then answer to this is 8.63e19, and trying to raise e to this power will produce an overflow error as most calculators can't handle numbers that large  They generally have to be smaller than 10^100, and anything much larger than e²³⁰ will produce an overflow error

[Sensei]

2 minutes ago, Janus said:

  However, I can get an answer when I use the calculator on my PC, as it carries out answers to many more decimal places. 

Professional computer calculators (rather not what is built-in OS) can theoretically handle as big number as there is available memory (or virtual memory on disk). But it requires making dynamically expanding floating point implementation.

https://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

 

List of arbitrary-precision arithmetic software

https://en.wikipedia.org/wiki/List_of_arbitrary-precision_arithmetic_software