SECOND ACTIVITY
ELT 2570 ELECTRICAL CIRCUITS
PRACTICE 2 THREE-PHASE NETWORK
1. Mid-point of the secondaries of a bank of 4000/440 V Transformers are used to provided a lower voltaje,
as shown in the diagram. Find (a) the voltaje of the bus-bars a b c, and (b) the current in the transformer
secondaries when currents of 100 A at unity power factor are taken from each of the two sets of low-voltaje
bus-bars, a b c and A B C.
2. A 100 HP induction motor has power factor 0.9 and efficiency 0.85 at full load, power factor 0.7 and
efficiency 0.8 at half load. At no load the current is 30% of the full-load currente and power factor 0.14.
Capacitors are supplied a make the line power factor 0.85 at half load. With these capacitors in circuit, find
the line power factor at (a) full load, (b) no load.
3. Two 500-ohms resistances and a condenser are jorned in star to a 400-V, 3-phase, 50 c/s supply. State the
phase rotation, and find the capacitance and equivalent series resistance of the condenser if el voltajes across
the resistances connected to the phase R and phase T are 400 V and 300 V respectively.
4. Three identical coil, symmetrically arranged in space, are star-connected to a 400-V, 50-c/s, 3-phase supply.
Each coil has resistance and inductance of 100 Ω and 0.8 H respectively, while the mutual inductance
between cada pair de coils es de 0.3 H. Calculate the current taken by each coil and its power factor.
5. A lagging load is supplied by a transmission line of resistance r= 2 Ω per phase. The tranmission loss is to
be reduced by installing a synchronous condenser, the armature resistance of which is R= 4 Ωper phase.
Show that for the greatest overall saving in line and condenser armature, the leading reactive current of the
condenser is Ic = rIr/(R + r), where Ir is the reactive component of the load current. If the 3-phase load is
1000 KW at power factor 0.707, 3000 V, and R = 2r, find the line power factor, the KVAR rating of the
syncronous condenser and ratio (reduced line-loss/original line-loss).
6. Three 1-phase Transformers connected in mesh supply 1000 A per line to a 3-phase, 3-wire system. (a)
What is the current in each transformer? One unit develops a fault and is removed: (b) by how mjuch is
the capacity of the set reduced for the same temperatura-rise? (c) Find the current in each of the remaining
transformer if the line current corresponds to the rating in (b). Draw the vector diagram.
7. A 12.5 HP, 400-V. 3-phase motor with power factor 0.8 and efficiency 0.85 is supplied from a line having
una resistance of 0.15 𝛺 per conductor. Lighting loads of 20, 15 and 5 A, are taken from phases R, S, and
T respectively. Calculate the voltaje of phase T to neutral at the sending end. The neutral has a resitance of
0.4 Ω
8. A 3-phase, 4-wire system has 420 V between lines at the sending end. The loads are: phase R, 40 A at power
factor 0.8 lagging, phase S, 30 A at unity power factor, phase T, 20 A at power factor 0.87 leading. The
resistance of each conductor is 0.2 Ω, and of the neutral 0.4 Ω. Find the load voltajes VRN and VBR.
9. The upper and lower current coil of a two-element wattmeter are connected in the R and T phasee of a
symmetrical 3-phase system suppling a 400-V star-conected balanced load. When the upper and lower
voltaje coil are connected between the S and R and the S and T phases, the wattmeter reads 4000 W, when
they are connected between the T phase and star point and the star point and R phase respectively the
wattmeter reads 900 W. What is the load current?
10. A Factory is supplied froma 3-phase, 4-wire, 400 V, simmetrical system. The resistance of each line is 0.4
Ωand of the neutral 0.6 Ω. The power input to the main is as follows: 10 KVA at a laggin poer factor ofd
0.7 to phase R, 10 KVA at a leading power factor of 0.7 to phase S, and 15 KVA at unity power factor to
phase T. Calculate the current in the neutral wire and the voltaje between line R and the neutral at the
Factory. Phase secuence RST.
11. A 3-phase, overhead line has resistance and reactance of 6 and 20 Ωrepetively per phase. The sending-end
voltaje is 66 KV while the receiving-end voltaje is maintained at 66 KV by a synchronous phase-modifier.
Determine the KVAR od the modifier when the load at the receiving-end is 75 MW at power factor 0.8
lagging, also the maximun load that can be transmitted.
12. A 3-phase, overhead line has resistance and ractance per phase of 5 and 20 Ω respectively. The load at the
receiving end is 25 000 KW, 33 KV, power factor 0.8 lagging. Find the voltaje at the sending end. If a
synchronous phase modifier is inserted at the receiving end and the voltaje at both ends of the line
maintained at 33 KV, find the KVAR of the modifier when the load is 25 000 KW at power factor 0.8
lagging. Find also the maximum load that can be transmitted.