Technique to solve this equation of 2 unkownsI 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?

Question

Technique to solve this equation of 2 unkownsI 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?

Ronald Hickman · Accepted Answer

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 · Accepted Answer

Alternate solutionDividing 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.