## Network Theory MCQ Set 1

1. Superposition theorem states that the response in any element is the ____________ of the responses that can be expected to flow if each source acts independently of other sources.

a) algebraic sum

b) vector sum

c) multiplication

d) subtraction

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2. Superposition theorem is valid for only linear systems.

a) true

b) false

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3. Determine the current through (2+j5) Ω impedance considering 50∠0⁰ voltage source.

a) 6.42∠77.47⁰

b) 6.42∠-77.47⁰

c) 5.42∠77.47⁰

d) 5.42∠-77.47⁰

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^{o}source is I

_{1}with the current source 20∠30⁰ A short-circuited. I

_{1}= (50∠0

^{o})/(2+j4+j5) = 5.42∠-77.47

^{o}A.

4. Find the voltage across (2+j5) Ω impedance considering 50∠0⁰ voltage source.

a) 30.16∠-9.28⁰

b) 30.16∠9.28⁰

c) 29.16∠-9.28⁰

d) 29.16∠9.28⁰

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_{1}= 5.42∠-77.47

^{o}(2+j5) = 29.16∠-9.28

^{o}V.

5. Find the current through (2+j5) Ω impedance considering 20∠30⁰ voltage source.

a) 8.68∠-42.53⁰

b) 8.68∠42.53⁰

c) 7.68∠42.53⁰

d) 7.68∠-42.53⁰

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_{2}= 20∠30

^{o}×j4/(2+j9) = 8.68∠42.53

^{o}A.

6. Determine the voltage across (2+j5) Ω impedance considering 20∠30⁰ voltage source.

a) 45.69∠-110.72⁰

b) 45.69∠110.72⁰

c) 46.69∠-110.72⁰

d) 46.69∠110.72⁰

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_{2}= 8.68∠42.53

^{o}(2+j5) = 46.69∠110.72⁰V.

7. Find the voltage across (2+j5) Ω impedance using Superposition theorem.

a) 40.85∠72.53⁰

b) 40.85∠-72.53⁰

c) 41.85∠72.53⁰

d) 41.85∠-72.53⁰

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_{1}and V

_{2}. => V = V

_{1}+V

_{2}= 29.16∠-9.28

^{o}+46.69∠110.72

^{o}=40.85∠72.53

^{o}V.

8. Determine the voltage V_{ab} considering the source 50∠0⁰V.

a) 50∠0⁰

b) 4∠0⁰

c) 54∠0⁰

d) 46∠0⁰

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9. Determine the voltage V_{ab} considering the source 4∠0⁰A in the circuit shown above.

a) 46∠0⁰

b) 4∠0⁰

c) 54∠0⁰

d) 50∠0⁰

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10. Find the voltage V_{ab} in the circuit shown above using Superposition theorem.

a) 4∠0⁰

b) 50∠0⁰

c) 54∠0⁰

d) 46∠0⁰

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_{1}and V

_{2}=> V

_{ab}= V

_{1}+V

_{2}= 50∠0⁰V.

## Network Theory MCQ Set 2

1. For the tank circuit shown below, find the resonant frequency.

a) 157.35

b) 158.35

c) 159.35

d) 160.35

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_{r}= (1/2π) √((1/LC)-(R

^{2}/L

^{2}) ).

2. The expression of ωr in parallel resonant circuit is?

a) 1/(2√LC)

b) 1/√LC

c) 1/(π√LC)

d) 1/(2π√LC)

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_{r}in parallel resonant circuit is ω

_{r}= 1/√LC.

3. The expression of bandwidth for parallel resonant circuit is?

a) 1/RC

b) RC

c) 1/R

d) 1/C

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4. The quality factor in case of parallel resonant circuit is?

a) C

b) ω_{r}RC

c) ω_{r}C

d) 1/ω_{r}RC

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_{r}RC. The impedance of parallel resonant circuit is maximum at the resonant frequency and decreases at lower and higher frequencies.

5. The quality factor is the product of 2π and the ratio of ______ to _________

a) maximum energy stored, energy dissipated per cycle

b) energy dissipated per cycle, maximum energy stored

c) maximum energy stored per cycle, energy dissipated

d) energy dissipated, maximum energy stored per cycle

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_{L}is very small and X

_{C}is very large so the total impedance is essentially inductive. The quality factor is the product of 2π and the ratio of maximum energy stored to energy dissipated per cycle.

6. The maximum energy stored in a capacitor is?

a) CV^{2}

b) CV^{2}/2

c) CV^{2}/4

d) CV^{2}/8

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^{2}/2. Maximum energy = CV

^{2}/2. As frequency increases the impedance also increases and the inductive reactance dominates until the resonant frequency is reached.

