Solution

Answer: 70.7%

Concept

CONCEPT

The condition for maximum efficiency in a 1ϕ transformer is:

P_C = (x)²P_cufl

where, PC = Core loss

P_cufl = Copper loss at full load

x = Fraction of loading

Calculation:

Given, PC = 400 W

Pcufl = 800 W

400 = (x)² × 800

x = 70.7%

Solution

Answer: 75°

Concept

• Ideally, a transformer draws the magnetizing current and lags the primary applied voltage by 90°.
• But the transformer also has a core loss current component which will be in phase with applied voltage.
• No-load current is nothing but the vector summation of these two currents.
• Hence, the no-load current will not lag behind applied voltage by exactly 90° but it lags somewhat less than 90°.
• It is in practice generally about 75°.

Additional Information

Circuit diagram for a transformer on no-load:

Where,
V₁ is the applied primary voltage
I_W is the working component of current through R_O (Magnetizing resistance)
I_μ is the magnetizing component of current through X_O (magnetizing reactance)
N₁ and N₂ are primary and secondary turns ratio

• In the case of no-load, the second terminal of the transformer is open.
• There is no path available for the current to flow on the secondary side.
• Hence, the transformer does not draw current from the source.
• A small ampere of current flows through the primary transformer (no-load current I ) called excitation current (used for excitation of the core).
• No-load current (I_O) is further divided into I_Wand I_μ

Phasor diagram when transformer on no-load:

Solution

Answer: 1/1

Eddy Current Loss:

• When an alternating magnetic field is applied to a magnetic material, an emf is induced in the material itself according to Faraday’s Law of Electromagnetic induction.
• Since the magnetic material is a conducting material, this EMF circulates current within the body of the material.
• These circulating currents are called Eddy Currents. They will occur when the conductor experiences a changing magnetic field.
• As these currents are not responsible for doing any useful work, and it produces a loss (I²R loss) in the magnetic material known as an Eddy Current Loss.

Mathematical Expression for Eddy Current Loss:

Pe=KeB2mt2f2V

where,
K_e – co-efficient of eddy current. Its value depends upon the nature of magnetic material
B_m – 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 – The volume of magnetic material in m³

From eddy current loss equation we can write

The eddy current loss at constant voltage is independent of transformer frequency

The ratio of eddy current loss at 60 Hz to 50 Hz at constant voltage is 1:1