## Network Theory MCQ Set 1

1. For the function F (s) = (s^{2}+s+1)/s(s+5)(s+3), after splitting this function into partial fractions, the co-efficient of the term 1/s is?

a) 1/5

b) 1/10

c) 1/15

d) 1/20

### View Answer

^{2}+s+1)/(s+5)(s+3) |s=0 =1/15.

2. For the question 1, the co-efficient of 1/(s+5) is?

a) 1.1

b) 2.1

c) 3.1

d) 4.1

### View Answer

^{2}+s+1)/s(s+3) |s=-5 =2.1.

3. For the question 1, co-efficient of 1/(s+3) is?

a) -1.17

b) 1.17

c) -2.27

d) 2.27

### View Answer

^{2}+s+1)/s(s+5) |s=-3 = -1.17.

4. The partial fraction expansion of the function in question 1 is?

a) 1/15s-2.1/(s+5)+1.17/(s+3)

b) 1/15s-2.1/(s+5)-1.17/(s+3)

c) 1/15s+2.1/(s+5)+1.17/(s+3)

d) 1/15s+2.1/(s+5)-1.17/(s+3)

### View Answer

^{2}+s+1)/s(s+5)(s+3) =1/15s+2.1/(s+5)-1.17/(s+3).

5. For the function F (s) = (s+5)/s(s^{2}+2s+5) , after splitting this function into the partial fractions, 1/s co-efficient is?

a) 1

b) 2

c) 3

d) 4

### View Answer

^{2}+2s+5) )=1.

6. For the question 5, the co-efficient of 1/(s+1-j2) is?

a) 1/2

b) -1/2

c) 1/4

d) -1/4

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7. For the question 5, determine the co-efficient of 1/(s+1-j2)?

a) -1/4

b) 1/4

c) -1/2

d) 1/2

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8. The expression of F (s) after splitting into partial fractions in the question 5 is?

a) 1/s-1/2(s+1-j2) -1/2(s+1+j2)

b) 1/s+1/2(s+1-j2) -1/2(s+1+j2)

c) 1/s+1/2(s+1-j2) +1/2(s+1+j2)

d) 1/s-1/2(s+1-j2) +1/2(s+1+j2)

### View Answer

^{2}+2s+5) =1/s-1/2(s+1-j2) -1/2(s+1+j2).

9. The inverse transform of F (s) in the question 5 is?

a) 1+ 1/2 e^{(-1+j2)t}-1/2 e^{(-1-j2)t}

b) 1+ 1/2 e^{(-1+j2)t}+1/2 e^{(-1-j2)t}

c) 1- 1/2 e^{(-1+j2)t}-1/2 e^{(-1-j2)t}

d) 1- 1/2 e^{(-1+j2)t}+1/2 e^{(-1-j2)t}

### View Answer

^{(-1+j2)t}-1/2 e

^{(-1-j2)t}.

10. The inverse transform of the function k/(s+a) is?

a) ke^{-at} u(t)

b) ke^{at} u(t)

c) ke^{-at} u(t-a)

d) ke^{at} u(t-a)

### View Answer

^{at}u(t). k/(s+a) <—–> ke

^{at}u(t).

## Network Theory MCQ Set 2

1. Kirchhoff’s Current law is based on law of conservation of

a) energy

b) momentum

c) mass

d) charge

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2. The current law represents a mathematical statement of fact that

a) voltage cannot accumulate at node

b) charge cannot accumulate at node

c) charge at the node is infinite

d) none of the mentioned

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3. Kirchhoff’s current law is applied at

a) loops

b) nodes

c) both loop and node

d) none of the mentioned

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4. Determine the current in all resistors in the circuit shown below:

a) 2A, 4A, 11A

b) 5A, 4.8A, 9.6A

c) 9.3A, 20.22A, 11A

d) 10.56A, 24.65A, 14.79A

### View Answer

_{1}=V/7 ,i

_{2}=V/3 , i

_{3}=V/5.By current law , 50A = V/7 + V/3 + V/5. On solving, we obtain V and then values of i

_{1},i

_{2}, i

_{3}.