7. The expression of quality factor is?

a) I_{L}/I

b) I/I_{L}

c) IL

d) I

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_{L}/I. Quality factor = I

_{L}/I. At the the point X

_{L}= X

_{C}, the impedance is at its maximum.

8. The quality factor is defined as?

a) I

b) I_{C}

c) I/I_{C}

d) I_{C}/I

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_{C}/I. Quality factor = I

_{C}/I. As the frequency goes above resonance capacitive reactance dominates and impedance decreases.

9. In the circuit shown in the figure, an inductance of 0.1H having a Q of 5 is in parallel with a capacitor. Determine the value coil resistance (Ω) of at a resonant frequency of 500 rad/sec.

a) 10

b) 20

c) 30

d) 40

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_{r}L/R. L = 0.1H, Q = 5, ω

_{r}= 500 rad/sec. On solving, R = 10Ω. While plotting the voltage and current variation with frequency, at resonant frequency, the current is maximum.

10. Find the value of capacitance (µF) in the circuit shown in the question 9.

a) 10

b) 20

c) 30

d) 40

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^{2}

_{r}= 1/LC. L = 0.1H, ωr = 500 rad/sec. On solving, C = 40 µF. In order to tune a parallel circuit to a lower frequency the capacitance must be increased.

## Network Theory MCQ Set 3

1. The dual pair of current is?

a) voltage

b) current source

c) capacitance

d) conductance

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2. The dual pair of capacitance is?

a) capacitance

b) resistance

c) current source

d) inductance

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3. The dual pair of resistance is?

a) inductance

b) capacitance

c) conductance

d) current

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4. The dual pair of voltage source is?

a) voltage

b) current source

c) current

d) resistance

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5. The dual pair of KCL is?

a) KVL

b) current

c) voltage

d) current source

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6. Tellegen’s Theorem is valid for _____ network?

a) linear or non-linear

b) passive or active

c) time variant or time invariant

d) all the above

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7. For Tellegan’s Theorem to satisfy, the algebraic sum of the power delivered by the source is _____ than power absorbed by all elements.

a) greater

b) less

c) equal

d) greater than or equal

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8. Consider the circuit shown below. Find whether the circuit satisfies Tellegan’s theorem.

a) satisfies

b) does not satisfy

c) satisfies partially

d) satisfies only for some elements

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_{1}=i

_{2}=2A, i

_{3}=2A. V

_{1}=-2V, V

_{2}=-8V, V

_{3}=10V. Algebraic sum =

9. The circuit shown below satisfies Tellegen’s theorem.

a) True

b) False

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_{1}=i

_{2}=4A, i

_{3}=4A. V

_{1}=-20V, V

_{2}=0V, V

_{3}=20V. Algebraic sum =

10. If two networks have same graph with different type of elements between corresponding nodes, then?

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## Network Theory MCQ Set 4

1. Calculate the Z –parameter Z_{11} in the circuit shown below.

a) 1.5

b) 2.5

c) 3.5

d) 4.5

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_{11}is V

_{1}/I

_{1}, port 2 is open circuited. V

_{1}= (1+1.5)I

_{1}=> V

_{1}/I

_{1}= 2.5 and on substituting, we get Z

_{11}= 2.5Ω.

2. Determine the Z-parameter Z_{12} in the circuit shown in question 1.

a) 1

b) 2

c) 3

d) 4

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_{12}is V

_{2}/I

_{1}|I

_{2}=0. On open circuiting port 2 we obtain the equation, V

_{1}= (1.5) I

_{2}=> V

_{1}/I

_{1}= 1.5. On substituting we get Z

_{12}= 1.5Ω.

3. Determine the Z-parameter Z_{21} in the circuit shown in question 1.

a) 4

b) 3

c) 2

d) 1

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_{21}is V

_{2}/I

_{1}|I

_{2}=0. On open circuiting port 2, we get V

_{2}= (1.5)I

_{1}=> V

_{2}/I

_{1}= 1.5. On substituting we get Z

_{21}= 1.5Ω.

4. Determine the Z-parameter Z_{22} in the circuit shown in question 1.

a) 1

b) 3

c) 2

d) 4

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_{21}is V

_{2}/I

_{2}|I

_{1}=0. This parameter is obtained by open circuiting port 1. So we get V

_{2}= ((2+2)||4)I

_{2}=> V

_{2}= 2(I

_{2}) => V

_{2}/I

_{2}= 2. On substituting Z

_{21}= 2Ω.

5. Find the value of V_{1}/I_{1} in the circuit shown in question 1.

a) 1.25

b) 2.25

c) 3.25

d) 4.25

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_{1}/I

_{1}=Z

_{11}– Z

_{12}Z

_{21}/(Z

_{L}+Z

_{21}) and Z

_{L}is the load impedance and is equal to 2Ω. On solving V

_{1}/I

_{1}=2.5-1/(2+2)=2.25Ω.

