## Network Theory MCQ Set 1

1. The value of one decibel is equal to?

a) 0.115 N

b) 0.125 N

c) 0.135 N

d) 0.145 N

### View Answer

_{e}(V

_{1}/V

_{2}).

2. A filter which passes without attenuation all frequencies up to the cut-off frequency f_{c} and attenuates all other frequencies greater than f_{c} is called?

a) high pass filter

b) low pass filter

c) band elimination filter

d) band pass filter

### View Answer

_{c}without attenuation and attenuates all other frequencies greater than f

_{c}. This transmits currents of all frequencies from zero up to the cut-off frequency.

3. A filter which attenuates all frequencies below a designated cut-off frequency f_{c} and passes all other frequencies greater than f_{c} is called?

a) band elimination filter

b) band pass filter

c) low pass filter

d) high pass filter

### View Answer

_{c}and passes all other frequencies greater than f

_{c}. Thus the pass band of this filter is the frequency range above f

_{c}and the stop band is the frequency range below f

_{c}.

4. A filter that passes frequencies between two designated cut-off frequencies and attenuates all other frequencies is called?

a) high pass filter

b) band elimination filter

c) band pass filter

d) low pass filter

### View Answer

_{2}-f

_{1}; f

_{1}is the lower cut-off frequency, f

_{2}is the upper cut-off frequency.

5. A filter that passes all frequencies lying outside a certain range, while it attenuates all frequencies between the two designated frequencies is called?

a) low pass filter

b) high pass filter

c) band elimination filter

d) band pass filter

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6. The expression of the characteristic impedance of a symmetrical T-section is?

a) Z_{OT}=√(Z_{1}^{2}/4-Z_{1}Z_{2})

b) Z_{OT}=√(Z_{1}^{2}/4+Z_{1})

c) Z_{OT}=√(Z_{1}^{2}/4+Z_{2})

d) Z_{OT}=√(Z_{1}^{2}/4+Z_{1}Z_{2})

### View Answer

_{o}is Z

_{in}=(Z

_{1}/2)+(Z

_{2}((Z

_{1}/2)+Z

_{o}))/((Z

_{1}/2)+Z

_{2}+Z

_{o}) and Z

_{in}=Z

_{o}. On solving, the expression of the characteristic impedance of a symmetrical T-section is Z

_{OT}=√(Z

_{1}

^{2}/4+Z

_{1}Z

_{2}).

7. The expression of the open circuit impedance Z_{oc} is?

a) Z_{oc}=Z_{1}/2+Z_{2}

b) Z_{oc}=Z_{2}/2+Z_{2}

c) Z_{oc}=Z_{1}/2+Z_{1}

d) Z_{oc}=Z_{1}/2-Z_{2}

### View Answer

_{oc}as Z

_{oc}=Z

_{1}/2+Z

_{2}.

8. The expression of short circuit impedance Z_{sc} is?

a) Z_{sc}=(Z_{1}^{2}-4Z_{1}Z_{2})/(2Z_{1}-4Z_{2})

b) Z_{sc}=(Z_{1}^{2}+4Z_{1}Z_{2})/(2Z_{1}+4Z_{2})

c) Z_{sc}=(Z_{1}^{2}-4Z_{1}Z_{2})/(2Z_{1}+4Z_{2})

d) Z_{sc}=(Z_{1}^{2}+4Z_{1}Z_{2})/(2Z_{1}-4Z_{2})

### View Answer

_{sc}as Z

_{sc}=(Z

_{1}/2)+((Z

_{1}/2)xZ

_{2})/((Z

_{1}/2)+Z

_{2}). On solving we get Z

_{sc}=(Z

_{1}

^{2}+4Z

_{1}Z

_{2})/(2Z

_{1}+4Z

_{2}).

9. The relation between Z_{OT}, Z_{oc}, Z_{sc} is?

a) Z_{OT}=√Z_{oc}Z_{sc}

b) Z_{oc}=√(Z_{OT} Z_{sc})

c) Z_{sc}=√(Z_{OT} Z_{oc})

d) Z_{oc}=√(Z_{OT} Z_{oc})

### View Answer

_{oc}=Z

_{1}/2+Z

_{2}and Z

_{sc}=(Z

_{1}

^{2}+4Z

_{1}Z

_{2})/(2Z

_{1}+4Z

_{2}) => Z

_{oc}xZ

_{sc}=Z

_{1}Z

_{2}+Z

_{1}

^{2}/4 =Z

_{o}

^{2}T. The relation between Z

_{OT}, Z

_{oc}, Z

_{sc}is Z

_{OT}=√Z

_{oc}Z

_{sc}.

