HW2 (1)

Nazarbayev University, 08/02/2019 (Due on 15/02/2019-10:00pm)
Dr. Ing. Michele Folgheraiter
Homework 2
ROBT304: Electromechanical Systems with Laboratory
Attention: report all the steps and explain from which fundamental equations the formulas
you used are derived (e.g. from Ampere law…). Consider that after you submit the
homework in Moodle (as a pdf) you may be asked for additional clarifications on how you
solved the problem.
A transformer is made up of a 1200-turn primary coil and an open-circuited 75-turn
secondary coil wound around a closed core of cross-sectional area 42 cm2. The core material
can be considered to saturate when the rms applied flux density reaches 1.45 T.
a) What maximum 60-Hz rms primary voltage is possible at the maximum flux density?
What is the corresponding secondary voltage?
b) How are these values modified if the applied frequency is lowered to 50 Hz?
A 100 Ω resistor is connected to the secondary of an ideal transformer with a turns ratio of
1:4 (primary to secondary). A 10-V rms, 1-kHz voltage source is connected to the primary.
a) Calculate the primary current and the voltage across the 100 Ω resistor.
b) Assuming now that instead of a pure resistive load we have an impedance
ZL=100+j10Ω connected at the secondary. Calculate the active, reactive, and apparent
powers at the primary and the correspondent power factor.
A 120-V:2400-V, 60-Hz, 50-kVA transformer has a magnetizing reactance (as measured
from the 120-V terminals) of 34.6 Ω . The 120-V winding has a leakage reactance of 27.4 Ω
and the 2400-V winding has a leakage reactance of 11.2 Ω.
a) With the secondary open-circuited and 120 V applied to the primary (120-V) winding,
calculate the primary current and the secondary voltage.
b) With the secondary short-circuited, calculate the primary voltage which will result in rated
current in the primary winding. Calculate the corresponding current in the secondary winding.
A 460-V:2400-V transformer has a series leakage reactance of 37.2 Ω as referred to the highvoltage side. A load connected to the low-voltage side is observed to be absorbing 25 kW,
with unity power factor, and the voltage is measured to be 460 V. Calculate the corresponding
voltage and power factor as measured at the high-voltage terminals.