Transformers
Example Sheet 1
1. Show that the expression of the rms value of the back emf E of a transformer is
E = 4.44 Nfφm
where N is the number of turns of the winding, f the frequency in Hz, and φm the magnitude of the
magnetic flux. Assume the excitation is sinusoidal.
2. Show that the hysteresis energy loss per unit volume per cycle due to an AC excitation in an iron
ring is equal to the area of the B-H loop, i.e.
∫ HdB
The hysteresis loop for a certain iron ring is drawn in terms the flux linkage λ of the excitation
coil and the excitation current im to the following scales
on the excitation current im axis: 1 cm = 500 A
on the flux linkage λ axis:
1 cm = 100 µWb
The area of the hysteresis loop is 50 cm2 and the excitation frequency is 50 Hz. Calculate the
hysteresis power loss of the ring.
Answer: 125 W
3. A single phase transformer has 480 turns on the primary and 90 turns on the secondary. The mean
length of the flux path in the iron is 1.8 m and the joints are equivalent to an air gap of 0.1 mm. If
the maximum value of the flux density is to be 1.1 T when a voltage of 2200 V at 50 Hz is applied
to the primary and the stacking factor is 0.91, calculate
(a) the gross cross sectional area of the core,
(b) the secondary voltage on no load, and
(c) the primary current and power factor on no load.
Assume the value of the magnetic field strength for 1.1 T in iron to be 400 A/m, the corresponding
iron loss to be 1.7 W/kg at 50 Hz and the density of the iron to be 7800 kg/m3.
Answer: 0.0205 m2, 412.5 V, 1.21 A, 0.168 lagging
4. A single phase transformer has 1000 turns on the primary and 200 turns on the secondary. The no
load current is 3 A at a power factor 0.2 lagging. Calculate the primary current and power factor
when the secondary current is 280 A at a power factor of 0.8 lagging. Assume the winding
resistance is negligible.
Answer: 58.3 A, 0.78 lagging
Example Sheet 2
(1) A 100 kVA, 11000:2200 V, 60 Hz, single-phase transformer has the following equivalent circuit
parameters referred to the high-potential side:
R1 = 6.1 Ohm
R'2 = 7.2 Ohm
Xl1 = 31.2 Ohm X'l2 = 31.2 Ohm
Xm = 57300 Ohm
Rc = 124000 Ohm
The transformer is supplying at 2200 V a load circuit of 50 Ohm impedance and a leading power
factor of 0.7. Draw a phasor diagram (not to scale) showing the various phasor magnitudes and angles
for this operating condition. Determine the potential difference and power factor at the high-potential
terminals of the transformer.
(10702, 0.746)
(2) A 20 kVA, 2200:220 V, 60 Hz, single-phase distribution transformer gave the following test
results:
i) Open-circuit test, low-potential winding excited:
Voc = 220 V,
Ioc = 1.52 A,
ii) Short-circuit test, high-potential winding excited:
Vsc = 205 V,
Isc = 9.1 A,
iii) Direct-current winding resistances:
Rlp = 0.0311 Ohm,
Rhp = 2.51 Ohm
Poc = 161 W
Psc = 465 W
Determine the equivalent circuit of the transformer referred to the high-potential side. (Rc 30150, Xm
16520, Xl1 & Xl2 10.91, R1 2.51, R'2 3.11)
(3) The following results were obtained on a 50 kVA transformer:
O.C. test
V1 = 3300 V,
V2 = 400 V,
primary power = 430 W
S.C. test V1 = 124 V,
I1 = 15.3 A,
primary power = 525 W
Calculate:
(a) the efficiencies at full load and half load for 0.7 power factor lagging;
(0.973, 0.969)
(b) the voltage regulation; (0.033)
(c) the secondary terminal voltage. (386.8)