Transformer
1179
Tutorial Problems 32.4
1. A 200-kVA transformer has an efficiency of 98 % at full-load. If the maximum efficiency occurs at
three-quarters of full-load, calculate (a) iron loss at F.L. (b) Cu loss at F.L. (c) efficiency at half-load.
Ignore magnetising current and assume a p.f. of 0.8 at all loads.
[(a) 1.777 kW (b) 2.09 kW (c) 97.92%]
2. A 600 kVA, 1-ph transformer has an efficiency of 92 % both at full-load and half-load at unity power
factor. Determine its efficiency at 60 % of full load at 0.8 power factor lag.
[90.59%] (Elect. Machines, A.M.I.E. Sec. B, 1992)
3. Find the efficiency of a 150 kVA transformer at 25 % full load at 0.8 p.f. lag if the copper loss at full
load is 1600 W and the iron loss is 1400 W. Ignore the effects of temperature rise and magnetising
current. [96.15%] (Elect. Machines, A.M.I.E. Sec. B, 1991)
4. The F.L. Cu loss and iron loss of a transformer are 920 W and 430 W respectively. (i) Calculate the
loading of the transformer at which efficiency is maximum (ii) what would be the losses for giving
maximum efficiency at 0.85 of full-load if total full-load losses are to remain unchanged ?
[(a) 68.4% of F.L. (ii) W
i
= 565 W ; W
cu
= 785 W]
5. At full-load, the Cu and iron losses in a 100-kVA transformer are each equal to 2.5 kW. Find the
efficiency at a load of 65 kVA, power factor 0.8. [93.58%] (City & Guilds London)
6. A transformer, when tested on full-load, is found to have Cu loss 1.8% and reactance drop 3.8%.
Calculate its full-load regulation (i) at unity p.f. (ii) 0.8 p.f. lagging (iii) 0.8 p.f. leading.
[(i) 1.80% (ii) 3.7 % (iii)
−−
−−
−0.88%]
7. With the help of a vector diagram, explain the significance of the following quantities in the open-
circuit and short-circuit tests of a transformer (a) power consumed (b) input voltage (c) input current.
When a 100-kVA single-phase transformer was tested in this way, the following data were obtained
: On open circuit, the power consumed was 1300 W and on short-circuit the power consumed was
1200 W. Calculate the efficiency of the transformer on (a) full-load (b) half-load when working at
unity power factor. [(a) 97.6% (b) 96.9%] (London Univ.)
8. An 11,000/230-V, 150-kVA, 50-Hz, 1-phase transformer has a core loss of 1.4 kW and full-load Cu
loss of 1.6 kW. Determine (a) the kVA load for maximum efficiency and the minmum efficiency (b)
the efficiency at half full-load at 0.8 power factor lagging. [140.33 kVA, 97.6% ; 97%]
9. A single-phase transformer, working at unity power factor has an efficiency of 90 % at both half-load
and a full-load of 500 kW. Determine the efficiency at 75 % of full-load. [90.5%] (I.E.E. London)
10. A 10-kVA, 500/250-V, single-phase transformer has its maximum efficiency of 94 % when delivering
90 % of its rated output at unity power factor. Estimate its efficiency when delivering its full-load
output at p.f. of 0.8 lagging. [92.6%] (Elect. Machinery, Mysore Univ, 1979)
11. A single-phase transformer has a voltage ratio on open-circuit of 3300/660-V. The primary and
secondary resistances are 0.8 Ω and 0.03 Ω respectively, the corresponding leakage reactance being
4 Ω and 0.12 Ω. The load is equivalent to a coil of resistance 4.8 Ω and inductive reactance 3.6 Ω.
Determine the terminal voltage of the transformer and the output in kW. [636 V, 54 kW]
12. A 100-kVA, single-phase transformer has an iron loss of 600 W and a copper loss of 1.5 kW at full-
load current. Calculate the efficiency at (a) 100 kVA output at 0.8 p.f. lagging (b) 50 kVA output at
unity power factor. [(a) 97.44% (b) 98.09%]
13. A 10-kVA, 440/3300-V, 1-phase transformer, when tested on open circuit, gave the following figures
on the primary side : 440V ; 1.3 A ; 115 W.
When tested on short-circuit with full-load current flowing, the power input was 140 W. Calculate
the efficiency of the transformer at (a) full-load unity p.f. (b) one quarter full-load 0.8 p.f.
[(a) 97.51% (b) 94.18%] (Elect. Engg-I, Sd. Patel Univ. June 1977)
14. A 150-kVA single-phase transformer has a core loss of 1.5 kW and a full-load Cu loss of 2 kW.
Calculate the efficiency of the transformer (a) at full-load, 0.8 p.f. lagging (b) at one-half full-load