10. The value of sinhϒ/2 in terms of Z_{1} and Z_{2} is?

a) sinhϒ/2=√(4Z_{1}/Z_{2})

b) sinhϒ/2=√(Z_{1}/Z_{2})

c) sinhϒ/2=√(Z_{1}/4Z_{2})

d) sinhϒ/2=√(2Z_{1}/Z_{2})

### View Answer

_{1}/2Z

_{2}-1))). The value of sinhϒ/2 in terms of Z

_{1}and Z

_{2}is sinhϒ/2=√(Z

_{1}/4Z

_{2}).

## Network Theory MCQ Set 2

1. The denominator polynomial in a transfer function may not have any missing terms between the highest and the lowest degree, unless?

a) all odd terms are missing

b) all even terms are missing

c) all even or odd terms are missing

d) all even and odd terms are missing

### View Answer

^{3}+3s is Hurwitz because all quotient terms are positive and all even terms are missing.

2. The roots of the odd and even parts of a Hurwitz polynomial P (s) lie on ____________

a) right half of s plane

b) left half of s-plane

c) on jω axis

d) on σ axis

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3. If the polynomial P (s) is either even or odd, then the roots of P (s) lie on __________

a) on σ axis

b) on jω axis

c) left half of s-plane

d) right half of s plane

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4. If the ratio of the polynomial P (s) and its derivative gives a continued fraction expansion with ________ coefficients, then the polynomial P (s) is Hurwitz.

a) all negative

b) all positive

c) positive or negative

d) positive and negative

### View Answer

^{‘}(s) gives a continued fraction expansion with all positive coefficients, then the polynomial P (s) is Hurwitz. If all the quotients in the continued fraction expansion are positive, the polynomial P(s) is positive.

5. Consider the polynomial P(s)=s^{4}+3s^{2}+2. The given polynomial P (s) is Hurwitz.

a) True

b) False

### View Answer

^{4}+3s

^{2}+2 => P

^{‘}(s)=4s

^{3}+6s After doing the continued fraction expansion, we get all the quotients as positive. So, the polynomial P (s) is Hurwitz.

6. When s is real, the driving point impedance function is _________ function and the driving point admittance function is _________ function.

a) real, complex

b) real, real

c) complex, real

d) complex, complex

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7. The poles and zeros of driving point impedance function and driving point admittance function lie on?

a) left half of s-plane only

b) right half of s-plane only

c) left half of s-plane or on imaginary axis

d) right half of s-plane or on imaginary axis

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8. For real roots of s_{k}, all the quotients of s in s^{2}+ω_{k}^{2} of the polynomial P (s) are __________

a) negative

b) non-negative

c) positive

d) non-positive

### View Answer

_{k}, all the quotients of s in s

^{2}+ω

_{k}

^{2}of the polynomial P (s) are non-negative. So by multiplying all factors in P(s) we find that all quotients are positive.

9. The real parts of the driving point function Z (s) and Y (s) are?

a) positive and zero

b) positive

c) zero

d) positive or zero

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10. For the complex zeros to appear in conjugate pairs the poles of the network function are ____ and zeros of the network function are ____________

a) complex, complex

b) complex, real

c) real, real

d) real, complex

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## Network Theory MCQ Set 3

1. A network is said to be symmetrical if the relation between A and D is?

a) A = D

b) A = 2 D

c) A = 3 D

d) A = 4 D

### View Answer

_{1}=AV

_{2}-BI

_{2}and I

_{1}=CV

_{2}-DI

_{2}. If the network is symmetrical, then the relation between A and D is A = D.

2. The relation between Z_{11} and Z_{12} if the network is symmetrical is?

a) Z_{11} = 2 Z_{12}

b) Z_{11} = Z_{12}

c) Z_{11} = 3 Z_{12}

d) Z_{11} = 4 Z_{12}

### View Answer

_{11}and Z

_{12}for the network is symmetrical is Z

_{11}= Z

_{12}.

