## Network Theory MCQ Set 1

1. If a resistor R_{x} is connected between nodes X and Y, R_{y} between X and Y, R_{z} between Y and Z to form a delta connection, then after transformation to star, the resistor at node X is?

a) R_{x}R_{y}/( R_{x}+R_{y}+R_{z})

b) R_{x}R_{z}/(R_{x}+R_{y}+R_{z})

c) R_{z}R_{y}/(R_{x}+R_{y}+R_{z})

d) (R_{x}+R_{y})/(R_{x}+R_{y}+R_{z})

### View Answer

_{x}R

_{y}/( R

_{x}+R

_{y}+R

_{z}) and this resistance lies between R

_{x}, R

_{y}in star connection.

2. In the question above the resistance at node Y is?

a) R_{z}R_{y}/(R_{x}+R_{y}+R_{z})

b) R_{z}R_{x}/(R_{x}+R_{y}+R_{z})

c) R_{x}R_{y}/(R_{x}+R_{y}+R_{z})

d) (R_{z}+R_{y})/(R_{x}+R_{y}+R_{z})

### View Answer

_{z}R

_{x}/(R

_{x}+R

_{y}+R

_{z}) and this resistance lies between R

_{x}, R

_{z}in star connection.

3. In the question above, the resistance at node Z is?

a) R_{y}R_{x}/(R_{x}+R_{y}+R_{z})

b) R_{y}R_{x}/(R_{x}+R_{y}+R_{z})

c) R_{z}R_{y}/(R_{x}+R_{y}+R_{z})

d) (R_{z}+R_{x})/(R_{x}+R_{y}+R_{z})

### View Answer

_{z}R

_{y}/(R

_{x}+R

_{y}+R

_{z}) and this resistance lies between R

_{z}, R

_{y}in star connection.

4. If the resistors of star connected system are R_{1}, R_{2}, R_{3} then the resistance between 1 and 2 in delta connected system will be?

a) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{3}

b) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{1}

c) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{2}

d) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/(R_{1}+R_{2})

### View Answer

_{1}R

_{2}+ R

_{2}R

_{3}+ R

_{3}R

_{1})/R

_{3}and this resistance lies between R

_{1}, R

_{2}in delta connection.

5. If the resistors of star connected system are R_{1}, R_{2}, R_{3} then the resistance between 2 and 3 in delta connected system will be?

a) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{3}

b) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{2}

c) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{1}

d) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/(R_{3}+R_{2})

### View Answer

_{1}R

_{2}+ R

_{2}R

_{3}+ R

_{3}R

_{1})/R

_{1}and this resistance lies between R

_{3}, R

_{2}in delta connection.

6. If the resistors of star connected system are R_{1}, R_{2}, R_{3} then the resistance between 3 and 1 in delta connected system will be?

a) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{1}

b) ( R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{3}

c) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/R_{2}

d) (R_{1}R_{2}+ R_{2}R_{3}+ R_{3}R_{1})/(R_{3}+R_{1})

### View Answer

_{1}R

_{2}+ R

_{2}R

_{3}+ R

_{3}R

_{1})/R

_{2}and this resistance lies between R

_{1}, R

_{3}in delta connection.

7. Find the equivalent resistance at node A in the delta connected circuit shown in the figure below.

a) 1

b) 2

c) 3

d) 4

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8. Find the equivalent resistance at node C in the delta connected circuit shown in the figure in the question 7.

a) 3.66

b) 4.66

c) 5.66

d) 6.66

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9. Find the equivalent resistance between node 1 and node 3 in the star connected circuit shown below.

a) 30

b) 31

c) 32

d) 33

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10. Find the equivalent resistance between node 1 and node 2 in the star connected circuit shown in the question 9.

a) 2

b) 29

c) 30

d) 31

### View Answer

## Network Theory MCQ Set 2

1. Impedance is a complex quantity having the real part as _______ and the imaginary part as ______

a) resistance, resistance

b) resistance, reactance

c) reactance, resistance

d) reactance, reactance

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2. The voltage function v(t) in the circuit shown below is?

a) v(t) = V_{m} e^{-tjω}

b) v(t) = V_{m}e^{tjω}

c) v(t) = e^{tjω}

d) v(t) = e^{-tjω}

### View Answer

_{m}e

^{tjω}=Vm(cosωt+jsinωt).

