156. The line A to neutral voltage is 10∠15°V for a balanced three phase star-connected load with phase sequence ABC. The voltage of line B with respect to line C is given by
     

1. 1. 10 √3 ∠105° V

   
   
   

   2. 10 ∠105° V

   
   
   

   3. 10 √3 ∠ -75° V

   
   
   

   4. -10 √3 ∠90° V

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   V_L = 3V_ph = √3 × 10 = 10 √3
   
   

   Correct Option: C

   
   V_L = 3V_ph = √3 × 10 = 10 √3
   
   

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157. A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R (> r) is
     

1. 1. 4πε₀ r

   
   
   

   2. 4πε₀²

   
   
   

   3. 4πε₀ R

   
   
   

   4. 4πε₀R²

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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158. The driving point impedance Z(s) for the circuit shown below is
     
     

1. 1. 	s4 + 3s2 + 1
      	s3 + 2s

      
      

   
   
   

   2. 	s4 + 2s2 + 4
      	s3 + 2s

      
      

   
   
   

   3. 	s2 + 1
      	s4 + s2 + 1

      
      

   
   
   

   4. 	s3 + 1
      	s4 + s2 + 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   S- Domain representation of the given circuit
   
   

   Z(s) = s +	1		s +	1
   	s			s
   	1	+		s +	1
   	s				s

   
   

   Z(s) =	s4 + 3s2 + 1
   	s3 + 2s

   Correct Option: A

   S- Domain representation of the given circuit
   
   

   Z(s) = s +	1		s +	1
   	s			s
   	1	+		s +	1
   	s				s

   
   

   Z(s) =	s4 + 3s2 + 1
   	s3 + 2s

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159. A perfectly conducting metal plate is placed in x-y plane in a right handed coordinate system. A charge of +32πε₀ √2 coulombs is placed at coordinate (0, 0, 2). ∈₀ is the permittivity of free space. Assume î , ĵ , k̂ to be unit vectors along x, y and z axes r espect i vely. At t he coor di nat e. (√2, √2,0), the electric field vector ^→E (Newtons/ Coulomb) will be
     
     

1. 1. 2√2 k̂
      

   
   
   

   2. -2 k̂
      

   
   
   

   3. 2 k̂
      

   
   
   

   4. -2√2 k̂

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   E = E1 + E2 =	1			Q1R1	+	Q2R2
   	4πε0			R13		R23

   
   
   

   E =	1			Q1	( √2ax + √2ay - 2az ) -	Q1	( √2ax + √2ay + 2az )
   	4πε0			16√2		16√2

   
   

   =	Q	[-4az ] =	32√2 πε0	(-az)
   	16√2 × 4πε0		16√2 πε0

   
   E = -2a_z
   

   Correct Option: B

   
   

   E = E1 + E2 =	1			Q1R1	+	Q2R2
   	4πε0			R13		R23

   
   
   

   E =	1			Q1	( √2ax + √2ay - 2az ) -	Q1	( √2ax + √2ay + 2az )
   	4πε0			16√2		16√2

   
   

   =	Q	[-4az ] =	32√2 πε0	(-az)
   	16√2 × 4πε0		16√2 πε0

   
   E = -2a_z
   

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160. A series RLC circuit s observed at two frequencies. At ω₁ = 1 k rad/s, we note that source voltage V₁ = 100 ∠0°V results in current I₁ = 0.03 ∠31° A. At ω₂ = 2 krad/s, the source volt age V₂ = 100 ∠0° V results in a current I₂ = 2 ∠0° A. The closest values for R, L, C out of the following options are
     

1. 1. R = 50 Ω ; L = 25mH ; C =10μF;

   
   
   

   2. R = 50 Ω ; L =10mH ; C = 25μF;

   
   
   

   3. R = 50 Ω ; L = 50mH ; C = 5μF;

   
   
   

   4. R = 50 Ω ; L = 5mH ; C = 50μF;

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   at ω₂ = 2000 r/sec
   
   

   φ = 31° ⇒ tan-1		XL - XC
   		R

   
   

   ⇒ tan31° =		XL - XC
   		R

   
   

   tan31° =		ω1L -	1
   			ω1C
   		R

   
   

   ⇒		ω1L -	1		= 0.600 × 50
   			ω1C

   
   

   ⇒		ω1L -	1		= 30.04 q ......(1)
   			ω1C

   
   

   ⇒	ω2L -	1	= 0 ......(2)
   		ω2C

   
   ω₁ = 1000 r / sec ;
   ω₂ = 2000 r / sec
   from 1 and 2, C = 25 μF
   L = 10 mH
   

   Correct Option: B

   
   at ω₂ = 2000 r/sec
   
   

   φ = 31° ⇒ tan-1		XL - XC
   		R

   
   

   ⇒ tan31° =		XL - XC
   		R

   
   

   tan31° =		ω1L -	1
   			ω1C
   		R

   
   

   ⇒		ω1L -	1		= 0.600 × 50
   			ω1C

   
   

   ⇒		ω1L -	1		= 30.04 q ......(1)
   			ω1C

   
   

   ⇒	ω2L -	1	= 0 ......(2)
   		ω2C

   
   ω₁ = 1000 r / sec ;
   ω₂ = 2000 r / sec
   from 1 and 2, C = 25 μF
   L = 10 mH
   

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