Question

The hysteresis cycle for the material of a transformer core is?
(A) Short and wide
(B) Tall and narrow
(C) Tall and wide
(D) Short and narrow

Answer 1

Hint:A transformer is working on the principle of electromagnetic induction.Soft Iron \[\left( {{\mathbf{silicon}}{\text{ }}{\mathbf{steel}}} \right)\]is used in transformer core. The material should have high retentivity so that the magnet is strong.
High coercivity so that the magnetization is not erased by stray magnetic fields, temperature fluctuations, or minor mechanical damage.The material should have a high permeability.

Complete step by step answer:
A transformer is a device that transfers electrical energy from one circuit to another by increasing or decreasing its current. For minimizing energy wastage we need to choose proper material for its core. For this, we need to check the hysteresis cycle. Magnetic Hysteresis results in the dissipation of wasted energy in the form of heat. The energy wasted being in proportion to the area of the magnetic hysteresis loop. Hysteresis losses will always be a problem in \[AC\] transformers where the current is constantly changing direction and thus the magnetic poles in the core will cause losses because they constantly reverse direction.
We know that\[B = \mu H\]and\[B = \phi /A\]
\[B = \] Magnetic flux
\[H = \] Magnetic field strength
\[A = \] Area of the loop.
\[\phi ,\mu = \]constants
For increasing \[B,\]we have to decrease \[A\] \[\left( {area{\text{ }}of{\text{ }}the{\text{ }}loop} \right).{\text{ }} = {\mathbf{NARROW}}\]
For soft iron core for a small \[H,\]there will be a large magnitude of \[B.{\text{ }} = {\mathbf{TALL}}\]

The energy loss during a magnetization and demagnetization cycle is proportional to the area of the hysteresis loop so, to reduce this loss the area of the loop should be minimum, and height of the loop should be maximum.
Transformer core is of soft iron material which has small coercivity and large retentivity. This implies that the hysteresis cycle for the material of a transformer core is tall and narrow.
Hence,option \[B\] is correct.

Note:Always use \[B = \mu H\] and \[B = \phi /A\] for checking the hysteresis loop and for checking \[H{\text{ }}and{\text{ }}B\] values. Check the coercivity values of different ferromagnetic material.