GATE EE 2023 Question Paper (05-Feb-2023) (Shift 1)

For the circuit shown, if 𝑖 = 𝑠𝑖𝑛 1000𝑡, the instantaneous value of the Thevenin’s equivalent voltage (in Volts) across the terminals a - b at time t = 5 ms is __________ (Round off to 2 decimal places).

The admittance parameters of the passive resistive two-port network shown in the figure are

𝑦₁₁ = 5 𝑆, 𝑦₂₂ = 1 𝑆, 𝑦₁₂ = 𝑦₂₁ = −2.5 𝑆

The power delivered to the load resistor RL in Watt is __________ (Round off to 2 decimal places).

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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 and the average core length traversed by the mutual flux is 500 mm. The maximum allowable flux density in the core is B${}_{max}$ = 1 Wb/m² 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 and (11.25 + j100π × 0.36) Ω, 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).

The circuit shown in the figure is initially in the steady state with the switch K in open condition and K̅ in closed condition. The switch K is closed and K̅ is opened simultaneously at the instant t = t₁, where t₁ > 0. The minimum value of t₁ in milliseconds, such that there is no transient in the voltage across the 100 μF capacitor, is ____________ (Round off to 2 decimal places).

The circuit shown in the figure has reached steady state with thyristor ‘T’ in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned ON at t = 0 sec. The duration in microseconds for which the thyristor would conduct, before it turns off, is _____ (Round off to 2 decimal places).