3. The relation between Z_{12} and Z_{11} and B and C parameters if the network is symmetrical is?

a) Z_{11} = Z_{12} = B/C

b) Z_{11} = Z_{12} = C/B

c) Z_{11} = Z_{12} =√(B/C)

d) Z_{11} = Z_{12} = √(C/B)

### View Answer

_{12}and Z

_{11}and B and C parameters if the network is symmetrical is Z

_{11}= Z

_{12}=√(B/C).

4. Determine the transmission parameter A in the circuit shown below.

a) 3/4

b) 4/3

c) 5/6

d) 6/5

### View Answer

_{1}=AV

_{2}-BI

_{2}and I

_{1}=CV

_{2}-DI

_{2}. A=(V

_{1}/V

_{2}) |I

_{2}=0. On solving we get the transmission parameter A as A = 6/5.

5. Determine the transmission parameter B in the circuit shown in question 4.

a) 17/5

b) 5/17

c) 13/5

d) 5/13

### View Answer

_{1}/I

_{2}|V

_{2}=0. On short cicuiting the port 2, from the circuit we get -I

_{2}= (5/17)V

_{1}=> -V

_{1}/I

_{2}= 17/5. On substituting we get B = 17/5.

6. Determine the transmission parameter C in the circuit shown in question 4.

a) 2/5

b) 1/5

c) 4/5

d) 3/5

### View Answer

_{1}/V

_{2}|I

_{2}=0. This parameter is obtained by open circuiting the port 2. So we get V

_{2}= 5I

_{1}=> I

_{1}/V

_{2}= 1/5. On substituting, we get C = 1/5.

7. Determine the transmission parameter D in the circuit shown in question 4.

a) 3/5

b) 4/5

c) 7/5

d) 2/5

### View Answer

_{1}/I

_{2}|V

_{2}=0. This is obtained by short circuiting the port 2. We get I

_{1}= (7/17)V

_{1}and -I

_{2}= (5/17)V

_{1}. On solving, we get -I

_{1}/I

_{2}= 7/5. On substituting we get D = 7/5.

8. The value of Z_{11} in the circuit shown in question 4 is?

a) 1.8

b) 2.8

c) 3.8

d) 4.8

### View Answer

_{11}and ABCD parameters is Z

_{11}=√(AB/CD). We know A = 6/5, B = 17/5, C = 1/5, D = 7/5. On substituting, Z

_{11}= √((6/5×17/5)/(1/5×7/5))=3.8Ω.

9. The value of Z_{12} in the circuit shown in question 4 is?

a) 1.1

b) 2.2

c) 3.3

d) 4.4

### View Answer

_{12}and ABCD parameters is Z

_{12}=√(BD/AC). We got B = 17/5, D = 7/5, A = 6/5, C = 1/5. On substituting Z

_{12}=√(BD/AC) = √((17/5×7/5)/(6/5×1/5))=4.4Ω.

10. Determine the value of Ø in the circuit shown in question 4.

a) 0.25

b) 0.5

c) 0.75

d) 1

### View Answer

^{-1}√(BC/AD) = tanh

^{-1}√(17/42)=0.75.

## Network Theory MCQ Set 4

1. The impedances Z_{1} and Z_{2}are said to be inverse if?

a) Z_{1}Z_{2} = R_{0}

b) Z_{1} + Z_{2} = R_{0}

c) 1/Z_{1}+1/Z_{2}=R_{0}

d) Z_{1}Z_{2} = R_{0}^{2}

### View Answer

_{1}and Z

_{2}are said to be inverse if the geometric mean of the two impedances is a real number.

2. An inverse network may be obtained by?

a) Converting each series branch into another series branch

b) Converting each series branch into another parallel branch

c) Converting each parallel branch into another series branch

d) None of the mentioned

### View Answer

3. An inverse network may be obtained by converting each resistance element R into a corresponding resistive element of value?

a) R_{0}^{2}/R

b) R/R_{0}^{2}

c) R_{0}/R

d) R/R_{0}

### View Answer

_{0}

^{2}/R.

4. An inverse network may be obtained by converting each inductance L into a capacitance of value?

a) L/R_{0}

b) L/R_{0}^{2}

c) R_{0}/L

d) R_{0}^{2}/L

### View Answer

_{0}

^{2}to obtain the inverse network.

