1
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).

2
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
$${J_a}{r^3}$$
3
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
4
GATE EE 2022
+1
-0.33

As shown in the figure below, to concentric conducting spherical shells, centred at r = 0 and having radii r = c and r = d are maintained at potentials such that the potential V(r) at r = c is V1 and V(r) at r = d is V2. Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

A
$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_1}c + {V_2}d - 2{V_1}d} \over {d - c}}$$
B
$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} + {{{V_2}d - {V_1}c} \over {d - c}}$$
C
$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} - {{{V_1}c - {V_2}c} \over {d - c}}$$
D
$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_2}c - {V_1}c} \over {d - c}}$$
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