3. The current i(t) in the circuit shown above is?

a) i(t)=(V_{m}/(R-jωL))e^{tjω}

b) i(t)=(V_{m}(R+jωL)) e^{tjω}

c) i(t)=(V_{m}(R-jωL)) e^{tjω}

d) i(t)=(V_{m}/(R+jωL)) e^{tjω}

### View Answer

_{m}e

^{tjω}. V

_{m}e

^{tjω}=RI

_{m}e

^{tjω}+L d/dt (I

_{m}e

^{tjω}). V

_{m}e

^{tjω}=RI

_{m}e

^{tjω}+L I

_{m}(jω)e

^{tjω}. I

_{m}= V

_{m}/(R+jωL). i(t)=(V

_{m}/(R+jωL)) e

^{tjω}.

4. The impedance of the circuit shown below is?

a) R + jωL

b) R – jωL

c) R + 1/jωL

d) R – 1/jωL

### View Answer

_{m}e

^{tjω}/((V

_{m}/(R+jωL)) e

^{tjω})=R+jωL.

5. The magnitude of the impedance of the circuit shown above.

a) √( R+ωL)

b) √(R-ωL)

c)√(R^{2}+(ωL)^{2} )

d) √(R^{2}-(ωL)^{2} )

### View Answer

^{2}+(ωL)

^{2}).

6. The phase angle between current and voltage in the circuit shown above is?

a) tan^{-1}ωL/R

b) tan^{-1}ωR/

c) tan^{-1}R/ωL

d) tan^{-1}L/ωR

### View Answer

^{-1}ωL/R

7. The voltage function v(t) in the circuit shown below is?

a) v(t) = e^{-tjω}

b) v(t) = e^{tjω}

c) v(t) = V_{m}e^{tjω}

d) v(t) = V_{m}e^{-tjω}

### View Answer

_{m}e

^{tjω}.

8. The impedance of the circuit shown above is?

a) R + jωC

b) R – jωC

c) R + 1/jωC

d) R – 1/jωC

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9. The magnitude of the impedance of the circuit shown above is?

a) √(R+1/ωC)

b) √(R-1/ωC)

c) √(R^{2}+(1/ωC)^{2} )

d) √(R^{2}-(1/ωC)^{2} )

### View Answer

^{2}+(1/ωC)

^{2}). Here the impedance is the vector sum of the resistance and the capacitive reactance.

10. The angle between resistance and impedance in the circuit shown above.

a) tan^{-1}1/ωRC

b) tan^{-1}C/ωR

c) tan^{-1}R/ωC

d) tan^{-1}ωRC

### View Answer

^{-1}1/ωRC. The angle between resistance and impedance is the phase angle between the applied voltage and current in the circuit.

## Network Theory MCQ Set 3

1. For the circuit shown below, find the voltage across the capacitor C_{1} at the time the switch is closed.

a) 0

b) V/4

c) V/2

d) V

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2. The charge on capacitor C_{2} in the circuit shown in question 1 is?

a) 0

b) 1

c) 2

d) 3

### View Answer

_{2}is zero. So, charge on capacitor C

_{2}= zero. Capacitor circuit and series inductor circuit are two different cicuits to illustrate how an impulse function can be created with a switching operation.

3. The current in the circuit shown in question 1 is?

a) (V/R)/(s+1/C_{e})

b) (V/R)/(s+1/RC_{e})

c) (V/R)/(s-1/RC_{e})

d) (V/R)/(s-1/C_{e})

### View Answer

_{1}+1/sC

_{2}) = (V/R)/(s+1/RC

_{e}) where the equivalent capacitance C

_{1}C

_{2}/(C

_{1}+C

_{2}) and is replaced by C

_{e}.

4. By taking the inverse transform of the current in the question 3, the value of the current is?

a) V/R e^{t/Ce}

b) V/R e^{t/RCe}

c) V/R e^{-t/RCe}

d) V/R e^{-t/Ce}

### View Answer

^{-t/RCe}which indicates that as R decreases, the initial current increases and the time constant decreases.

