Stuck on a formula... Any Help would be Awesome!!!

[AnthonyR23]

Hi, I have a question about a new formula that just came up in a chapter I am studying... it is to determine the time elapsed between a switch closing and the control relay energizing. It is found using the following equation:

t = R1 C1 ln 1/1-η

where t = elapsed time, in seconds
R1 = resistance, in ohms
C1 = capacitance, in farads.
η = intrinsic standoff ratio of UJT

so I have a question and answer: with diagram but you guys can probably help without having to see the diagram:

I am trying to find t

20 k ohms for R1
1000 µF for capacitance
0.75 for η

The answer is t = 27.7 seconds

I don't know what ln is in the equation is so that is probably is why I can't figure it out, and can't find that anywhere in the chapter.

So if anyone can explain the ln in this equation that would be awesome!!!! Thanks guys!!

t = R1 C1 ln 1/1-η

 

[Papabravo]

`ln' stands for natuaral logarithms. `log' is generally used to denote common logarithms, also known as logarithms to the base 10. Natural logarithms use the transcendental number `e' as the base. The value of e to 10 significant figures is

e = 2.718281828...

Don't be deceived, the sequence 1828 does not repeat, it is just one of those strange coincidences.
BTW ln(1 / 1 - n) for n = .75 is ln (4) ≈ 1.386

 

[Willbe]

t = R1 C1 ln 1/1-η
where t = elapsed time, in seconds
R1 = resistance, in ohms
C1 = capacitance, in farads.
η = intrinsic standoff ratio of UJT
20 k ohms for R1
1000 µF for capacitance
0.75 for η
The answer is t = 27.7 seconds
t = R1 C1 ln 1/1-η

Haven't done unijunctions for a while, but

20k x 1000µF is 20 sec. for this RC circuit to reach 63.2% of final value and
Vo = V[1-e^(-t/rc)]
if Vo= 0.75V then 0.75 = 1-e()
so e() = 0.25.
ln 0.25 = -t/rc
-1.386 = -t/20
t = 27.7

 

[AnthonyR23]

thanks guys!! Much appreciated!! I figured it out, found the ln function on my calc., haven't used that before!!

 

[Papabravo]

Booyah! I just love it when that happens.