Calculations and substitutions to derive a formula

kalemaxon89

Joined Oct 12, 2022
262
I am not able to derive this formula:

starting from this data:
I re-write the first formula better because it reads poorly: Irr = (dir/dt)*t4

They are probably simple mathematical calculations where you add subtract the same sum until you find the result but I am finding difficulty.

WBahn

Joined Mar 31, 2012
30,252
I'm having a hard time deciphering your writing, but if there really are t4's and t5's in there, then I think I've got it.

It's just a couple lines of algebra.

Start with what you want -- t_rr. You have two options: Start with the second equation, which already has t_rr on the left, or solve the third equation for t_rr. Either will work, but the first seems more direct.

Write t5 in terms of S and t4.

Then write t4 in terms of what is in the first equation.

Then get rid of I_rr based on the third equation.

Now solve this for t_rr.

kalemaxon89

Joined Oct 12, 2022
262
I'm having a hard time deciphering your writing, but if there really are t4's and t5's in there, then I think I've got it.

It's just a couple lines of algebra.

Start with what you want -- t_rr. You have two options: Start with the second equation, which already has t_rr on the left, or solve the third equation for t_rr. Either will work, but the first seems more direct.

Write t5 in terms of S and t4.

Then write t4 in terms of what is in the first equation.

Then get rid of I_rr based on the third equation.

Now solve this for t_rr.
Thank you! I followed your steps and found the final formula.

Can you help me find this formula as well:
Irr = sqrt{ 2*Qrr*dir/dt / (S+1) }

I'm trying to derive it directly from trr =sqrt(..) that we just found, is that the easiest approach?

WBahn

Joined Mar 31, 2012
30,252
Probably is the easiest. Just solve the third equation for t_rr and set it equal to the earlier result and then solve for I_rr.