166. Consider the network graph shown in figure. Which one of the following is 'not' a tree of this graph?
     
     
     

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   Because tree is a graph which have all the nodes but there is no loop formed.

   Correct Option: B

   Because tree is a graph which have all the nodes but there is no loop formed.

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167. For a given network, the number of independent mesh equations (m) and the number of independent node equations (n) are related as follows— (A) (B) (C) (D)

1. 1. m > n always

   
   
   

   2. m < n always

   
   
   

   3. m = n always

   
   
   

   4. m ≥ or < n depending upon the form of the network.

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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168. For the given graph the incidence matrix `A' is given by—
     
     
     

1. 1. -1 -1 0
      0 1 0
      -1 0 -1

   
   
   

   2. 1 0 -1
      1 1 0
      0 -1 1

   
   
   

   3. 1 -1 0
      0 1 1
      -1 0 -1

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Since the incidance matrix is given by
   

   
   

   Correct Option: C

   Since the incidance matrix is given by
   

   
   

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169. A connected graph has `b' number of branches and `n' number of nodes. Its ranks is—
     

1. 1. b

   
   
   

   2. n

   
   
   

   3. b – 1

   
   
   

   4. n – 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   The rank of graph having node n = n – 1.

   Correct Option: D

   The rank of graph having node n = n – 1.

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170. The Norton equivalent across BB′ is given by—
     
     
     

1. 1. 
      

      RN =		50	Ω, Isc =	2	amp
      		26		5

   
   
   

   2. 
      

      RN =		50	Ω, Isc =	1	amp
      		13		5

   
   
   

   3. 
      

      RN =		50	Ω, Isc =	2	amp
      		13		5

   
   
   

   4. None of the above

   
   
   

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1. View Hint View Answer Discuss in Forum

   Calculation for R_N (i.e. R_th):
   The equivalent circuit is given by
   
   R_N = (20 || 10 + 10) || 5
   

   =		20	+ 10		|| 5 = 50 3 || 5
   		3

   
   

   =		250 / 3	=	250	=	50	Ω
   		(50 / 3) + 5		65		13

   
   Calculation for I_sc
   The equivalent circuit drawn in order to calculate I _sc first calculate I.
   

   I =	V
   	Req

   
   where R v_eq = the equivalent resistance as seen from the terminal AA′
   
   or R _eq = 20 + 10 || 10 = 20 + 5 = 25 Ω
   

   I =		10	=	2	amp. (Given, V = 10 Volt)
   		25		5

   
   =
   2
   

   =	1	amp.
   	5

   Correct Option: B

   Calculation for R_N (i.e. R_th):
   The equivalent circuit is given by
   
   R_N = (20 || 10 + 10) || 5
   

   =		20	+ 10		|| 5 = 50 3 || 5
   		3

   
   

   =		250 / 3	=	250	=	50	Ω
   		(50 / 3) + 5		65		13

   
   Calculation for I_sc
   The equivalent circuit drawn in order to calculate I _sc first calculate I.
   

   I =	V
   	Req

   
   where R v_eq = the equivalent resistance as seen from the terminal AA′
   
   or R _eq = 20 + 10 || 10 = 20 + 5 = 25 Ω
   

   I =		10	=	2	amp. (Given, V = 10 Volt)
   		25		5

   
   =
   2
   

   =	1	amp.
   	5

   
   

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