This question was previously asked in

MPSC Assistant Engineer EE Mains 2018 - Paper 1

Option 3 : the hysteresis loss of the transformer increases while eddy current loss remains the same

CT 1: Basic Concepts

18600

10 Questions
10 Marks
6 Mins

__Concept:__

Hysteresis losses: These are due to the reversal of magnetization in the transformer core whenever it is subjected to alternating nature of magnetizing force.

\({W_h} = \eta B_{max}^xfv\)

\({B_{max}} \propto \frac{V}{f}\)

Where

x is the Steinmetz constant

Bm = maximum flux density

f = frequency of magnetization or supply frequency

v = volume of the core

At a constant V/f ratio, hysteresis losses are directly proportional to the frequency.

Wh ∝ f

Eddy current losses: Eddy current loss in the transformer is I2R loss present in the core due to the production of eddy current.

\({W_e} = K{f^2}B_m^2{t^2}V\)

\({B_{max}} \propto \frac{V}{f}\)

Where,

K - coefficient of eddy current. Its value depends upon the nature of magnetic material

Bm - Maximum value of flux density in Wb/m2

t - Thickness of lamination in meters

f - Frequency of reversal of the magnetic field in Hz

V - Volume of magnetic material in m3

At a constant V/f ratio, eddy current losses are directly proportional to the square of the frequency.

We ∝ f2

Iron losses or core losses or constant losses are the sum of both hysteresis and eddy current losses.

Wi = Wh + We

At constant V/f ratio, Wi = Af + Bf2

__Calculation:__

In the given question, voltage kept constant and frequency is varied.

The V/f ratio is not constant.

Hysteresis losses, **W _{h} ∝ V^{1.6} f^{-0.6}**

As the frequency is decreased to 40 Hz from 50 Hz, the hysteresis losses will increase.

Eddy current losses, **W _{e} ∝ V^{2}**

As eddy current losses are independent of frequency, the eddy current losses remain the same.