Apparent power, impedance and alternating current.

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SUMMARY

The discussion focuses on calculating the total apparent power of two serially connected impedances with apparent powers S1 and S2, both equal to 200 VA. The first impedance has a phase angle of π/3, while the second has a phase angle of 0. The solution involves using the formula for complex power, S = S1 + S2, and requires determining the vector sum of the two powers in the complex plane to find the total apparent power.

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  • Understanding of complex power in AC circuits
  • Familiarity with impedance and phase angles
  • Knowledge of trigonometric functions related to power calculations
  • Ability to represent complex numbers in the polar form
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Homework Statement


Two serially connected impedances one with \Phi = π/3 and other with \Phi = 0. They have apparent power of S1=S2=200VA. Find total apparent power.



Homework Equations



S = sqrt(P^2 + Q^2)



The Attempt at a Solution



so cosPhi = P1/S1. So P1=cosπ/3*200=100W. For other one P2 = cos0*200=200W. How should I continue? Should I find Q too and derive somehow a equation to sum those powers?
 
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The complex power, S, delivered to the load is:
S = S1 + S2

and the angle between S1 and S2 is the same as the angle between the impedances.

You want to find the apparent power |S| = |S1 + S2|. If, say:
S1 = 200∠0
S2 = 200∠π/3

Try drawing them in the complex plane. The length of their sum is the answer you're after.
 

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