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of the impedances in the circuit shown in Figure P726 if: Vs1 = 170 0 V s2 = 170 V ( /2) V V = 377 rad/s Z1 = 07 ( /6) Z2 = 15 0105 Z3 = 03 + j 04
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b The voltage gain v2 /vg c The value to which the 16- load resistance should be changed so it will absorb maximum power from the given source
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Figure P729
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730 An ideal transformer is rated to deliver 400 kVA at
460 V to a customer as shown in Figure P730 a How much current can the transformer supply to the customer b If the customer s load is purely resistive (ie, if pf = 1), what is the maximum power that the customer can receive c If the customer s power factor is 08 (lagging), what is the maximum usable power the customer can receive d What is the maximum power if the pf is 07 (lagging) e If the customer requires 300 kW to operate, what is the minimum power factor with the given size transformer
Figure P726
727 If the voltage and current supplied to a circuit or
load by a source are: Vs = 170 0157 V Is = 13 028 A
Determine: a The power supplied by the source which is dissipated as heat or work in the circuit (load) b The power stored in reactive components in the circuit (load) c The power factor angle and power factor
Section 3: Transformers 728 A center-tap transformer has the schematic
representation shown in Figure P728 The primary-side voltage is stepped down to a secondary-side voltage, Vsec , by a ratio of n : 1 On the sec1 = Vsec2 = 1 Vsec secondary side, V 2 a If Vprim = 120 32 V and n = 9, nd Vsec , Vsec1 , and Vsec2 b What must n be if Vprim = 208 0175 V and we desire |Vsec2 | to be 87 V
n:1 + + ~ Vprim _ + ~ Vsec1 _ + ~ Vsec2 _ 100 ~ Vsec vS(t) + _ 25:1 + 25 vo(t) _ _ Z Customer s load
Ideal transformer
Customer
Figure P730
731 For the ideal transformer shown in Figure P731,
nd vo (t) if vS (t) is 294 cos 377t
Figure P731 Figure P728
729 For the circuit shown in Figure P729, nd:
a The total resistance seen by the voltage source
732 If the transformer shown in Figure P732 is ideal,
nd the turns ratio N = 1/n that will provide maximum power transfer to the load
7
AC Power
RS vS(t) + _
n:1 + RL vo(t) _
leaving the secondary side open The current into the primary side is measured, as is the power dissipated
A ~ Vs + _
RS = 1800
RL = 8
Figure P732
733 Assume the 8- resistor is the load in the circuit
shown in Figure P733 Assume a turns ratio of 1 : n What value of n will result in the load resistor absorbing maximum power from the source
A + ~ Vs _ V W
3 1:n rw vg + _ 4 8 rc Lw
+ ~ Ip Lc ~ IS Vsecondary
Figure P733 Figure P735
734 If we knew that the transformer shown in Figure
P734 was to deliver 50 A at 110 V rms with a certain resistive load, what rms phasor voltage source, VS , would provide this voltage and current The short-circuit test, shown in Figure P735(b), is performed by increasing the primary voltage until rated current is going into the transformer while the secondary side is short-circuited The current into the transformer, the applied voltage, and the power dissipated are measured The equivalent circuit of a transformer is shown in Figure P735(c), where rw and Lw represent the winding resistance and inductance, respectively, and rc and Lc represent the losses in the core of the transformer and the inductance of the core The ideal transformer is also included in the model With the open-circuit test, we may assume that IP = IS = 0 Then all of the current that is measured is directed through the parallel combination of rc and Lc We also assume that |rc ||j Lc | is much greater than rw + j Lw Using these assumptions and the open-circuit test data, we can nd the resistance rc and the inductance Lc In the short-circuit test, we assume that Vsecondary is zero, so that the voltage on the primary side of the ideal transformer is also zero, causing no current ow through the rc Lc parallel combination Using this
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