## Network Theory MCQ Set 1

1. The driving point impedance of an LC network is given by Z(s)=(2s^{5}+12s^{3}+16s)/( s^{4}+4s^{2}+3). By taking the continued fraction expansion using first Cauer form, find the value of L_{1}.

a) s

b) 2s

c) 3s

d) 4s

### View Answer

_{1}= 2s.

2. Find the first reminder obtained by taking the continued fraction expansion in question 1.

a) 4s^{3}+10s

b) 12s^{3}+10s

c) 4s^{3}+16s

d) 12s^{3}+16s

### View Answer

^{3}+10s.

3. Find the value of C_{2} in question 1.

a) 1

b) 1/2

c) 1/3

d) 1/4

### View Answer

_{2}. So the value of C

_{2}= 1/4.

4. Find the value of L_{3} in question 1.

a) 8

b) 8/3

c) 8/5

d) 8/7

### View Answer

_{3}= 8s/3. So L

_{3}= 8/3H.

5. Find the value of C_{4} in question 1.

a) 1/2

b) 1/4

c) 3/4

d) 1

### View Answer

_{4}= 3s/4. C

_{4}= 3/4F.

6. Find the value of L_{5} in question 1.

a) 2

b) 2/5

c) 2/7

d) 2/3

### View Answer

_{5}= 2s/3 So L

_{5}= 2/3H.

7. The driving point impedance of an LC network is given by Z(s)=(s^{4}+4s^{2}+3)/(s^{3}+2s) . By taking the continued fraction expansion using second Cauer form, find the value of C_{1}.

a) 2/3

b) 2/2

c) 1/2

d) 4/2

### View Answer

_{1}= 3/2s C

_{1}= 2/3F..

8. Find the value of L_{2} in question 7.

a) 1/5

b) 2/5

c) 3/5

d) 5/4

### View Answer

_{2}= 4/5s So L

_{2}= 5/4H.

9. Find the value of C_{3} in question 7.

a) 25/s

b) 2/25s

c) 25/3s

d) 25/4s

### View Answer

_{3}= 25/2s. C

_{3}= 2/25F.

10. Find the value of L_{4} in question 7.

a) 5

b) 2/5

c) 3/5

d) 4/5

### View Answer

_{4}= 1/5s L

_{4}= 5H.

## Network Theory MCQ Set 2

1. The attenuation in dB in terms of input power (P_{1}) and output power (P_{2}) is?

a) log_{10} (P_{1}/P_{2})

b)10 log_{10} (P_{1}/P_{2})

c) log_{10} (P_{2}/P_{1})

d) 10 log_{10} (P_{2}/P_{1})

### View Answer

_{1}) and output power (P

_{2}) is Attenuation in dB = 10 log

_{10}(P

_{1}/P

_{2}).

2. If V_{1} is the voltage at port 1 and V_{2} is the voltage at port 2, then the attenuation in dB is?

a) 20 log_{10} (V_{1}/V_{2})

b) 10 log_{10} (V_{1}/V_{2})

c) 20 log_{10} (V_{2}/V_{1})

d) 10 log_{10} (V_{2}/V_{1})

### View Answer

_{1}is the voltage at port 1 and V

_{2}is the voltage at port 2, then the attenuation in dB is Attenuation in dB =20 log

_{10}(V

_{1}/V

_{2}) where V

_{1}is the voltage at port 1 and V

_{2}is the voltage at port 2.

3. What is the attenuation in dB assuming I_{1} is the input current and I_{2} is the output current leaving the port?

a) 10 log_{10} (I_{1}/I_{2})

b) 10 log_{10} (I_{2}/I_{1})

c) 20 log_{10} (I_{2}/I_{1})

d) 20 log_{10} (I_{1}/I_{2})

### View Answer

_{1}is the input current and I

_{2}is the output current leaving the port, the attenuation in dB is Attenuation in dB =20 log

_{10}(I

_{1}/I

_{2}) where I

_{1}is the input current and I

_{2}is the output current leaving the port.

4. The value of one decibel is equal to?

a) log_{10} (N)

b) 10 log_{10} (N)

c) 20 log_{10} (N)

d) 40 log_{10} (N)

### View Answer

_{10}(N). One decibel = 20 log

_{10}(N) where N is the attenuation.

