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 June 18th, 2017, 08:58 AM #1 Newbie   Joined: Jun 2017 From: N/A Posts: 4 Thanks: 0 obtaining a solution using phasors I feel good about the basics transformation of complex numbers to polar and ec and vice versa. I have hit a wall in trying to solve the equation by hand. I feel like it should just be adding the fractions and if the complex values are to be multiplied then change to polar but must be wrong or my calculations are wrong 1/(10-j40)+1/120-1/12(1-j4) the ans is 91.2 -j38.4 Thank you for any help
 June 18th, 2017, 10:02 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314 I don't get anything like your answer so please repost the expression using parentheses to make it's interpretation unique. Thanks from topsquark
June 19th, 2017, 11:50 AM   #3
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Joined: Jun 2017
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How we did in class was different from the text but maybe this will help, and the equation was
It=Vt[(1/(10-j40))+(1/120)-(1/12(1-j4))]
the Zth=Vt/It = 91.2 -j38.4

Sorry I messed that question up.
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 June 19th, 2017, 06:32 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,629 Thanks: 2077 1/(10 - 40j) + 1/120 - 1/(12(1 - 4j)) = (10 + 40j)/1700 + 1/120 - (1 + 4j)/204 = 1/170 + 1/120 - 1/204 + (4/170 - 1/51)j = (12 + 17 - 10)/2040 + ((12 - 10)/510)j = 19/2040 + 1/255j = 1/2040(19 + 8j) Hence 1/(1/(10 - 40j) + 1/120 - 1/(12(1 - 4j))) = 2040/(19 + 8j) = 2040(19 - 8j)/425 = 48/10(19 - 8j) = 91.2 - 38.4j Thanks from bdewbac
 June 19th, 2017, 06:46 PM #5 Senior Member     Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314 ok so you want the reciprocal of the sum of those 3 terms. $Z^{-1}=\dfrac {1}{10}\dfrac{1}{1-j4} + \dfrac{1}{120} -\dfrac{1}{12(1-j4)}$ $Z^{-1} = \dfrac{1}{10}\dfrac{1+j4}{17}+\dfrac{1}{120}-\dfrac{1+j4}{12\cdot 17}$ $Z^{-1} = \left(\dfrac{1}{170}+\dfrac{1}{120}-\dfrac{1}{204}\right) + j \left(\dfrac{4}{170} - \dfrac{1}{51}\right)$ $Z^{-1} = \dfrac{19}{2040} + j\dfrac{1}{255}$ $Z^{-1} = \dfrac{1}{24 \sqrt{17}}e^{\arctan\left(\frac{8}{19}\right)}$ $Z = 24\sqrt{17} e^{-\arctan\left(\frac{8}{19}\right)}$ $Z = \dfrac{456}{5}-j\dfrac{192}{5}$ $Z \approx 91.2\, -j38.4$ Thanks from bdewbac

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