Technique to solve this equation of 2 unkownsI was solving a problem of single phase...

Desirae Washington

Desirae Washington

Answered

2022-07-09

Technique to solve this equation of 2 unkowns
I was solving a problem of single phase eletrical circuits where I had to find the inductor L and resistance R. I managed to get two equations containing the two unknowns.
R R 2 + ( w L ) 2 = c 1
and
w L R 2 + ( w L ) 2 = c 2
where w , c 1  and  c 2 are known.How do I solve this?

Answer & Explanation

Ronald Hickman

Ronald Hickman

Expert

2022-07-10Added 18 answers

Squaring both equations and adding them you get
R 2 ( R 2 + ( w L ) 2 ) 2 + ( w L ) 2 ( R 2 + ( w L ) 2 ) 2 = c 1 2 + c 2 2
or
1 R 2 + ( w L ) 2 = c 1 2 + c 2 2
This yields:
R 2 + ( w L ) 2 = 1 c 1 2 + c 2 2
Now replace the denominators in both equations.
Holetaug

Holetaug

Expert

2022-07-11Added 8 answers

Alternate solution
Dividing the two equations you get
w L R = c 2 c 1
Thus
w L = c 2 R c 1 .
Replacing in either equation you get an equation in R.

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