5. Consider the circuit shown below. On applying the Kirchhoff’s current law, the equation will be?

a) V/(2s-15)+(V-[(100/s)+30])/(3s+10)=0

b) V/(2s-15)+(V-[(100/s)+30])/(3s-10)=0

c) V/(2s+15)+(V-[(100/s)+30])/(3s+10)=0

d) V/(2s+15)+(V-[(100/s)+30])/(3s-10)=0

### View Answer

6. The value of the voltage V in the circuit shown in question 5 is?

a) 40(s+7.5)/s(s+5) -12(s+7.5)/(s-5)

b) 40(s+7.5)/s(s+5) -12(s+7.5)/(s+5)

c) 40(s+7.5)/s(s+5) +12(s+7.5)/(s-5)

d) 40(s+7.5)/s(s+5) +12(s+7.5)/(s+5)

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7. The value of the voltage V after taking the partial fractions in the question 5 is?

a) 12+ 60/s+10/(s+5)

b) 12- 60/s+10/(s+5)

c) 12- 60/s-10/(s+5)

d) 12+ 60/s-10/(s+5)

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8. Determine the voltage V after taking the inverse transform in the question 5.

a) 12δ(t)-(60-10e^{-5t})u(t)

b) 12δ(t)+(60+10e^{-5t})u(t)

c) 12δ(t)-(60+10e^{-5t})u(t)

d) 12δ(t)+(60-10e^{-5t})u(t)

### View Answer

^{-5t})u(t) volts and we have to derive the expression for the current when t > 0.

9. The current equation for the circuit shown in question 5 is?

a) I=4/s-2/(s-5)

b) I=4/s-2/(s+5)

c) I=4/s+2/(s+5)

d) I=4/s+2/(s-5)

### View Answer

_{1}is the same as the current in L

_{1}. The current equation is I=(100/s+30)/(5s+25). On solving we get I = 4/s-2/(s+5).

10. The value of the current after taking the inverse transform of the current in the question 5 is?

a) (4-2e^{5t} )u(t)

b) (4-2e^{-5t})u(t)

c) (4+2e^{5t})u(t)

d) (4-2e^{-5t})u(t)

### View Answer

^{-5t})u(t). Before the switch is opened,the current in L

_{1}is 10A and the current in L

_{2}is 0A.

## Network Theory MCQ Set 4

1. In purely resistive circuit, energy delivered by source is ____________ by resistance.

a) dissipated in the form of heat

b) stored as electric field

c) stored as magnetic field

d) returned to source

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2. In inductor, the energy delivered by source is ____________ by inductor.

a) stored as magnetic field

b) dissipated in the form of heat

c) returned to source

d) stored as electric field

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3. In capacitor, the energy delivered by source is ____________ by capacitor.

a) returned to source

b) dissipated in the form of heat

c) stored as electric field

d) stored as magnetic field

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4. If there is complex impedance in a circuit, part of energy is ____________ by reactive part and part of its energy is ____________ by the resistance.

a) alternately stored and returned, alternately stored and returned

b) alternately stored and returned, dissipated

c) dissipated, alternately stored and returned

d) dissipated, dissipated

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5. The equation of instantaneous power is?

a) P (t) = (V_{m}I_{m}/2)(cos(2ωt+θ)+sinθ)

b) P (t) = (V_{m}I_{m}/2)(sin(2ωt+θ)+cosθ)

c) P (t) = (V_{m}I_{m}/2)(cos(2ωt+θ)+cosθ)

d) P (t) = (V_{m}I_{m}/2)(sin(2ωt+θ)+sinθ)

### View Answer

_{m}I

_{m}/2)(cos(2ωt+θ)+cosθ). It consists of two parts. One is a fixed part and the other is time varying which has frequency twice that of the voltage or current wave forms.

6. The time varying part in the equation of instantaneous power has frequency ________________ that of the frequency of voltage or current wave forms.

a) equal to

b) twice

c) thrice

d) four times

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7. Instantaneous power is negative, when the polarities of voltage and current are of __________

a) opposite sign

b) same sign

c) voltage is zero

d) current is zero

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8. In P (t) equation, if θ=0, then P (t) =?

a) (V_{m}I_{m}/2)(1+cosωt)

b) (V_{m}I_{m}/2)(cosωt)

c) (V_{m}I_{m}/2)(cos2ωt)

d) (V_{m}I_{m})(1+cos2ωt)

### View Answer

_{m}I

_{m}/2)(1+cos2ωt). The power wave has a frequency twice that of the voltage or current. Here the average value of power is V

_{m}I

_{m}/2.

