41. A parabolic dish antenna has a conical beam 2º wide. The directivity of the antenna is approximately—

1. 1. 20 dB

   
   
   

   2. 30 dB

   
   
   

   3. 40 dB

   
   
   

   4. 50 dB

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here conical beamwidth is given so we assume that the parabolic reflector is of circular type so we have relation of BWFN and D & λ as follows
   

   BWFN =	140λ
   	D

   
   where,
   D = diameter
   λ = wavelength
   

   2 =	140λ
   	D

   
   so we got here,
   

   D	= 70
   λ

   
   

   we have directivity = ∏2		D		2	= 9.86		D		2
   		λ					λ

   
   

   10 logDi = 10 log		9.86		D		2		= 46.8 ≈ 50 dB
   				λ

   Correct Option: D

   Here conical beamwidth is given so we assume that the parabolic reflector is of circular type so we have relation of BWFN and D & λ as follows
   

   BWFN =	140λ
   	D

   
   where,
   D = diameter
   λ = wavelength
   

   2 =	140λ
   	D

   
   so we got here,
   

   D	= 70
   λ

   
   

   we have directivity = ∏2		D		2	= 9.86		D		2
   		λ					λ

   
   

   10 logDi = 10 log		9.86		D		2		= 46.8 ≈ 50 dB
   				λ

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42. The skin depth at 10 MHz for a conductor is 1 cm. The phase velocity of an electromagnetic wave in the conductor at 1000 MHz is about—

1. 1. 6 × 10⁶ m/s

   
   
   

   2. 6 × 10⁷ m/s

   
   
   

   3. 3 × 10⁸ m/s

   
   
   

   4. 6 × 10⁸ m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   Skin depth δ = 1 cm = 0.01 m
   

   Phase velocity vP =	ω	= ωδ
   	β

   
   = 2π f δ ⇒ 2π × 1000 × 10⁶ × 0.01
   = 2π × 10⁷ m/s
   = 6.28 × 10⁷ m/s

   Correct Option: B

   Skin depth δ = 1 cm = 0.01 m
   

   Phase velocity vP =	ω	= ωδ
   	β

   
   = 2π f δ ⇒ 2π × 1000 × 10⁶ × 0.01
   = 2π × 10⁷ m/s
   = 6.28 × 10⁷ m/s

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43. Intrinsic impedance of copper at high frequencies is—

1. 1. Purely resistive

   
   
   

   2. Purely inductive

   
   
   

   3. Complex with capacitive component

   
   
   

   4. Complex with an inductive component

   
   
   

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1. View Hint View Answer Discuss in Forum

   Intrinsic impedance of metal σ >> ωε, we have
   

   η =	√	jωμ
   		σ + jωμ

   
   

   ≅	√	jωμ	=	ωμ	∠45º
   		σ		σ

   Correct Option: D

   Intrinsic impedance of metal σ >> ωε, we have
   

   η =	√	jωμ
   		σ + jωμ

   
   

   ≅	√	jωμ	=	ωμ	∠45º
   		σ		σ

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44. The time average Poynting vector in W/m² for a wave
    
    

    →	→
    E = 24ej (ωt + βz)	ay

    V/m in free space is -

1. 1. -	2.4	→	az
      	∏

   
   
   

   2. 
      
      

      2.4	→	az
      ∏

   
   
   

   3. 
      
      

      4.8	→	az
      ∏

   
   
   

   4. 
      
      

      -	4.8	→	az
      	∏

   
   
   

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1. View Hint View Answer Discuss in Forum

   Time average Poynting vector is given by
   

   
   
   

   →	→
   E = 24ej (ωt + βz)	ay

   
   
   
   

   	→	→⋅
   	Ex ×	Hy

   
   
   
   

   →
   |Ey|2	=	-(24)2	=	2.4	→az
   2 η		2 × 120 ∏		∏

   
   

   Correct Option: A

   Time average Poynting vector is given by
   

   
   
   

   →	→
   E = 24ej (ωt + βz)	ay

   
   
   
   

   	→	→⋅
   	Ex ×	Hy

   
   
   
   

   →
   |Ey|2	=	-(24)2	=	2.4	→az
   2 η		2 × 120 ∏		∏

   
   

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45. The wavelength of a wave with propagation constant (0.1 π + j 0.2 π) m^{– 1} is—

1. 1. 2	m
      √0.05

   
   
   

   2. 10 m

   
   
   

   3. 20 m

   
   
   

   4. 30 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here propagation constant
   Y = (0.1 π + j 0.2 π) m^{– 1} is given
   β = 0.2 π
   so

   β =		2∏	= λ =	2∏	=	2∏	= 10m
   		λ		β		⋅2∏

   
   

   Correct Option: B

   Here propagation constant
   Y = (0.1 π + j 0.2 π) m^{– 1} is given
   β = 0.2 π
   so

   β =		2∏	= λ =	2∏	=	2∏	= 10m
   		λ		β		⋅2∏

   
   

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