# Electromagnetic Theory Questions and Answers – Phase and Group Velocity

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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

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

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 108 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

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.
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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

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

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 = c2 is the relation.

6. The phase velocity of a wave having a group velocity of 6 x 106 is (in order of 108 m/s)
a) 2.4
b) 3
c) 15
d) 150

Explanation: We know that the phase and the group velocities are given by Vp x Vg = c2. On substituting for Vg = 6 x 106 and the speed of light, we get Vp = 150 x 108 m/s.

7. The group velocity of a wave with a phase velocity of 60 x 109 is (in 106 order)
a) 1.5
b) 2
c) 2.5
d) 3

Explanation: We know that the phase and the group velocities are given by Vp x Vg = c2. On substituting for Vp = 60 x 109 and the speed of light, we get Vg = 1.5 x 106 m/s.

8. The phase velocity of a wave having a phase constant of 4 units and a frequency of 2.5 x 109 radian/sec is (in 108 order)
a) 3.25
b) 3.75
c) 6.25
d) 6.75

Explanation: The phase velocity and the phase constant are related by Vp = ω/βg. On substituting for ω = 2.5 x 109 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

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

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

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

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

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