5. For the circuit below , find the voltage across 5Ω resistor and the current through it

a) 1.93 V

b) 2.83 V

c) 3.5 V

d) 5.7 V

### View Answer

_{15}=V/15 , i

_{5}=V/5 , i

_{2}=V/2 , i

_{1}=V/1. By kirchhoff’s current law, V/15 + V/5 + V/2 V/1 +5 = 10. On solving equation, we obtain the value of V. As all resistors are in parallel, voltage across each is same as V.

6. Determine the current through the resistor R3 shown in the figure using KCL

a) 25mA

b) 10mA

c) 20mA

d) 35mA

### View Answer

_{3}.

7. Find the current i3 in the circuit shown below

a) 2A

b) 1A

c) 3A

d) 0.5A

### View Answer

_{3}.

8. Kirchhof’s current law can be mathematically stated as :

a) ∑_{k=0}^{n} I = 0

b) i^{2}∑_{k=0}^{n} I = 0

c) i∑_{k=0}^{n} I = 0

d) none of the mentioned

### View Answer

9. Determine the current if a 20 coulomb charge passes a point in 0.25 seconds

a) 10 A

b) 20 A

c) 2 A

d) 80 A

### View Answer

10. Find the current through the branch containing resistance R3

a) 2A

b) 3.25A

c) 2A

d) 2.75A

### View Answer

_{3}.

## Network Theory MCQ Set 3

1. Kirchhoff’s voltage law is based on principle of conservation of

a) energy

b) momentum

c) mass

d) charge

### View Answer

2. In a circuit with more number of loops, which law can be best suited for the analysis?

a) KCL

b) Ohm’s law

c) KVL

d) None of the mentioned

### View Answer

3. Determine the unknown voltage drop in the circuit below

a) 11V

b) 10V

c) 19V

d) 5V

### View Answer

4. Determine V in the circuit

a) 28.8V

b) 34.4v

c) -28.8V

d) 28V

### View Answer

5. Find V and I in the circuit

a) -39V , -4.875A

b) 39V , -4.875A

c) -39v , 4.875a

d) 39V , 4.875A

### View Answer

6. Mathematically, Kirchhoff’s Voltage law can be as

a) ∑_(k=0)^{n}(V) = 0

b) V2∑_(k=0)^{n}(V) = 0

c) V∑_(k=0)^{n}(V) = 0

d) none of the mentioned

### View Answer

7. Determine the value of V and the power supplied by the independent current source

a) 20V , 300mw

b) 27V , 498mW

c) 26.6v , 532mW

d) 25V , 322mW

### View Answer

8. Determine V in the circuit

a) -11.6V

b) 23.2V

c) -23.2V

d) 11.6V

### View Answer

_{1}+ V6 =0. But V4 = 4*4=16V. Obtain V6 and I6=V6/6. Again apply KVL to central loop i.e, -V6 + V8 + V = 0. Apply KCL to the first node again, seek the value of V8 and finally we get V.

9. Find V and I in the circuit

a) 19V, 0.0633A

b) -19V, 0.0633A

c) 19V, -0.0633A

d) -19V,- 0.0633A

### View Answer

## Network Theory MCQ Set 4

1. The current in a closed path in a loop is called?

a) loop current

b) branch current

c) link current

d) twig current

### View Answer

2. Tie-set is also called?

a) f loop

b) g loop

c) d loop

d) e loop

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3. Consider the graph shown below. If a tree of the graph has branches 4, 5, 6, then one of the twigs will be?

a) 1

b) 2

c) 3

d) 4

### View Answer

4. Consider the graph shown in the question 3 above. If a tree of the graph has branches 4, 5, 6, then one of the links will be?

a) 3

b) 4

c) 5

d) 6

### View Answer

5. The loop current direction of the basic loop formed from the tree of the graph is?

a) same as the direction of the branch current

b) opposite to the direction of the link current

c) same as the direction of the link current

d) opposite to the direction of the branch current

### View Answer

6. Consider the graph shown below. The direction of the loop currents will be? (ACW – Anticlockwise, CW – Clockwise).

a) I_{1} ACW

b) I_{2} ACW

c) I_{3} CW

d) I_{4} ACW

### View Answer

_{1}– ACW, I

_{2}– CW, I

_{3}– ACW, I

_{4}– CW.