5. The value of N in dB is?

a) N= anti log (dB)

b) N= anti log(dB/10)

c) N=anti log(dB/20)

d) N=anti log(dB/40)

### View Answer

6. In the circuit shown below, find the value of I_{1}/I_{2}.

a) (R_{1}-R_{2}+R_{0})/R_{2}

b) (R_{1}+R_{2}+R_{0})/R_{2}

c) (R_{1}-R_{2}-R_{0})/R_{2}

d) (R_{1}+R_{2}-R_{0})/R_{2}

### View Answer

_{2}(I

_{1}-I

_{2})=I

_{2}(R

_{1}+R

_{0}) => I

_{2}(R

_{2}+R

_{1}+R

_{0})I

_{1}R

_{2}. On solving, I

_{1}/I

_{2}=(R

_{1}+R

_{2}+R

_{1})/R

_{2}.

7. Determine the value of N in the circuit shown in question 6.

a) (R_{1}+R_{2}-R_{0})/R_{2}

b) (R_{1}-R_{2}-R_{0})/R_{2}

c) (R_{1}+R_{2}+R_{0})/R_{2}

d) (R_{1}-R_{2}+R_{0})/R_{2}

### View Answer

_{1}/I

_{2}. We got I

_{1}/I

_{2}=(R

_{1}+R

_{2}+R

_{1})/R

_{2}. So on substituting we get N = (R

_{1}+R

_{2}+R

_{0})/R

_{2}.

8. The value of the characteristic impedance R_{0} in terms of R_{1} and R_{2} and R_{0} in the circuit shown in question 6 is?

a) R_{1}+R_{2}(R_{1}+R_{0})/(R_{1}+R_{0}+R_{2})

b) R_{1}+ R_{2}(R_{1}+R_{0})/(R_{1}+R_{0}+R_{2})

c) R_{2}+ R_{2}(R_{1}+R_{0})/(R_{1}+R_{0}+R_{2})

d) R_{0}+R_{2}(R_{1}+R_{2})/(R_{1}+R_{0}+R_{2})

### View Answer

_{0}in terms of R

_{1}and R

_{2}and R

_{0}when it is terminated in a load of R

_{0}is R

_{0}=R

_{1}+ R

_{2}(R

_{1}+R

_{0})/(R

_{1}+R

_{0}+R

_{2}).

9. Determine the value of R_{1} in terms of R_{0} and N in the circuit shown in question 6 is?

a) R_{1}= R_{0}(N-1)/(N+1)

b) R_{1}= R_{0}(N+1)/(N+1)

c) R_{1}= R_{0}(N-1)/(N-1)

d) R_{1}= R_{0}(N+1)/(N-1)

### View Answer

_{0}= R

_{1}+(R

_{1}+R

_{0})/N. On solving, the value of R

_{1}in terms of R

_{0}and N is R

_{1}= R

_{0}(N-1)/(N+1).

10. Determine the value of R_{2} in terms of R_{0} and N in the circuit shown in question 6 is?

a) R_{2}= NR_{0}/(N^{2}-1)

b) R_{2}= 2 NR_{0}/(N^{2}-1)

c) R_{2}= 3 NR_{0}/(N^{2}-1)

d) R_{2}= 4 NR_{0}/(N^{2}-1)

### View Answer

_{2}= R

_{1}+R

_{0}+R

_{2}. On substituting the value of R

_{1}, we get the value of R

_{2}in terms of R

_{0}and N as R

_{2}= 2 NR

_{0}/(N

^{2}-1).

