EE11001 Tutorial 5 (Single Phase Transformers)
1. A 1-phase, 50 Hz, core type transformer has square cores of 20 cm side. The permissible
maximum density is 1 Wb/m2. Calculate the number of turns per limb on the high and
low voltage sides for a 3000/ 220 V ratio.
[Ans. 338, 25]
2. A single phase transformer has the following data; Peak Flux Density in core: 1.4 T, Net
core Area: 0.012 m2, Current Density in Conductors: 2.5 MA/m2, Conductor Diameter: 2
mm, Primary Voltage: 230 V, 50 Hz. Calculate the kVA rating of the transformer and
number of turns on the primary winding.
[Ans. 1.80642 kVA and 62 turns]
3. A 1-phase transformer has 400 primary and 1000 secondary turns. The net cross-sectional
area of the core is 60 cm2. The primary winding is connected to a 50 Hz supply of 500 V
(RMS). The mean length of the flux path in core is 0.7 m. Determine the flux density of
the core and the magnetizing current. The B-H curve of the material used in
manufacturing the core is given in Table.
[Ans. 0.94 Wb/m2, 1.225 A]
B (Wb/m2) 0.1
0.2 0.3
0.4 0.5
0.6 0.8 0.9 1.0 1.1 1.2
1.3
H (AT/m)
62.5 125 187.5 250 312.5 375 500 625 750 900 1200 1500
4. Determine the input current I1 if RAB=50 Ω and ZAC=30+j40 Ω. No. of turns between DE
is 100, between AB is 150 and BC is 50.
[Ans. 11.29∠-34.530 A]
5. A 240 kVA, 480/4800 V step-up transformer has the following parameters: RHV=2.5 Ω,
XHV=5.75 Ω, RLV=25 mΩ, XLV=57.5 mΩ. The transformer is operating at 50% of rated
load. If the load is purely resistive, determine (a) the applied voltage on primary side (b)
the secondary current (c) the primary current.
[Ans. (a) 493.34 V, (b) 25 A, (c) 250 A]
Fig. Circuit Diagram Corresponding to Problem 4.
6. The parameters of a 12 kVA, 120/480 V, 60 Hz, two winding transformer are RHV=0.6 Ω,
XHV=1.2 Ω, RLV=0.1 Ω, XLV=0.3 Ω, RcHV=3.2 kΩ, and XmHV=1.2 kΩ. The transformer is
operating at 80% of its full load at rated terminal voltage and 0.866 power factor lag.
Determine the input current, copper loss and core loss if primary voltage is 120 V.
[Ans. 81.32∠-30.760 A, 901.3 W, 72 W]
7. A 50 Hz, 1-phase transformer is having a turns ratio of 6. The resistances are 0.9 Ω and
0.03 Ω and the reactances are 5 Ω and 0.13 Ω for high voltage and low-voltage windings
respectively. Find (a) the voltage to be applied on the high-voltage side to obtain a full-
load short-circuit current of 200 A on the low-voltage winding (b) the power factor on
short-circuit.
[Ans. (a) 330 V, (b) 0.2]
8. A 20 kVA, 2500/250 V, 50 Hz, 1-phase transformer gave the following results :
OC Test: 250 V, 1.4 A, 105 W
SC Test: 104 V, 8A, 320 W
Compute the parameters of the approximate equivalent circuit referred to HV and LV
sides.
9. a) A voltage v=200 sin (314t) is applied to the Transformer in no load test. The resulting
current is i= 3 sin(314t-60). Determine the core loss and rms value of the no-load current.
b) Transformer has the following data:
Test -1: 100% volt, 6% current, pf=.2
Test-2: 8% volt, 100% current, pf=.3
Identify the tests. Obtain the parameters of the transformer in p.u.
[Ans. (a) 150 W, 2.12 A, (b) Winding Resistance and Leakage Reactance: 0.024 p.u. and
0.0763 p.u., Magnetizing Reactance: 17.01 p.u., Core Loss Resistance: 83.33 p.u.]
10. A 100 kVA, 6600/330 V, 50 Hz, Single-Phase Transformer took 10 A and 436 W at 100
V in a short circuit test, the figures referring to High Voltage Side. Calculate the voltage
to be applied to the high-voltage side on full load at power factor 0.8 lagging when the
secondary terminal voltage is 330 V.
[Ans. 6734 V]
11. A 4 kVA, 200/400 V, 50 Hz, single-phase transformer gave the following test figures:
No Load: LV Side: 200 V, 0.7 A, 60 W
SC Test: HV Side: 9V, 6A, 21.6 W
Calculate
a) The magnetizing current and the iron loss component of current
b) The secondary terminal voltage on full load at power factors of unity, 0.8 lag and
0.8 lead.
[Ans. (a) 0.63 A, 0.3 A, (b) 394 V, 387 V, 403.4 V]
12. The equivalent circuit parameters of a single-phase transformer is given by:
Core Loss Resistance= 400 Ω
Magnetizing Reactance=231 Ω
Winding Resistance= 0.16 Ω
Winding Leakage Reactance= 0.7 Ω
Load Specification: 𝑍𝑍𝐿𝐿 = 5.96 + 𝑗𝑗 4.44 Ω
If the input voltage is 200 V on the primary side, determine the efficiency. All the
parameters are referred to Primary Side.
[Ans. 94.9 %]
13. Find the efficiency of a 150 kVA transformer at 25%, 33% and 100% full load at unity
power factor. The copper loss is 1600 W at full load and the iron loss is 1400 W.
[Ans. 96.15, 96.94, 98.04%]
14. In a 25 kVA, 2000/200 V transformer, the iron and copper losses are 350 and 400 W
respectively. Calculate the load for which the efficiency is maximum and determine the
maximum efficiency at unity power factor.
[Ans. 23.4 kVA, 97.1%]
15. The daily variation of load of a 100 kVA transformer is as follows:
8 AM to 1 PM: 65 kW, 45 kVAR
1 PM to 6 PM: 80 kW, 50 kVAR
6 PM to 1 AM: 30 kW, 30 kVAR
1 AM to 8 AM: No load
This transformer has no-load core-loss of 370 W and a full load ohmic loss of 1200 W.
Determine the all-day efficiency of transformer.
[Ans. 97.959%]
16. A 20 kVA, 2500/500 V, single-phase transformer has the following parameters:
HV Winding: r1= 8 Ω, x1= 17 Ω
LV Winding: r2=0.3 Ω, x2=0.7 Ω.
Find the voltage regulation at full load for (a) 0.9 pf lag (b) 0.9 pf lead.
The supply Voltage is held constant at 2500 V.
[Ans. (a) 8.944%, (b) -1.075%]
17. Calculate the regulation of a transformer in which the ohmic loss is 1% of the output and
reactance drop is 5% of output voltage, when the power factor is 0.8 lagging, unity and
0.8 leading.
[Ans. 3.8 %, 1% and -2.2%]
18. A 400/100 V, 5 kVA, single-phase two winding transformer is to be used as an autotransformer to supply 400 V from a 500 V supply. When tested as a two-winding
transformer at rated load and 0.8 pf lagging, its efficiency is found to be 0.95.
a) Determine the kVA rating as an auto-transformer. Also calculate the transformed
kVA and conducted kVA.
b) Find its efficiency as an Auto-transformer at rated load and 0.8 pf lagging.
[Ans. (a) 25 kVA, 5 kVA, 20 kVA, (b) 98.958%]