7. For Tie-set matrix, if the direction of current is same as loop current, then we place ___ in the matrix.

a) +1

b) -1

c) 0

d) +1 or -1

### View Answer

8. If a row of the tie set matrix is as given below, then its corresponding equation will be?

1 2 3 4 5 6 7 8

I_{1} -1 +1 0 0 +1 0 0 0

a) -V_{1}+V_{2}+V_{3}=0

b) -I_{1}+I_{2}+I_{3}=0

c) -V_{1}+V_{2}-V_{3}=0

d) -I_{1}+I_{2}-I_{3}=0

### View Answer

_{1}+V

_{2}+V

_{3}=0.

9. The matrix formed by link branches of a tie set matrix is?

a) Row matrix

b) Column matrix

c) Diagonal matrix

d) Identity matrix

### View Answer

10. The number of tie set matrices formed from a graph are?

a) N^{N-1}

b) N^{N}

c) N^{N-2}

d) N^{N+1}

### View Answer

^{N-2}tie set matrices.

## Network Theory MCQ Set 5

1. The maximum power is delivered from a source to its load when the load resistance is ______ the source resistance.

a) greater than

b) less than

c) equal to

d) less than or equal to

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2. If source impedance is complex, then maximum power transfer occurs when the load impedance is _______ the source impedance.

a) equal to

b) negative of

c) complex conjugate of

d) negative of complex conjugate of

### View Answer

3. If the source impedance is complex, then the condition for maximum power transfer is?

a) Z_{L} = Z_{S}

b) Z_{L} = Z_{S}*

c) Z_{L} = -Z_{S}

d) Z_{L} = -Z_{S}*

### View Answer

_{L}= Z

_{S}*.

4. If Z_{L} = Z_{S}*, then?

a) R_{L} = 1

b) R_{L} = 0

c) R_{L} = -R_{S}

d) R_{L} = R_{S}

### View Answer

_{L}= Z

_{S}*, then R

_{L}= R

_{S}. This means that the maximum power transfer occurs when the load impedance is equal to the complex conjugate of source impedance Z

_{S}.

5. For Z_{L} = Z_{S}*, the relation between X_{L} and X_{S} is?

a) X_{L} = X_{S}

b) X_{L} = 0

c) X_{L} = 1

d) X_{L} = -X_{S}

### View Answer

_{L}= Z

_{S}*, the relation between X

_{L}and X

_{S}is X

_{L}= -X

_{S}. Maximum power transfer is not always desirable since the transfer occurs at a 50 percent efficiency.

6. In the circuit shown below, find the value of load impedance for which source delivers maximum power.

a) 15-j20

b) 15+j20

c) 20-j15

d) 20+j15

### View Answer

_{S}. Z

_{L}= Z

_{S}

^{*}= (15-j20) Ω.

7. The load current in the circuit shown in the question 6 is?

a) 1.66∠90⁰

b) 1.66∠0⁰

c) 2.66∠0⁰

d) 2.66∠90⁰

### View Answer

^{o})/(15+j20+15-j20) =1.66∠0

^{o}A.

8. The maximum power delivered by the source in the circuit shown in the question 6 is?

a) 39.33

b) 40.33

c) 41.33

d) 42.33

### View Answer

^{2}RxZ = 1.66

^{2}×15 = 41.33W.

9. For the circuit shown, the resistance R is variable from 2Ω to 50Ω. What value of R_{S} results in maximum power transfer across terminals ‘ab’.

a) 1

b) 2

c) 3

d) 4

### View Answer

_{L}is fixed, the maximum power transfer theorem does not apply. Maximum current flows in the circuit when R

_{S}is minimum. So R

_{S}= 2Ω.

10. Find the maximum power delivered by the source in the circuit shown in the question 9.

a) 96.6

b) 97.6

c) 98.6

d) 99.6

### View Answer

_{T}= R

_{S}– j5+ R

_{L}= 2-j5+20 = 22.56∠-12.8⁰Ω. I=V

_{S}/Z

_{T}= -50∠0⁰/22.56∠-12.8⁰ = 2.22∠-12.8⁰A. P = I

^{2}R= 2.22

^{2}×20=98.6W.