5. An inverse network may be obtained by converting each capacitance C into an inductance of value?

a) CR_{0}^{2}

b) CR_{0}

c) R_{0}^{2}/C

d) C/R_{0}^{2}

### View Answer

_{0}

^{2}where R

_{0}is resistance.

6. Consider the network shown below. Find the value of capacitance C_{1}^{‘} after converting the inductance L_{1} into a capacitance.

a) R_{0}^{2}/L_{1}

b) R_{0}/L_{1}

c) L_{1}/R_{0}^{2}

d) L_{1}/R_{0}

### View Answer

_{0}

^{2}to obtain the inverse network. The value of capacitance C

_{1}

^{‘}after converting the inductance into a capacitance is L

_{1}/R

_{0}

^{2}. C

_{1}

^{’}= L

_{1}/R

_{0}

^{2}.

7. In the network showed in question 6, find the value of inductance L_{1}^{‘} after converting the capacitance into an inductance.

a) C_{1}/R_{0}^{2}

b) R_{0}^{2}/C_{1}

c) C_{1}R_{0}

d) C_{1}R_{0}^{2}

### View Answer

_{0}

^{2}where R

_{0}is resistance. The value of inductance L

_{1}

^{‘}after converting the capacitance into an inductance is L

_{1}

^{‘}= C

_{1}R

_{0}

^{2}.

8. From the network showed in question 6, find the value of resistance R_{1}^{‘} after converting the resistance R_{1}.

a) R_{1}/R_{0}

b) R_{0}/R_{1}

c) R_{1}/R_{0}^{2}

d) R_{0}^{2}/R_{1}

### View Answer

_{0}

^{2}/R. The value of resistance R

_{1}

^{‘}after converting R

_{1}is R

_{1}

^{‘}= R

_{0}

^{2}/R

_{1}.

9. The value of the capacitance C_{2}^{‘} after converting the inductor into the C_{2}^{‘} in the network showed in question 6.

a) L_{2}/R_{0}^{2}

b) L_{2}/R_{0}

c) R_{0}^{2}/L_{2}

d) R_{0}/L_{2}

### View Answer

_{0}

^{2}to obtain the inverse network. The value of the capacitance C

_{2}

^{‘}after converting the inductor into the capacitance is C

_{2}

^{‘}= L

_{2}/R

_{0}

^{2}.

10. The value of the inductor L_{2}^{‘} after converting the capacitor into the L_{2}^{‘} in the network showed in question 6.

a) R_{0}^{2}/C_{2}

b) C_{2}R_{0}^{2}

c) C_{2}R_{0}

d) R_{0}^{2}/C_{2}

### View Answer

_{0}

^{2}where R

_{0}is resistance. The value of the inductor L

_{2}

^{‘}after converting the capacitor into the inductance is L

_{2}

^{‘}= C

_{2}R

_{0}

^{2}.

## Network Theory MCQ Set 5

1.The relation between Z_{oT} and Z_{oT}^{‘} in the circuits shown below.

a) Z_{oT} = Z_{oT}^{‘}

b) Z_{oT} = 2 Z_{oT}^{‘}

c) Z_{oT} = 3 Z_{oT}^{‘}

d) Z_{oT} = 4 Z_{oT}^{‘}

### View Answer

_{oT}and Z

_{oT}

^{’}is Z

_{oT}= Z

_{oT}

^{’}where Z

_{oT}

^{’}is the characteristic impedance of the modified (m-derived) T-network.

2. The value of Z_{2}^{’} in terms of Z_{1}, Z_{2} from the circuits shown in question 1 is?

a) Z_{2}^{‘}=Z_{2}/4 m (1-m^{2} )+Z_{2}/m

b) Z_{2}^{‘}=Z_{1}/4 m (1-m^{2} )+Z_{1}/m

c) Z_{2}^{‘}=Z_{2}/4 m (1-m^{2} )+Z_{1}/m

d) Z_{2}^{‘}=Z_{1}/4 m (1-m^{2} )+Z_{2}/m

### View Answer

_{oT}= Z

_{oT}

^{’}, √(Z

_{1}

^{2}/4+Z

_{1}Z

_{2})=√(m

^{2}Z

_{1}

^{2}/4+m Z

_{2‘}). On solving, Z

_{2}

^{‘}=Z

_{1}/(4 m (1-m

^{2}))+Z

_{2}/m.

