Unknown reactance how to solve?

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SUMMARY

The discussion centers on solving for an unknown reactance in a circuit consisting of two parallel impedances, Z1 = 4 - j8 and Z2 = 1 + j10, with a total power factor of 0.707. The user has calculated the individual impedances, Z1 and Z2, as 8.94 at an angle of -63.43 degrees and 10.05 at an angle of 84.29 degrees, respectively. The combined impedance of Z1 and Z2 was determined to be 16.68 at an angle of -0.94 degrees, or equivalently, 16.68 - j0.27. The next step involves using the correct formula to find the total impedance and subsequently the unknown reactance.

PREREQUISITES
  • Understanding of complex impedance in AC circuits
  • Familiarity with power factor calculations
  • Knowledge of series and parallel impedance combinations
  • Proficiency in using phasor notation for electrical engineering
NEXT STEPS
  • Learn how to calculate total impedance in parallel circuits
  • Study the relationship between power factor and impedance
  • Explore the use of phasor diagrams in AC circuit analysis
  • Review the concept of reactance and its role in AC circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in AC circuit analysis will benefit from this discussion, particularly those working with complex impedance and power factor calculations.

herbgriffin
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unknown reactance ...how to solve?

Homework Statement


a circuit with the unknown X (pure reactance) in sereis with a two parallel impedance.Z1= 4-j8 ; Z2= 1+j10 ...and total power factor is 0.707.. find the unknown reactance.


Homework Equations


p.f. = Rtotal/Ztotal...


The Attempt at a Solution


Z1= 8.94 angle of -63.43 degrees
Z2=10.05 angle of 84.29 degrees
i simplified the parallel Z1and Z2
Z12= 16.68 angle of -0.94 degrees..
or Z12= 16.68-j0.27
and i don't know how to continue...
 
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hi herbgriffin! :smile:

(have a degree: ° and try using the X2 icon just above the Reply box :wink:)

start by finding the combined impedance of the two parallel impedances …

what formula should you be using for that? :smile: