- #1
ChasW.
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Homework Statement
I am following along in a book which provides the equation below.
I have also included the book's stated solution.
Homework Equations
The Equation:
[tex]{R_T+jX_T \over 1+jB_C(R_T+jX_T)}+jX_L = R_A-jX_A[/tex]
The Book's Solution:
[tex]R_T=R_A(1-B_CX_T)+(X_A+X_L)B_CR_T[/tex]
The Attempt at a Solution
When attempting to solve for RT, so far I have:
[tex]{R_T+jX_T \over 1+jB_CR_T-B_CX_T} = R_A-jX_A-jX_L[/tex]
[tex]R_T=(R_A-jX_A-jX_L)(1+jB_CR_T-B_CX_T)-jX_T[/tex]
[tex]R_T=
R_A+R_AjB_CR_T-R_AB_CX_T
-jX_A+X_AB_CR_T+jX_AB_CX_T
-jX_L+X_LB_CR_T+jX_LB_CX_T -jX_T[/tex]
I then begin to simplify:
[tex]R_T=
R_A(1+jB_CR_T-B_CX_T)
+X_A(-j+B_CR_T+jB_CX_T)
+X_L(-j+B_CR_T+jB_CX_T) -jX_T[/tex]
[tex]R_T=
R_A(1+jB_CR_T-B_CX_T)
+(X_A+X_L)(-j+B_CR_T+jB_CX_T) -jX_T[/tex]
I seem to be having some issue identifying further simplification.
Any assistance would be appreciated.
Charles