parallel resistors

[kinarfi]

RT=R1*R2/(R1+R2) So if I know RT and R2, What's the formula for R1?
Thank,
Kinarfi

 

[Jaguarjoe]

For two resistors:

First way

Product/Sum:

Rt = R1R2/R1 + R2)
Rt(R1 + R2) = R1R2
R1Rt + R2Rt = R1R2
R1Rt = R1R2 - R2Rt
R1Rt = R2(R1 - Rt)
R1Rt/(R1 - Rt) = R2

Second way:

Reciprocal of reciprocals:

Rt = 1/[(1/R1) + (1/R2)]
Rt(1/R1 + 1/R2) = 1
Rt/R1 + Rt/R2 = 1
Rt/R1 = 1 - Rt/R2
Rt = (1- Rt/R2)R1
Rt/(1-Rt/R2) = R1

My wife strenuously objected when I wanted to try doing it three ways

 

[MRCecil]

Hi Kinarfi

Use the general formula for resistors in parallel; Rt = 1/(1/R1+1/R2+1/R3+...). Then transpose terms in the equation in terms of the unknown resistance. Then plug and chug for the solution.

For instance in the simplest terms of one unknown and two known variables, Rt = 1/(1/R1+1/R2). If Rt and R2 are known then solving for the unknown yields the following:

Rt = 1/(1/R1+1/R2) so:
1/Rt = 1/R1+1/R2 so:
1/Rt-1/R2 = 1/R1 so:
R1 = 1/(1/Rt-1/R2)

I know you know this, but sometimes the grey matter just forces one to bang ones head against the wall flattening the head, then when it dawns one flattens the forehead also. LOL! Been there, done that.

 

[kinarfi]

Hi Kinarfi

Use the general formula for resistors in parallel; Rt = 1/(1/R1+1/R2+1/R3+...). Then transpose terms in the equation in terms of the unknown resistance. Then plug and chug for the solution.

For instance in the simplest terms of one unknown and two known variables, Rt = 1/(1/R1+1/R2). If Rt and R2 are known then solving for the unknown yields the following:

Rt = 1/(1/R1+1/R2) so:
1/Rt = 1/R1+1/R2 so:
1/Rt-1/R2 = 1/R1 so:
R1 = 1/(1/Rt-1/R2)

I know you know this, but sometimes the grey matter just forces one to bang ones head against the wall flattening the head, then when it dawns one flattens the forehead also. LOL! Been there, done that.

Not to mention it was late while doing my math and trying to make it much harder,
Thanks to both of you,
Kinarfi

 

[kinarfi]

For two resistors:

First way

Product/Sum:

Rt = R1R2/R1 + R2)
Rt(R1 + R2) = R1R2
R1Rt + R2Rt = R1R2
R1Rt = R1R2 - R2Rt
R1Rt = R2(R1 - Rt)
R1Rt/(R1 - Rt) = R2

Second way:

Reciprocal of reciprocals:

Rt = 1/[(1/R1) + (1/R2)]
Rt(1/R1 + 1/R2) = 1
Rt/R1 + Rt/R2 = 1
Rt/R1 = 1 - Rt/R2
Rt = (1- Rt/R2)R1
Rt/(1-Rt/R2) = R1

My wife strenuously objected when I wanted to try doing it three ways

Sometimes it's fun to do mental exercises, but as MRCecil says about flat for heads, I was running out of paper and walls.
Thank you both,
Kinarfi