231. The equation for distortionless transmission if R/ G = L/ C. To attain it, in a line—

1. 1. Of all the parameters, it is best to increase L for distortionless transmission

   
   
   

   2. Keeping R and L constant it is preferrable to increase or decrease G and C

   
   
   

   3. The inductance can be added at any interval

   
   
   

   4. The inductance can be of any value

   
   
   

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1. View Hint View Answer Discuss in Forum

   It is best to increase L for distortionless transmission.

   Correct Option: A

   It is best to increase L for distortionless transmission.

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232. Match List-I with List-II and select the correct answer using the codes given the lists:
     

     List-I	List-II
     (Maxwell's equation)
     (a) ∇ × H = J + ∂D/∂t	1. Faraday's law
     (b) ∇ × E = −∂B/∂t	2. Gauss' law
     (c) ∇ ⋅ D = ρ	3.Ampere's law

1. 1. (a) (b) (c)
      3  1  2

   
   
   

   2. (a) (b) (c)
      2  1  3

   
   
   

   3. (a) (b) (c)
      3  2  1

   
   
   

   4. (a) (b) (c)
      1  2  3
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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233. When a lossy capacitor with a dielectric of permittivity ε and conductivity σ operates at a frequency ω, the loss tangent for the capacitor is given by—

1. 1. ω σ/ ε

   
   
   

   2. ω ε/ σ

   
   
   

   3. σ/ ω ε

   
   
   

   4. σ ω ε
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   tan δ =	IR	=	V
   	Ic		RVωC

   
   = 1/ωCR
   C = A∈/d,
   R = d/σA
   

   ∴ CR =	A∈	d	=	∈
   	d	σA		σ

   
   

   ∴ tan δ =	1	=	∈
   	ω∈/σ		ω∈

   
   
   

   Correct Option: C

   tan δ =	IR	=	V
   	Ic		RVωC

   
   = 1/ωCR
   C = A∈/d,
   R = d/σA
   

   ∴ CR =	A∈	d	=	∈
   	d	σA		σ

   
   

   ∴ tan δ =	1	=	∈
   	ω∈/σ		ω∈

   
   
   

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234. Two electric dipoles aligned parallel to each other and having the same axis exert a force F on each other, when a distance d apart. If the dipoles are a distance 2d apart, then the mutual force between them would be—

1. 1. F/ 2

   
   
   

   2. F/ 4

   
   
   

   3. F/ 8

   
   
   

   4. F/ 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   The force of repulsion between the two dipoles
   

   F =	q2		1 –	1
   	2πεd2			[1 + (I2/d2)]

   
   Assuming that I << d, we have
   

   F =	q2		1 – 1 +	3	3
   	2πεd2			2	d2

   
   

   F =	q2
   	2πεd2

   
   Therefore, if with distance d, the force is F, the force with distance 2d would be F/16.

   Correct Option: D

   The force of repulsion between the two dipoles
   

   F =	q2		1 –	1
   	2πεd2			[1 + (I2/d2)]

   
   Assuming that I << d, we have
   

   F =	q2		1 – 1 +	3	3
   	2πεd2			2	d2

   
   

   F =	q2
   	2πεd2

   
   Therefore, if with distance d, the force is F, the force with distance 2d would be F/16.

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235. If a conductor of cross-section A and carrying a current current | ^→a y| is oriented along the y-axis in a magnetic field B = B₀ ^→a x + B₀ ^→a y, the force density exerted on the conductor is—

1. 1. 
      

      		→
      +	B0	az N/m2
      	a

   
   
   

   2. 
      

      		→
      +	B0	ax N/m2
      	a

   
   
   

   3. 
      

      		→
      −	B0	az N/m3
      	a

   
   
   

   4. 
      

      		→
      +	B0	ay N/m3
      	a

   
   
   

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1. View Hint View Answer Discuss in Forum

   The force on a current carrying mass lying in a magnetic field B is given by
   

   F =		.	(J × B) dv
   		vol

   
   J = 1/y i_y
   ∴ The force density = 1/y i_y × B₀ (i_x + i_y)
   = 1/a B₀ (– i_z) N/m³
   = B₀/a ^→a_>z N/m³
   Hence alternative (C) is the correct choice.
   

   Correct Option: C

   The force on a current carrying mass lying in a magnetic field B is given by
   

   F =		.	(J × B) dv
   		vol

   
   J = 1/y i_y
   ∴ The force density = 1/y i_y × B₀ (i_x + i_y)
   = 1/a B₀ (– i_z) N/m³
   = B₀/a ^→a_>z N/m³
   Hence alternative (C) is the correct choice.
   

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