- #1
gruba
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Homework Statement
[itex][/itex]
Given the circuit of sinusoidal current (attachment1) with given data:
[itex]\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.[/itex]
After the switch is closed, the increment of voltage 1-2 is given: [itex]\Delta \underline{U_{12}}=(4+j3)V[/itex].
Find the complex apparent power of [itex]\underline{I_{g2}}[/itex] after the switch is closed.
2. The attempt at a solution
Attempt:
By using current compensation theorem (note: I don't have to use this theorem, anything can be used to solve the problem) on the branch with the switch and impedance [itex]\underline{Z}[/itex], we get the following circuit (attachment2 - switch and impedance [itex]\underline{Z}[/itex] are replaced by [itex]\underline{I_c}[/itex]):
In the case when switch is open, compensation current [itex]\underline{I_c}[/itex] is equal to zero, and in the case when the switch is closed, it has some unknown value.
By using superposition theorem (note: I don't have to use this theorem, anything can be used to solve the problem), we can analyze the circuit from attachment2 by looking at [itex]\underline{I_c}[/itex] and other generators are removed. Now, we get the following circuit (attachment3):
From this circuit, we know potentials of nodes 1 and 2 since [itex]\Delta \underline{U_{12}}=\underline{V_1}-\underline{V_2}[/itex], so we can use potential of nodes method to find the complex value of [itex]\underline{I_{c}}[/itex] and the voltage [itex]\underline{U_{23}}[/itex]. By setting the potential [itex]\underline{V_2}[/itex] to zero, and after solving the system of two linear complex equations with [itex]\underline{V_3}[/itex] and [itex]\underline{I_{c}}[/itex] as unknowns, we get:
[tex]\underline{V_2}=0,\underline{V_1}=(4+j3)V,\underline{V_3}=(12.48+j53.4)V,\underline{I_c}=(-6.44-j41.57)mA,\underline{U_{23}}=(-12.48-j53.4)V[/tex]
Complex apparent power of [itex]\underline{I_{g2}}[/itex] (attachment1) after the switch is closed can be found by the following equation:
[tex]\underline{S_{I_{g2}}}^{(c)}=\underline{U_{35}}^{(c)}\cdot \underline{I_{g2}}^{*}[/tex]
where [itex]\underline{U_{35}}^{(c)}[/itex] is the voltage across [itex]\underline{I_{g2}}[/itex] when the switch is closed, and [itex]\underline{I_{g2}}^{*}[/itex] is the complex conjugate of [itex]\underline{I_{g2}}[/itex].
We can find the voltage [itex]\underline{U_{35}}^{(c)}[/itex] from the following equation:
[tex]\underline{U_{35}}^{(c)}=\underline{U_{35}}^{(o)}+\Delta \underline{U_{35}}[/tex]
where [itex]\underline{U_{35}}^{(o)}[/itex] is the voltage across [itex]\underline{I_{g2}}[/itex] when the switch is opened, and [itex]\Delta \underline{U_{35}}[/itex] is the voltage across [itex]\underline{I_{c}}[/itex] from the attachment3 and is equal to [itex]\Delta \underline{U_{35}}=(-12.48-j53.4)V[/itex] (look at attachment3).
In order to find the voltage [itex]\underline{U_{35}}^{(o)}[/itex], we look at the circuit from attachment1, where only the generator [itex]\underline{I_c}[/itex] is removed.
Question: Since the following parameters are not given: [itex]\underline{I_{g1}},\underline{Z_1},\underline{E_2},\underline{E_6},\underline{Z_2}[/itex], how to find the voltage [itex]\underline{U_{35}}^{(o)}[/itex]?
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