Question 1: Fig. 1 shows the voltage and current waveforms for a circuit supplied from a voltage source:

a. Draw the phasor diagram representing the voltage and current waveforms, showing the phase relationship between the voltage and current phasors.

b. Determine the real power associated with the waveforms.

c. Determine the reactive power associated with the waveforms.

Question 2: A balanced delta connected load of 5 + j48 Ohms per phase is connected at the end of a three-phase line, as shown in Fig. 2.  The line impedance is 1 + j3 Ohms per phase.  The line is supplied from a three-phase source with a line voltage of 207.85 V rms. Taking the voltage across phase a and neutral as the reference, find:  

a) Current in phase a

b) Total complex power supplied from the source

c) Magnitude of the line voltage at the load terminals

Question 3: Fig. 3 shows the cross section of a synchronous generator, where a, a', b, b', c, c', f, f' represent the stator phase a, b and c, and rotor field windings respectively.  With the rotor in the position shown:

i. State whether the absolute value of flux linkage between the stator phase a winding and the field winding will be at a maximum, or a minimum for the rotor position shown.

ii. State whether the absolute value of the voltage induced in the stator phase a winding will be at a maximum, or a minimum for the rotor position shown.

iii. Justify your answer to part ii of this question.

Question 4: The waveforms v(t) and i(t) in (1) represent voltage and current waveforms associated with a circuit.  

v(t) = 100 sin(2π400t - 0.262 rad.)   V

i(t) = 2 sin(2π400t + 0.524 rad.)   A

i. State the power factor associated with the circuit with waveforms v(t) and i(t).

ii. Draw the power triangle resulting from the equations in (1)

Question 5: The one-line diagram of a three-phase power system is shown in Fig. 4.  Impedances are marked in per unit on a 100 MVA, 220 kV base.  The load at bus 2 is S₂ = 15 MW - j 33 MVAR, and at bus 3 is S3 = 70 MW + j10 MVAR.  It is required to hold the voltage at bus 3 at 220 ∠ 0^o kV.  Working in per unit, determine the voltages at buses 2 and 1.

Question 6: For the balanced three-phase circuit shown in Fig. 5, the line voltage of the supply, V_S, is 208 V, the absolute  value  of  the  load  impedance,  Z_L,  is  10 Ω  and  the  power  factor  is  0.8  lagging.    Find the capacitive reactance needed, in parallel with the load in each phase, to make the power factor 0.90 lagging.