31. The voltage V_C1, V_C2 and V_C3 across the capacitors in the circuit in the given figure, under steady state are respectively
    
    

1. 1. 80 V, 32 V, 48 V

   
   
   

   2. 80 V, 48 V, 32 V

   
   
   

   3. 20 V, 8 V, 12 V

   
   
   

   4. 20 V, 12 V, 8 V

   
   
   

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1. View Hint View Answer Discuss in Forum

   In steady state, capacitors are open and inductances are short.
   
   For V_C1
   

   VC1 = 100 ×	40	= 80 V
   	50

   
   For V_C2 and V_C3
   

   VC2 = 80 ×	C3
   	C2 + C3

   
   

   = 80 ×	3	= 48 V
   	5

   
   

   VC3 = 80 ×	C2
   	C2 + C3

   
   = 16 × 2 = 32 V
   

   Correct Option: B

   In steady state, capacitors are open and inductances are short.
   
   For V_C1
   

   VC1 = 100 ×	40	= 80 V
   	50

   
   For V_C2 and V_C3
   

   VC2 = 80 ×	C3
   	C2 + C3

   
   

   = 80 ×	3	= 48 V
   	5

   
   

   VC3 = 80 ×	C2
   	C2 + C3

   
   = 16 × 2 = 32 V
   

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32. When the angular frequency ω in the given figure is varied from 0 to ∞ , the locus of the current phasor I₂ is given by
    

1. 1. 
      

   
   
   

   2. 
      

   
   
   

   3. 
      

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   I2(ω) =	Em cosωt
   	R2 +	1
   		jωC

   
   
   
   

   At ω = ∞ , I2ω =	Em
   	R2

   
   Also, I₂ is leading with voltage phasor.
   At ω = 0, I₂ (0) = 0
   Thus desired locus should be as shown.

   Correct Option: A

   I2(ω) =	Em cosωt
   	R2 +	1
   		jωC

   
   
   
   

   At ω = ∞ , I2ω =	Em
   	R2

   
   Also, I₂ is leading with voltage phasor.
   At ω = 0, I₂ (0) = 0
   Thus desired locus should be as shown.

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33. The circuit shown in the given figure in resonates at
    
    

1. 1. all frequencies

   
   
   

   2. 0.5 rad/sec

   
   
   

   3. 5 rad/sec

   
   
   

   4. 1 rad/sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   Input impedance of the circuit,
   

   Z = 10 +		1	||		4jω +	1
   		jω				jω

   
   
   

   = 10 +	[1 - 4ω2]
   	jω[2 - 4ω2]

   Correct Option: B

   Input impedance of the circuit,
   

   Z = 10 +		1	||		4jω +	1
   		jω				jω

   
   
   

   = 10 +	[1 - 4ω2]
   	jω[2 - 4ω2]

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34. For the circuit show in the (given figure) i(t) under steady state is
    
    

1. 1. zero

   
   
   

   2. 5

   
   
   

   3. 7.07 sin t

   
   
   

   4. 7.07 sin (t – 45°)

   
   
   

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1. View Hint View Answer Discuss in Forum

   d.c. voltage 5V would encounter an open circuit in the capacitor and hence the current is 0.
   
   

   For a.c , i(t) =	10 sin t
   	1 + j2 +	1
   		j

   
   

   =	10 sin t	=	10	sin (t - 45°)
   	1 + j		√2

   
   = 7.07 sin (t – 45°)
   

   Correct Option: D

   d.c. voltage 5V would encounter an open circuit in the capacitor and hence the current is 0.
   
   

   For a.c , i(t) =	10 sin t
   	1 + j2 +	1
   		j

   
   

   =	10 sin t	=	10	sin (t - 45°)
   	1 + j		√2

   
   = 7.07 sin (t – 45°)
   

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35. Switch S in the given figure is closed at t = 0. If v₂ (0) = 10 V and v_g (0) = 0 V respectively, voltage across the capacitors in steady state will be
    
    

1. 1. v₂ (∞) = v_g (∞) = 0

   
   
   

   2. v₂ (∞) = 2V, v_g (∞) = 8 V

   
   
   

   3. v₂ (∞) = v_g (∞) = 8 V

   
   
   

   4. v₂ (∞) = v_g (∞) = 2 V

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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