Sinusoidal steady state

Exemplary problems

    Circuits according to the table below are supplied by the sinusoidal voltage source u(t ) =  Um sin(j wt + j) or U = U ejj. The circuits are in the steady state.
  1. a) Draw the topographic phasor diagram of all voltages and currents.
    b) Find the voltage ux(t).
  2. Compute active power, reactive power and apparent power delivered to the circuit by the voltage source.

    problem 1


    A

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    B

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    		problem 2


    A

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    B

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    problem 3


    A

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    B

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    		problem 4



    A

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    B

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    Circuits according to the table below are supplied by the sinusoidal current source i(t ) =  Im sin(j wt + j) or I = I ejj. The circuits are in the steady state.

  3. a) Draw the topographic phasor diagram of all voltages and currents.
    b) Find the current ix(t).
  4. Compute active power, reactive power and apparent power delivered to the circuit by the current source.

    problem 1


    C

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    D

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    		problem 2


    C

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    D

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  5. Circuits according to the table below are supplied by the sinusoidal voltage source U = U ejj . The circuits are in the steady state.
    1. Draw the topographic phasor diagram of all voltages and currents.
    2. Find the phasor of the voltage Ux.


    problem 1




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    		problem 2




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  6. Circuits according to the table below are supplied by the sinusoidal voltage source U1 = U 1 ejj1. The circuits are in the steady state.
    1. Find the general expression of the transfer function P = U2 / U1.
    2. Find angular frequency wx  when the phase shift of the transfer function P = U2 / U1 is equal to the phase j for given values of the circuit elements.
    3. Compute the magnitude of the transfer function P , if the frequency is wx.


    problem 1




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    		problem 2




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    problem 3




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    		problem 4




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    problem 5




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    		problem 6




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  7. Bridge circuits according to the table below are supplied by the sinusoidal voltage source. U1 = U 1 ejj1. The circuits are in the steady state.
    1. Draw the topographic phasor diagram of all voltages and currents.
    2. Find the general expression of the transfer function of the circuit P = U2 / U1.
    3. Find bridge balance condition (the relation among parameters R, L, C and w  when the output voltage U2 is zero).


    problem 1





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    		problem 2


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    problem 3


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  8. To the distribution net with voltage  Uf (rms value) and with frequency f are connected in parallel 3 single phase consumers of an inductance character and power factor capacitor of the capacity C = 15 mF. The active powers of the particular consumers are P1, P2, P3 and power factors are cos j1, cos j2, cos j3.
    1. Find the total active power, reactive power and apparent power delivered from the network.
    2. Find the total power factor and value of the current loaded from the network.



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  9. The resistive heating element with the nominal parameters Ut, Pt should be connected to the distribution net with voltage  Uf  (rms value) and with frequency f together with a serial choke coil with inductance L and negligible resistance R .
    Compute the inductance L  of the coil to obtain nominal voltage across the heating element. Find the power factor of the circuit.



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  10. The lighting bulb of an resistive character should be connected to the distribution net with voltage Uf (rms value) and with frequency f together with a serial capacitor with a capacity C. Nominal parameters of the lighting bulb are Ut, Pt .
    Compute the capacitance C of this capactitor to obtain nominal voltage across the lighting bulb. Find the power factor of the circuit.



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  11. The circuits according to the table below contains sinusoidal voltage source U of the rms value Uf and frequency f (or sinusoidal current source I of rms value If and frequency f). The circuits are loaded by the load impedance Zs.
    1. Find the load impedance to reach the power matching condition (to reach the maximum active power in the load).
    2. Find the power delivered to the load.


    problem 1




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    		problem 2




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    problem 3




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    		problem 4







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  12. The circuits according to the table below contains sinusoidal voltage source U and sinusoidal current source I. Both the voltage source and current source have the same frequency f. Draw the Thévenin's equivalent circuit between output terminals A and B and find its parameters. Find phasor of the voltage across load impedance Zs between output terminals A and B if the load is power matched to the source.

    problem 1




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    		problem 2




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    problem 3




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    		problem 4




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  13. The circuits according to the table below contains sinusoidal voltage source U and sinusoidal current source I. Both the voltage source and current source have the same frequency f. Draw the Norton's equivalent circuit between output terminals A and B and find its parameters. Find phasor of the voltage across load impedance Zs between output terminals A and B if the load is power matched to the source.

    problem 1




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    		problem 2




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    problem 3




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    		problem 4




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