Three-phase circuits (XEO1)

Exemplary problems

  1. The circuit is supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Compute the phasor of voltage U0 and its waveform u0(t).
    2. Compute the phasor of current IR.
    3. Evaluate active and reactive power delivered to the circuit from the source UR (assuming that three-phase source consist of star-connected sources UR, US, UT).
    Take the phase of UR as 0 phase angle.






    result

  2. The circuit is supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Compute the phasor of current IR and its waveform iR(t).
    2. Compute the phasor of current IN.
    3. Evaluate total active and reactive power delivered to the circuit.
    Take the phase of UR as 0 phase angle.






    result

  3. The circuit is supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Compute the phasor of voltage U0 and its waveform u0(t).
    2. Compute the phasor of current IR.
    3. Evaluate active and reactive power delivered to the circuit by the source UR (assuming that three-phase source consist of star-connected sources UR, US, UT).
    Take the phase of UR as 0 phase angle.




    result

  4. The circuit is supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Compute the phasor of current IR and its waveform iR(t).
    2. Compute the phasor of current IN.
    3. Evaluate total active and reactive power delivered to the circuit.
    Take the phase of UR as 0 phase angle.




    result

  5. The circuit is supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Compute the phasor of current IR and its waveform iR(t).
    3. Evaluate total active, reactive and apparent power delivered to the circuit.
    Take the phase of URS as 0 phase angle.






    result

  6. The circuit is supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Compute the phasor of current IR and its waveform iR(t).
    3. Evaluate total active, reactive and apparent power delivered to the circuit.
    Take the phase of URS as 0 phase angle.






    result

  7. The circuits in the table below are supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Compute the phasors of currents IR, IS, IT and waveform of the current iR(t).
    Take the phase of URS as 0 phase angle.

    problem 1




    result     		problem 2




    result
    problem 3




    result     		problem 4




    result
    problem 5




    result     		problem 6




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  8. The circuits in the table below are supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Evaluate total active, reactive and apparent power delivered to the circuit.
    Take the phase of URS as 0 phase angle.

    problem 1




    result     		problem 2




    result
    problem 3




    result     		problem 4




    result
    problem 5




    result     		problem 6




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  9. The circuits in the table below are supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Compute the phasor of voltage UAB and its waveform uAB(t).
    Take the the phase of URS as 0 phase angle.

    problem 1




    result     		problem 2




    result
    problem 3




    result     		problem 4










    result
    problem 5




    result     		problem 6




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  10. The circuits in the table below are supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Evaluate total active power delivered to the circuit.
    Take the phase of URS as 0 phase angle.

    problem 1




    result     		problem 2




    result
    problem 3




    result     		problem 4










    result
    problem 5




    result     		problem 6




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  11. The circuits in the table below are supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Evaluate total reactive power delivered to the circuit.
    Take the phase of UR as 0 phase angle.

    problem 1




    result     		problem 2




    result
    problem 3




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  12. The circuits in the table below are supplied by a symmetrical voltage source with line voltages 3×400V (rms value) of frequency 50 Hz.
    1. Compute the phasor of voltage UAB and its waveform uAB(t).
    2. Evaluate total active power delivered to the circuit.
    Take the phase of UR as 0 phase angle.

    problem 1




    result     		problem 2




    result
    problem 3




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  13. Electric furnace which contains three equal resistances R in star connection is supplied by a symmetrical three-phase voltage sources 3×400V (line voltages, rms value) of frequency 50 Hz.
    1. Sketch the topographic phasor diagram for all circuit currents and voltages.
    2. Compute total load power of the furnace.
    3. How will the total load power change if the heating element connected to the phase T burns out? Sketch the corresponding phasor diagram.
    Take the phase of UR as 0 phase angle, (central node 0 of the star connected furnace resistors is not interconnected with neutral wire).


    		result

  14. Electric furnace which contains three equal resistances R in star connection is supplied by a symmetrical three-phase voltage sources 3×400V (line voltages, rms value) of frequency 50 Hz.
    1. Compute total load power of the furnace.
    2. How will the total load power change if connection of the heating elements (resistors) will be changed from star connection to delta connection?
    3. Sketch the topographic phasor diagram for all circuit currents and voltages both for star connection and delta connection.


    		result