1
GATE EE 2022
Numerical
+1
-0.33

A star-connected 3-phase, 400 V, 50 kVA, 50 Hz synchronous motor has a synchronous reactance of 1 ohm per phase with negligible armature resistance. The shaft load on the motor is 10 kW while the power factor is 0.8 leading. The loss in the motor is 2 kW. The magnitude of the per phase excitation emf of the motor, in volts, is ________. (round off to nearest integer).

2
GATE EE 2022
Numerical
+1
-0.33

A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ________. (round off to two decimal places).

3
GATE EE 2022
+1
-0.33

A long conducting cylinder having a radius b is placed along the z-axis. The current density is $$\overrightarrow J = {J_a}{r^3}\widehat z$$ for the region r < b where r is the distance in the radial direction. The magnetic field intensity ($$\overrightarrow H$$) for the region inside the conductor (i.e., for r < b) is

A
$${{{J_a}} \over 4}{r^4}$$
B
$${{{J_a}} \over 3}{r^3}$$
C
$${{{J_a}} \over 5}{r^4}$$
D
$${J_a}{r^3}$$
4
GATE EE 2022
+1
-0.33

If the magnetic field intensity ($$\overrightarrow H$$) in a conducting region is given by the expression, $$\overrightarrow H = {x^2}\widehat i + {x^2}{y^2}\widehat j + {x^2}{y^2}{z^2}\widehat k$$ A/m. The magnitude of the current density, in A/m2, at x = 1 m, y = 2 m and z = 1 m is

A
8
B
12
C
16
D
20
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