This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Phase and Group Velocity”.

1. In a waveguide, which of the following condition is true always?

a) phase velocity = c

b) group velocity = c

c) phase velocity > c

d) phase velocity < c

View Answer

Explanation: The phase velocity is always greater than the speed of light in waveguides. This implies the group velocity is small.

2. The term cos θ is given by 2.5. Find the phase velocity.

a) 3

b) 5

c) 7.5

d) 2.5

View Answer

Explanation: The phase velocity is given by Vp = c cos θ. On substituting for cos θ = 2.5 and the speed of light, we get the phase velocity as 7.5 x 10

^{8}m/s.

3. The cut off wavelength and the guided wavelength are given by 0.5 and 2 units respectively. Find the wavelength of the wave.

a) 0.48

b) 0.32

c) 0.45

d) 0.54

View Answer

Explanation: The cut off wavelength and the guided wavelength are related as (1/λ)

^{2}= (1/λc)

^{2}+ (1/λg)

^{2}. On substituting for λc = 0.5 and λg = 2, we get λ = 0.48 units.

4. The cut off wavelength of the rectangular waveguide in dominant mode with dimensions 6 cm x 4 cm is

a) 12cm

b) 6cm

c) 4cm

d) 2cm

View Answer

Explanation: The cut off wavelength in the dominant mode is given by λc = 2a/m, where a is the broad wall dimension. On substituting for m = 1 and a = 6cm, we get the cut off wavelength as 12cm.

5. The product of the phase and the group velocities is given by the

a) Speed of light

b) Speed of light/2

c) 2 x Speed of light

d) (speed of light)/4

View Answer

Explanation: The product of the phase and the group velocities is given by the square of the speed of the light. Thus Vp x Vg = c

^{2}is the relation.

6. The phase velocity of a wave having a group velocity of 6 x 10^{6} is (in order of 10^{8} m/s)

a) 2.4

b) 3

c) 15

d) 150

View Answer

Explanation: We know that the phase and the group velocities are given by Vp x Vg = c

^{2}. On substituting for Vg = 6 x 10

^{6}and the speed of light, we get Vp = 150 x 10

^{8}m/s.

7. The group velocity of a wave with a phase velocity of 60 x 10^{9} is (in 10^{6} order)

a) 1.5

b) 2

c) 2.5

d) 3

View Answer

Explanation: We know that the phase and the group velocities are given by Vp x Vg = c

^{2}. On substituting for Vp = 60 x 10

^{9}and the speed of light, we get Vg = 1.5 x 10

^{6}m/s.

8. The phase velocity of a wave having a phase constant of 4 units and a frequency of 2.5 x 10^{9} radian/sec is (in 10^{8} order)

a) 3.25

b) 3.75

c) 6.25

d) 6.75

View Answer

Explanation: The phase velocity and the phase constant are related by Vp = ω/βg. On substituting for ω = 2.5 x 10

^{9}and β = 4, we get the phase velocity as 6.25 units.

9. The guided wavelength and the phase constant are related by

a) 2π/βg = λg

b) 1/βg = λg

c) 1/2πβg = λg

d) βg = λg

View Answer

Explanation: The guided wavelength and the phase constant are related by 2π/βg = λg, where βg is the guided phase constant and λg is the guided wavelength.

10. The phase velocity refers to a group of waves and the group velocity refers to a single wave. State true/false.

a) True

b) False

View Answer

Explanation: The phase velocity refers to a single wave and the group velocity refers to a group of waves.

11. The phase and group velocities does not depend on which of the following?

a) Frequency

b) Wavelength

c) Phase constant

d) Attenuation constant

View Answer

Explanation: The phase and the group velocities are directly related by the frequency, wavelength and the phase constant. It is independent of the attenuation constant.

12. The distance between two successive points in a waveguide is the

a) Guided wavelength

b) 2 x guided wavelength

c) Guided wavelength/2

d) (guided wavelength)/4

View Answer

Explanation: The distance between two successive points in a waveguide is equal to half of the guided wavelength.

**Sanfoundry Global Education & Learning Series – Electromagnetic Theory.**

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