Test: Magnetically Coupled Circuits

QUESTION: 1

In the circuit shown in fig

i₁ = 5sin 3t A and i₂= 3 cos 3t A.

v₂ = ?

A.
9(-4sin 3t + 5cos 3t)V
B.
9(4sin 3t - 5cos 3t) V
C.
9 (- 4sin 3t - 5cos 3t) V
D.
9(4sin 3t + 5cos 3t ) V

Solution:

=36 sin 3t + 45 cos 3t = 9(4sin 3t + 5cos 3t) V

QUESTION: 2

In the circuit shown in fig. if current i₁ = 5 cos (500t - 20°) mA and i₂ = 20 cos (500t - 20°) mA, the total energy stored in system at t = 0 is

A.
151.14 μJ
B.
45.24 μJ
C.
249.44 μJ
D.
143.46 μJ

Solution:

At t = 0, i₁ = 4 cos (-20°) = 4.7 mA
i₂ = 20 cos (-20°) = 18.8 mA,

= 151.3 μJ

QUESTION: 3

L_{eq =} ?

A.
4 H
B.
6 H
C.
7 H
D.
0 H

Solution:

QUESTION: 4

L_eq= ?

A.
2 H
B.
4 H
C.
6 H
D.
8 H

Solution:

QUESTION: 5

L_eq= ?

A.
8 H
B.
6 H
C.
4 H
D.
2 H

Solution:

QUESTION: 6

L_eq = ?

A.
0.4 H
B.
2 H
C.
1.2 H
D.
6 H

Solution:

QUESTION: 7

The equivalent inductance of a pair of a coupled inductor in various configuration are
(a) 7 H after series adding connection
(b) 1.8 H after series opposing connection
(c) 0.5 H after parallel connection with dotted terminal connected together.

The value of L₁ L₂, and M are

A.
3 H, 1.6 H, 1.2 H
B.
1.6 H, 3 H, 1.4 H
C.
3.7 H, 0.7 H, 1.3 H
D.
2 H, 3 H, 3 H

Solution:

⇒

QUESTION: 8

L_eq = ?

A.
0.2 H
B.
1 H
C.
0.4 H
D.
2 H

Solution:

QUESTION: 9

L_eq = ?

A.
1 H
B.
2 H
C.
3 H
D.
4 H

Solution:

QUESTION: 10

L_eq = ?

A.
1 H
B.
2 H
C.
3 H
D.
4 H

Solution:

QUESTION: 11

L_eq = ?

A.
41/5H
B.
49/5H
C.
51/5H
D.
39/5H

Solution:

Let I₁ be the current through 4 H inductor and I₂ and I₃ be the current through 3 H, and 2 H inductor respectively

QUESTION: 12

Consider the circuit shown in fig.

The voltage V_AG of terminal AD is

A.
60 V
B.
-60 V
C.
180 V
D.
240 V

Solution:

QUESTION: 13

Consider the circuit shown in fig

The voltage v_BG of terminal BD is

A.
45 V
B.
33 V
C.
69 V
D.
105 V

Solution:

QUESTION: 14

Consider the circuit shown in fig.

The voltage v_GC of terminal CD is

A.
30 V
B.
0 V
C.
-36 V
D.
36 V

Solution:

QUESTION: 15

In the circuit of fig. the ω =2 rad/s. The resonance occurs when C is

A.
1 F
B.
1/2 F
C.
1/3 F
D.
1/6 F

Solution:

QUESTION: 16

In the circuit of fig, the voltage gain is zero at ω= 333.33 rad/s.

The value of C is

A.
100μF
B.
75 μF
C.
50μF
D.
25 μF

Solution:

QUESTION: 17

In the circuit of fig. at ω = 333.33 rad/s, the voltage gain v_out / v_in is zero. The value of C is

A.
3.33 mF
B.
33.33 mF
C.
3.33 μF
D.
33.33μF

Solution:

The π equivalent circuit of coupled coil is shown in fig

Output is zero if

QUESTION: 18

The evenin equivalent at terminal ab for the network shown in fig. is

A.
6 V, 10 Ω
B.
6 V, 4Ω
C.
0 V, 4 Ω
D.
0 V, 10Ω

Solution:

Applying 1 V test source at ab terminal,

= 0.25 A

QUESTION: 19

In the circuit of fig. the maximum power delivered to RL is

A.
250 W
B.
200 W
C.
150 W
D.
100 W

Solution:

Impedance seen by R_L = 10 x 4² = 160 Ω
For maximum poer R_L = 160Ω, Zo = 10Ω
= 250 W

QUESTION: 20

The average power delivered to the 8 Ω load in the circuit of fig. is

A.
8 W
B.
1.25 kW
C.
625 kW
D.
2.50 kW

Solution:

20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Magnetically Coupled Circuits

In the circuit shown in fig

i₁ = 5sin 3t A and i₂= 3 cos 3t A.

v₂ = ?

In the circuit shown in fig. if current i₁ = 5 cos (500t - 20°) mA and i₂ = 20 cos (500t - 20°) mA, the total energy stored in system at t = 0 is

L_{eq =} ?

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