6. Determine the input impedance of the network shown in question 1.

a) 4.25

b) 3.25

c) 2.25

d) 1.25

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_{in}= (V

_{1}/I

_{1}) + Source resistance. We had V

_{1}/I

_{1}= 2.25. On substituting Z

_{in}=1+2.25=3.25Ω.

7. Determine the value of source admittance in the circuit shown below.

a) 1

b) 2

c) 3

d) 4

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_{s}= 1 mho.

8. Find the value of I_{2}/V_{2} in the circuit shown in question 7.

a) 7/6

b) 6/7

c) 7/12

d) 12/7

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_{2}/V

_{2}and Y-parameters is I

_{2}/V

_{2}=(5/8×1+5/8×1/2-1/16)/(1+1/2)=7/12 mho.

9. The value of the Y-parameter Y_{22} in the circuit shown in question 7.

a) 12/7

b) 6/7

c) 7/6

d) 7/12

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_{22}and I

_{2}/V

_{2}is Y

_{22}= I

_{2}/V

_{2}. We have the relation I

_{2}/V

_{2}= (Y

_{22}Y

_{s}+Y

_{22}Y

_{11}-Y

_{21}Y

_{12})/(Y

_{s}+Y

_{11}). On substituting their values in the equation we get Y

_{22}= 7/12 mho.

10. The value of the Z-parameter Z_{22} in the circuit shown in question 7.

a) 6/7

b) 7/12

c) 12/7

d) 7/6

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_{22}is inverse of the Y-parameter Y

_{22}i.e., Z

_{22}= 1/Y

_{22}. We got Y

_{22}= 7/12. So on substituting we get Z

_{22}= 12/7 mho.

## Network Theory MCQ Set 5

1. The condition for maximum voltage to be transferred to the load is?

a) Source resistance greater than load resistance

b) Source resistance less than load resistance

c) Source resistance equal to load resistance

d) Source resistance greater than or equal to load resistance

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2. The condition for maximum current to be transferred to the load is?

a) Source resistance greater than or equal to load resistance

b) Source resistance equal to load resistance

c) Source resistance less than load resistance

d) Source resistance greater than load resistance

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3. The condition for maximum power to be transferred to the load is?

a) Source resistance equal to load resistance

b) Source resistance greater than load resistance

c) Source resistance greater than or equal to load resistance

d) Source resistance less than load resistance

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4. In the circuit shown determine the value of load resistance when the load resistance draws maximum power?

a) 50

b) 25

c) 75

d) 100

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5. Find the value of the maximum power in the circuit shown in the question 4.

a) 25

b) 50

c) 75

d) 100

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^{2}×R

_{L}. On substituting the values obtained and given we get maximum power in the circuit is (1)

^{2}×25=25W.

6. If the source Z_{S} is complex, then the condition for the maximum power to be transferred is?

a) Z_{L}=Z_{S}

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

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

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

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_{L}=Z

_{S}* that is load impedance is complex conjugate of source impedance.

7. If Z_{S}=R_{S}+jX_{S}, Z_{L}=R_{L}, then condition for maximum power to be transferred is?

a) R_{L}=|Z_{S}|

b) R_{L}=Z_{S}

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

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

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_{S}=R

_{S}+jX

_{S}, Z

_{L}=R

_{L}, then condition for maximum power to be transferred is R

_{L}=|Z

_{S}| that is maximum power is transferred when the load resistance is equal to the magnitude of the source impedance.

8. Find the load resistance so that the load draws maximum power.

a) 6

b) 7

c) 8

d) 9

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9. Find the maximum power (mW) that is delivered by the source in the circuit shown in the question 8.

a) 50

b) 51

c) 52

d) 53

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_{a}=50×6/(10+6)=18.75V, V

_{b}=50×8/(15+8)=17.39V. V

_{ab}= V

_{a}– V

_{b}= 18.75 – 17.39 = 1.36V. I=1.36/(9+9)=75mA. P=I

^{2}R=(0.075)

^{2}×9=0.051W ≅51mW.

10. If Z_{S}= R_{S}+jX_{S}, Z_{L}=R_{L}+jX_{L}, then if R_{L} is fixed, the condition for maximum power to be transferred is?

a) X_{S}=X_{L}

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

c) X_{S}+X_{L}=0

d) None of the above

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_{S}= R

_{S}+jX

_{S}, Z

_{L}=R

_{L}+jX

_{L}, then if R

_{L}is fixed, the condition for maximum power to be transferred is X

_{S}=-X

_{L}.