191. In the circuit shown in the given figure, the values of I(0⁺) and I(∞), will be, respectively
     
     

1. 1. zero and 1.5 A

   
   
   

   2. 1.5 A and 3 A

   
   
   

   3. 3 A and zero

   
   
   

   4. 3 A and 1.5 A

   
   
   

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1. View Hint View Answer Discuss in Forum

   I(s) =	3
   	(s + 1)		1 +	1
   				2s

   
   

   =	3
   	(s + 0.5)(s + 1)

   
   

   =	-3	+	6
   	(s + 0.5)		(s + 1)

   
   ⇒ i (t) = L^{– 1}(I(s)) = 6e^{– t} – 3e^{– 0.5t}
   At t = 0, i (0⁺) = 3A,
   and at t = ∞, i (∞) = 0

   Correct Option: C

   I(s) =	3
   	(s + 1)		1 +	1
   				2s

   
   

   =	3
   	(s + 0.5)(s + 1)

   
   

   =	-3	+	6
   	(s + 0.5)		(s + 1)

   
   ⇒ i (t) = L^{– 1}(I(s)) = 6e^{– t} – 3e^{– 0.5t}
   At t = 0, i (0⁺) = 3A,
   and at t = ∞, i (∞) = 0

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192. Consider the graph and tree (dotted) of the given figure. The fundamental loops include the set of lines
     
     

1. 1. (1, 5, 3), (5, 4, 2) and (3, 4, 6)

   
   
   

   2. (1, 2, 4, 3), (1, 2, 6), (3, 4, 6) and (1, 5, 4, 6)

   
   
   

   3. (1, 5, 3), (5, 4, 2), (3, 4, 6) and (2, 4, 3, 1)

   
   
   

   4. (1, 2, 3) and (3, 4, 6)

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA
   

   Correct Option: D

   NA
   

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193. A connected network of N > 2 nodes has at most one branch directly connecting any pair of nodes. The graph of the network
     

1. 1. must have at least N branches for one or more closed paths to exist

   
   
   

   2. can have an unlimited number of branches

   
   
   

   3. can only have at most N branches

   
   
   

   4. can have a minimum number of branches not decided by N.

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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194. The number of independent loops for a network with n nodes and b branch is
     

1. 1. n – 1

   
   
   

   2. b – n

   
   
   

   3. b – n + 1

   
   
   

   4. independent of the number of nodes

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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195. In the circuit shown in the figure, X is an element which always absorbs power during a particular operation it sets up a current of 1 amp in the direction shown and absorbs a power P_x. It is possible that X can absorb the same power P_x for another current I. the value of this current is
     
     
     

1. 1. (3 – √14) amps

   
   
   

   2. (3 + √14 amps

   
   
   

   3. 5 amps

   
   
   

   4. none of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   As element absorbs power, let it be R_x.
   

   i = 1 =	6
   	Rx + 1

   
   ⇒ R_x = 5 Ω
   

   P =		6		2	× 5 = 5 W
   		6

   
   For 5A, P = 5² × 5 = 125 W
   For 3 + √14, P = 227 W
   For 3 – √14, P = 2.75 W
   Hence none of the above is correct.

   Correct Option: D

   As element absorbs power, let it be R_x.
   

   i = 1 =	6
   	Rx + 1

   
   ⇒ R_x = 5 Ω
   

   P =		6		2	× 5 = 5 W
   		6

   
   For 5A, P = 5² × 5 = 125 W
   For 3 + √14, P = 227 W
   For 3 – √14, P = 2.75 W
   Hence none of the above is correct.

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