3. The relation between Z_{oπ} and Z_{oπ}^{’} in the circuits shown below is?

a) Z_{oπ} = 2 Z_{oπ}^{’}

b) Z_{oπ} = 4 Z_{oπ}^{’}

c) Z_{oπ} = Z_{oπ}^{’}

d) Z_{oπ} = 3 Z_{oπ}^{’}

### View Answer

_{oπ}and Z

_{oπ}

^{‘}is Z

_{oπ}= Z

_{oπ}

^{’}.

4. The value of Z_{1}^{‘} in terms of Z_{1}, Z_{2} from the circuits shown in question 3 is?

a) Z_{1}^{‘}=(m Z_{2}(Z_{2} 4 m)/(1-m^{2} ))/m Z_{1}(Z_{2} 4 m/(1-m^{2} ))

b) Z_{1}^{‘}=(m Z_{1}(Z_{2} 4 m)/(1-m^{2} ))/m Z_{2}(Z_{2} 4 m/(1-m^{2} ))

c) Z_{1}^{‘}=(m Z_{1}(Z_{2} 4 m)/(1-m^{2} ))/m Z_{1}(Z_{2} 4 m/(1-m^{2} ))

d) Z_{1}^{‘}=(m Z_{1}(Z_{2} 4 m)/(1-m^{2} ))/m Z_{1}(Z_{1} 4 m/(1-m^{2} ))

### View Answer

_{oπ}= Z

_{oπ}

^{’}, √(Z

_{1}Z

_{2}/(1+Z

_{1}/4 Z

_{2}))=√(((Z

_{1}

^{‘}Z

_{2})/m)/(1+(Z

_{1}

^{‘})/(4 Z

_{2}/m))). On solving, Z

_{1}

^{‘}=(m Z

_{1}(Z

_{2}4 m)/(1-m

^{2}))/m Z

_{1}(Z

_{2}4 m/(1-m

^{2})) .

5. The value of resonant frequency in the m-derived low pass filter is?

a) f_{r}=1/(√(LC(1+m^{2} ) ))

b) f_{r}=1/(√(πLC(1+m^{2} ) ))

c) f_{r}=1/(√(LC(1-m^{2} ) ))

d) f_{r}=1/(√(πLC(1-m^{2} ) ))

### View Answer

_{r}

^{2}= 1/(LC(1-m

^{2})). So the value of resonant frequency in the m-derived low pass filter is f

_{r}=1/√(πLC(1-m

^{2}) ).

6. The cut-off frequency of the low pass filter is?

a) 1/√LC

b) 1/(π√LC)

c) 1/√L

d) 1/(π√L)

### View Answer

_{c}=1/(π√LC).

7. The resonant frequency of m-derived low pass filter in terms of the cut-off frequency of low pass filter is?

a) f_{c}/√(1-m^{2} )

b) f_{c}/√(1+m^{2} )

c) f_{c}/(π√(1-m^{2} ))

d) f_{c}/(π√(1+m^{2} ))

### View Answer

_{c}. The resonant frequency of m-derived low pass filter in terms of the cut-off frequency of low pass filter is f

_{r}=f

_{c}/√(1-m

^{2}).

8. The expression of m of the m-derived low pass filter is?

a) m=√(1+(f_{c}/f_{r})^{2} )

b) m=√(1+(f_{c}/f)^{2})

c) m=√(1-(f_{c}/f_{r})^{2} )

d) m=√(1-(f_{c}/f)^{2} )

### View Answer

_{r}=f

_{c}/√(1-m

^{2}). The expression of m of the m-derived low pass filter is m=√(1-(f

_{c}/f

_{r})

^{2}).

9. Given a m-derived low pass filter has cut-off frequency 1 kHz, design impedance of 400Ω and the resonant frequency of 1100 Hz. Find the value of k.

a) 400

b) 1000

c) 1100

d) 2100

### View Answer

10. The value of m from the information provided in question 9.

a) 0.216

b) 0.316

c) 0.416

d) 0.516

### View Answer

_{c}/f

_{r})

^{2}) f

_{c}= 1000, f

_{r}= 1100. On substituting m=√(1-(1000/1100)

^{2})=0.416.