a) Explain the operating principle of a transformers.
b) A 10 kVA, single-phase transformers has a turn ratio of 12:1 and is supplied from a 2.4 kV supply. Neglecting losses, determine:
i. the full load secondary current.
ii. the minimum value of load resistance which can be connected across the secondary winding.
iii. the primary current.
A transformer operates on the principle of electromagnetic induction and mutual induction between two or more windings (or coils). The core of the transformer is typically made from laminated steel to minimize eddy current losses.
Primary Winding: The primary winding receives an alternating current (AC) voltage source. When an AC voltage is applied, it creates a time-varying magnetic field around the winding.
Magnetic Core: The magnetic field generated by the primary winding induces a magnetic flux in the core of the transformer. This flux travels through the core to the secondary winding.
Secondary Winding: The changing magnetic flux in the core induces an alternating voltage across the secondary winding through electromagnetic induction.
Where:
= Primary voltage
= Secondary voltage
Impedance Transformation: The turns ratio also affects the ratio of the primary and secondary currents.
Where:
Transformers are used to increase (step-up) or decrease (step-down) voltage levels while ideally maintaining the same power (neglecting losses).
Given:
To determine the full load secondary current ():
Step 1: Determine the secondary voltage ():
Given , so:
Step 2: Use the power equation to find :
To determine the minimum load resistance () that can be connected across the secondary winding:
To find the primary current ():
First, use the turns ratio relationship for current:
Therefore, the full load primary current is approximately 4.17 A.
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