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GATE EE 2023 Set 1 — Question 53

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NAT+2 / -0HardSelf & Mutual InductanceMagnetic Circuits & InductanceElectromagnetic FieldsEquivalent Circuit & PhasorSingle-Phase TransformersElectrical Machines

Electrical Machines → Magnetic Circuits & Inductance → Equivalent Circuit & Phasor

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Question

When the winding c-d of the single-phase, 50 Hz, two winding transformer is supplied from an AC current source of frequency 50 Hz, the rated voltage of 200 V (rms), 50 Hz is obtained at the open-circuited terminals a-b. The cross sectional area of the core is 5000 mm2^2 and the average core length traversed by the mutual flux is 500 mm. The maximum allowable flux density in the core is Bmax=1 Wb/m2B_{max} = 1\text{ Wb/m}^2 and the relative permeability of the core material is 5000. The leakage impedance of the winding a-b and winding c-d at 50 Hz are (5+j100π×0.16) Ω(5 + j100\pi \times 0.16)\ \Omega and (11.25+j100π×0.36) Ω(11.25 + j100\pi \times 0.36)\ \Omega, respectively. Considering the magnetizing characteristics to be linear and neglecting core loss, the self-inductance of the winding a-b in millihenry is ___________ (Round off to 1 decimal place).
Diagram of a single-phase transformer core with two windings. Winding a-b is on the left limb and winding c-d is on the right limb. Winding c-d is connected to a 50 Hz AC current source. Winding a-b is open-circuited with a measured voltage $V_{ab} = 200\text{ V}$.
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