9. The average value of power if θ=0⁰ is?

a) V_{m}I_{m}/2

b) V_{m}I_{m}/2

c) V_{m}I_{m}/4

d) V_{m}I_{m}/8

### View Answer

_{m}I

_{m}/2. So, average power = V

_{m}I

_{m}/2 at θ=0⁰. When phase angle is increased the negative portion of the power cycle increases and lesser power is dissipated.

10. At θ=π/2, positive portion is __________ negative portion in power cycle.

a) greater than

b) less than

c) equal to

d) greater than or equal to

### View Answer

## Network Theory MCQ Set 5

1.In the circuit shown below, find the Z-parameter Z_{11}.

a) 1

b) 2

c) 3

d) 4

### View Answer

_{11}is V

_{1}/I

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

_{1}= (1+2)I

_{1}=> V

_{1}/I

_{1}= 3 and on substituting, we get Z

_{11}= 3Ω.

2. In the circuit shown in question 1, find the Z-parameter Z_{12}.

a) 4

b) 3

c) 2

d) 1

### View Answer

_{12}is V

_{2}/I

_{1}|I

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

_{1}= (2) I

_{2}=> V

_{1}/I

_{1}= 2. On substituting we get Z

_{12}= 2Ω.

3. In the circuit shown in question 1, find the Z-parameter Z_{21}.

a) 2

b) 4

c) 1

d) 3

### View Answer

_{21}is V

_{2}/I

_{1}|I

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

_{2}= (2)I

_{1}=> V

_{2}/I

_{1}= 2. On substituting we get Z

_{21}= 2Ω.

4. In the circuit shown in question 1, find the Z-parameter Z_{22}.

a) 3

b)2

c) 4

d) 1

### View Answer

_{21}is V

_{2}/I

_{2}|I

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

_{2}= (2 + 1)I

_{2}=> V

_{2}= 3(I

_{2}) => V

_{2}/I

_{2}= 3. On substituting Z

_{21}= 3Ω.

5. In the circuit shown below, find the Z-parameter Z_{11}.

a) 10

b) 15

c) 20

d) 25

### View Answer

_{11}is V

_{1}/I

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

_{1}= (10 + 5)I

_{1}=> V

_{1}/I

_{1}= 15 and on substituting, we get Z

_{11}= 2.5Ω.

6. In the circuit shown in question 5, find the Z-parameter Z_{12}.

a) 15

b) 10

c) 5

d) 1

### View Answer

_{12}is V

_{2}/I

_{1}|I

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

_{1}= (5) I

_{2}=> V

_{1}/I

_{1}= 5. On substituting we get Z

_{12}= 5Ω.

7. From the circuits shown in question 1 in question 5, find the combined Z-parameter Z_{11}.

a) 8

b) 18

c) 28

d) 38

### View Answer

_{11}is Z

_{11}= Z

_{11x}+ Z

_{11y}and Z

_{11x}= 3, Z

_{11y}= 15. On substituting we get Z

_{11}= 3 +15 = 18Ω.

8. From the circuits shown in question 1 in question 5, find the combined Z-parameter Z_{12}.

a) 4

b) 5

c) 6

d) 7

### View Answer

_{12}is Z

_{12}= Z

_{12x}+ Z

_{12y}and we have Z

_{12x}= 2, Z

_{12y}. On substituting we get Z

_{12}= 2 + 5 = 7Ω.

9. From the circuits shown in question 1 in question 5, find the combined Z-parameter Z_{21}.

a) 7

b) 6

c) 5

d) 4

### View Answer

_{21}is Z

_{21}= Z

_{21x}+ Z

_{21y}and we have Z

_{21x}= 2, Z

_{21y}= 5. On substituting we get Z

_{21}= 2 + 5 = 7Ω.

10. From the circuits shown in question 1 in question 5, find the combined Z-parameter Z_{22}.

a) 38

b) 28

c) 18

d) 8

### View Answer

_{22}is Z

_{22}= Z

_{22x}+ Z

_{22y}and we have Z

_{22x}= 3, Z

_{22y}= 25. On substituting we get Z

_{22}= 3 +25 = 28Ω.