Circuit analysis -- Find the complex apparent power of I(g2)

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SUMMARY

The discussion focuses on calculating the complex apparent power of the current source I(g2) in a circuit with given impedances and voltage increments. The impedances are Z3 = 200(3-j4)Ω, Z4 = 100(3+j20)Ω, Z5 = 100(3+j4)Ω, and Z = 100(2+j5)Ω, with I(g2) specified as -10(2-j)mA. The voltage increment ΔU12 is given as (4+j3)V. The solution involves applying the superposition theorem to analyze the circuit and find the necessary voltages to compute the total complex apparent power using the formula S(I(g2)) = I(g2)* (U34' + U34'').

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  • Understanding of complex impedance and phasor representation.
  • Familiarity with the superposition theorem in circuit analysis.
  • Knowledge of calculating complex apparent power in AC circuits.
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  • Study the application of the superposition theorem in AC circuit analysis.
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Homework Statement


Given the circuit of sinusoidal current (attachment 1) with given data:
\underline{Z_3}=200(3-j4)\Omega, \underline{Z_4}=100(3+j20)\Omega, \underline{Z_5}=100(3+j4)\Omega, \underline{Z}=100(2+j5)\Omega, \underline{I_{g2}}=-10(2-j)mA
After the switch is closed, the increment of voltage 1-2 is given: \Delta U_{12}=(4+j3)V.
Find the complex apparent power of \underline{I_{g2}} after the switch is closed.
im_x.PNG
2. The attempt at a solution
By using superposition theorem, we can separate the given circuit into two circuits (attachment 2 and 3):
im_x1.PNG
im_x4.PNG

From the second circuit (attachment 2), we can find the voltage \underline{U_{34}'}.

In the next circuit (attachment 3) \underline{I_{g1}},\underline{Z_1},\underline{Z_2},\underline{E_2},\underline{E_6} are not given.
Question: How to find the voltage U_{34}=U_{34}'' in this case?

Total complex apparent power is given by \underline{S_{I_{g2}}}=\underline{{I_{g2}}^{*}}(\underline{U_{34}'}+\underline{U_{34}''}).
 
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