146. 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

   We know that loop = b – n + 1
   where b = no. of branch,
   n = no. of nodes
   so alternative (C) is correct.

   Correct Option: C

   We know that loop = b – n + 1
   where b = no. of branch,
   n = no. of nodes
   so alternative (C) is correct.

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147. A network has 7 nodes and 5 independent loops. The number of branches in the network is—

1. 1. 13

   
   
   

   2. 12

   
   
   

   3. 11

   
   
   

   4. 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that network has 7 nodes and 5 independent loop.
   B – L + 1 = nodes
   B – 5 + 1 = 7
   B = 12 – 1 = 11

   Correct Option: C

   Given that network has 7 nodes and 5 independent loop.
   B – L + 1 = nodes
   B – 5 + 1 = 7
   B = 12 – 1 = 11

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148. 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 minimum number of branches not decided by N.

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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149. If the number of branches in a network is B, the number of nodes is N and the number of dependent loop is L, then the number of independent node equations will be—

1. 1. N + L – 1

   
   
   

   2. B – 1

   
   
   

   3. N – 1

   
   
   

   4. B – N

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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150. The incandescent bulbs respectively as P₁ and P₂ for operation at a specified main voltage are connected in series across the mains as shown in the figure, then the total power supplied by the mains to the two bulbs—
     
     
     

1. 1. 	P1 P2
      	P1 + P2

   
   
   

   2. P² ₁ + P² ₂

   
   
   

   3. (P₁ + P₂)

   
   
   

   4. P₁ × P₂
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Since the bulbs are connected in series
   so, P₁ = I₁ ² R₁
   P₂ = I₁ ² R₂
   Total power supplied
   (P) = I₁ ² (R₁ + R₂) = P₁ + P₂

   Correct Option: D

   Since the bulbs are connected in series
   so, P₁ = I₁ ² R₁
   P₂ = I₁ ² R₂
   Total power supplied
   (P) = I₁ ² (R₁ + R₂) = P₁ + P₂

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