Two coaxial cables, 1 and 2, are filled with different dielectric constants $$ varepsilon_{r_1}$$ and $$ varepsilon_{r_2}$$ respectively. The ratio of the wavelengths in the two cables $$ left( frac{ lambda_1}{ lambda_2} ight)$$ is(GATE 2000|| EC || MCQ ||2 MARK)

$$ sqrt{ frac{ varepsilon_{r_2}}{ varepsilon_{r_1}}}$$

$$ sqrt{ frac{ varepsilon_{r_1}}{ varepsilon_{r_2}}}$$

$$ frac{ varepsilon_{r_1}}{ varepsilon_{r_2}}$$

$$ frac{ varepsilon_{r_2}}{ varepsilon_{r_1}}$$

GATE EC||ELCTROMAGNETIC FIELD THEORY|| TRANSMISSION LINE|| PYQS(2000-2025)

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Question 1

Two coaxial cables, 1 and 2, are filled with different dielectric constants [Tex]\varepsilon_{r_1}[/Tex] and [Tex]\varepsilon_{r_2}[/Tex] respectively. The ratio of the wavelengths in the two cables [Tex]\left(\frac{\lambda_1}{\lambda_2}\right)[/Tex] is
(GATE 2000|| EC || MCQ ||2 MARK)

[Tex]\sqrt{\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}}}[/Tex]
[Tex]\sqrt{\frac{\varepsilon_{r_2}}{\varepsilon_{r_1}}}[/Tex]
[Tex]\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}}[/Tex]
[Tex]\frac{\varepsilon_{r_2}}{\varepsilon_{r_1}}[/Tex]

Question 2

The magnitudes of the open-circuit and short-circuit input impedances of a transmission line are 100 Ω and 25 Ω, respectively. The characteristic impedance of the line is

(GATE 2000|| EC || MCQ ||1 MARK)

25 Ω
50 Ω
75 Ω
100 Ω

Question 3

A transmission line is distortionless if

(GATE 2001|| EC || MCQ ||1 MARK)

[Tex]\text{RL} = \frac{1}{\text{GC}}[/Tex]
RL = GC
LG = RC
RG = LC

Question 4

The VSWR can have any value between

(GATE 2002|| EC || MCQ ||1 MARK)

0 and 1
—1 and +1
0 and ∞
1 and ∞

Question 5

In an impedance Smith chart, a clockwise movement along a constant resistance circle gives rise to

(GATE 2002|| EC || MCQ ||1 MARK)

a decrease in the value of reactance
an increase in the value of reactance
no change in the reactance value
no change in the impedance value

Question 6

A short-circuited stub is shunt connected to a transmission fine as shown in the figure. If Z 0 = 50 Ω, the admittance /seen at the junction of the stub and the transmission line is

(GATE 2003|| EC || MCQ ||2 MARK)

(0.01–j0.02) mho
(0.02 –j0.01) mho
(0.04 –j0.02) mho
(0.02 - j0) mho

Question 7

Consider a 300 Ω, quarter-wave long (at 1 GHz) transmission line as shown in the figure. It is connected to a 10 V, 50 Ω source at one end and is left open circuited at the other end. The magnitude of the voltage at the open circuit end of the line is

(GATE 2004|| EC || MCQ ||2 MARK)

10 V
5V
60 V
60/7 V

Question 8

A lossless transmission line is terminated in a load that reflects a part of the incident power. The measured VSWR is 2. The percentage of the power that is reflected back is

(GATE 2004|| EC || MCQ ||2 MARK)

57.73
33.33
0.11
11.11

Question 9

Consider an impedance Z = R + jX marked with point P in an impedance Smith chart as shown in the figure. The movement from point P along a constant resistance circle in the clockwise direction by an angle 45° is equivalent to

(GATE 2004|| EC || MCQ ||2 MARK)

adding an inductance in series with Z
adding a capacitance in series with Z
adding an inductance in shunt across Z
adding a capacitance in shunt across Z

Question 10

The characteristic impedance of a transmission line is 50 Ω. Input impedance of the open-circuited line is 100 + j150Ω. When the transmission line is short-circuited, the value of the input impedance will be

(GATE 2005|| EC || MCQ ||2 MARK)

50 Ω
100 + j150 Ω
7.69 + j11.54 Ω
7.69 -j11.54 Ω

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