Hi.
I need to show the following equivalence
\(\displaystyle Z\, =\, i\omega\, (L_1\, -\, M)\, +\, \dfrac{i\omega M\, \left(i\omega\, (L_2\, -\, M)\, +\, X\right)}{i\omega M\, +\, i\omega\, (L_2\, -\, M)\, +\, X}\)
. . . . .\(\displaystyle =\, ...\, \dfrac{i\omega L_1\, \left(i\omega\, (L_2 n^2\, -\, L_1)\, +\, Xn^2\right)}{i\omega L_1\, +\, i\omega\, \left(L_2 n^2\, -\, L_1\right)\, +\, Xn^2}\)
\(\displaystyle \mbox{with }\, n\, =\, \dfrac{L_1}{M}\, \mbox{ and }\, i\, \mbox{ the imaginary unit.}\)
Here is what I tried:
- bring everything to one fraction
- I see that the denominator can be simplified by dropping the iwM term, however I am not sure that it's helpful
- different approaches to combine terms
I am not getting there. Thanks for help.
Best,
Olli
I need to show the following equivalence
\(\displaystyle Z\, =\, i\omega\, (L_1\, -\, M)\, +\, \dfrac{i\omega M\, \left(i\omega\, (L_2\, -\, M)\, +\, X\right)}{i\omega M\, +\, i\omega\, (L_2\, -\, M)\, +\, X}\)
. . . . .\(\displaystyle =\, ...\, \dfrac{i\omega L_1\, \left(i\omega\, (L_2 n^2\, -\, L_1)\, +\, Xn^2\right)}{i\omega L_1\, +\, i\omega\, \left(L_2 n^2\, -\, L_1\right)\, +\, Xn^2}\)
\(\displaystyle \mbox{with }\, n\, =\, \dfrac{L_1}{M}\, \mbox{ and }\, i\, \mbox{ the imaginary unit.}\)
Here is what I tried:
- bring everything to one fraction
- I see that the denominator can be simplified by dropping the iwM term, however I am not sure that it's helpful
- different approaches to combine terms
I am not getting there. Thanks for help.
Best,
Olli
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