## Network Theory MCQ Set 3

1. Based on the location of zeros and poles, a reactive one-port can have ____________ types of frequency response.

a) 1

b) 2

c) 3

d) 4

### View Answer

2. A driving point impedance with poles at ω = 0, ω = ∞ must have ___________ term in the denominator polynomial.

a) s

b) s+1

c) s+2

d) s+3

### View Answer

3. A driving point impedance with poles at ω = 0, ω = ∞ must have excess ___________ term in the numerator polynomial.

a) s^{1}+ω_{n}^{1}

b) s^{1}+ω_{n}^{2}

c) s^{2}+ω_{n}^{2}

d) s^{2}+ω_{n}^{1}

### View Answer

4. A driving point impedance with zeros at ω = 0, ω = ∞ must have ___________ term in the numerator polynomial.

a) s+3

b) s+2

c) s+1

d) s

### View Answer

5. A driving point impedance with zeros at ω = 0, ω = ∞ must have an excess ___________ term in the denominator polynomial.

a) s^{2}+ω_{n}^{1}

b) s^{2}+ω_{n}^{2}

c) s^{1}+ω_{n}^{2}

d) s^{1}+ω_{n}^{1}

### View Answer

6. A driving point impedance with zero at ω = 0 and pole at ω = ∞ must have ___________ term in the numerator polynomial.

a) s+1

b) s

c) s+3

d) s+2

### View Answer

7. A driving point impedance with zero at ω = 0 and pole at ω = ∞ must have ___________ term in the numerator polynomial.

a) s^{1}+ω_{n}^{1}

b) s^{2}+ω_{n}^{1}

c) s^{1}+ω_{n}^{2}

d) s^{2}+ω_{n}^{2}

### View Answer

^{2}+ω

_{n}

^{2}type terms in the numerator polynomial and the denominator polynomial.

8. A driving point impedance with zero at ω = 0 and pole at ω = ∞ must have ___________ term in the denominator polynomial.

a) s^{2}+ω_{n}^{2}

b) s^{1}+ω_{n}^{1}

c) s^{2}+ω_{n}^{1}

d) s^{1}+ω_{n}^{2}

### View Answer

9. A driving point impedance with pole at ω = 0 and zero at ω = ∞ must have ___________ term in the denominator polynomial.

a) s

b) s+3

c) s+1

d) s+2

### View Answer

10. A driving point impedance with pole at ω = 0 and zero at ω = ∞ must have ____________ term in the numerator and denominator.

a) s^{1}+ω_{n}^{2}

b) s^{2}+ω_{n}^{2}

c) s^{1}+ω_{n}^{1}

d) s^{2}+ω_{n}^{1}

### View Answer

## Network Theory MCQ Set 4

1. A network either T or π, is said to be of the constant-k type if Z_{1} and Z_{2} of the network satisfy the relation?

a) Z_{1}Z_{2} = k

b) Z_{1}Z_{2} = k^{2}

c) Z_{1}Z_{2} = k^{3}

d) Z_{1}Z_{2} = k^{4}

### View Answer

_{1},Z

_{2}are inverse if their product is a constant, independent of frequency, k is real constant, that is the resistance. k is often termed as design impedance or nominal impedance of the constant k-filter.

2. In the circuit shown below, find the value of Z_{1}.

a) jωL

b) 2 jωL

c) jωL/2

d) 4 jωL

### View Answer

_{1}is jωL.

3. In the circuit shown in the question 2, find the value of Z_{2}.

a) jωC

b) 2 jωC

c) 1/jωC

d) 1/2 jωC

### View Answer

_{2}is 1/jωC.

4. The value of Z_{1}Z_{2} in the circuit shown in the question 2 is?

a) L/C

b) C/L

c) 1/LC

d) LC

### View Answer

_{1}= jωL and Z

_{2}= 1/jωC. So the product Z

_{1}Z

_{2}is jωL x 1/jωC = L/C.

5. Determine the value of k in the circuit shown in the question 2.

a) √LC

b) √((L/C) )

c) √((C/L) )

d) √((1/CL) )

### View Answer

_{1}Z

_{2}= L/C. And we know Z

_{1}Z

_{2}= k

^{2}. So k

^{2}= L/C. So the value of k is √(L/C).

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

a) 1/√LC

b) 1/(π√LC)

c) √LC

d) π√LC

### View Answer

_{1}/4Z

_{2}= 0. Z

_{1}= jωL and Z

_{2}= 1/jωC. On solving the cut-off frequency of the constant k-low pass filter is f

_{c}= 1/(π√LC).

7. The value of α in the pass band of constant k-low pass filter is?

a) 2 cosh^{-1}(f_{c}/f)

b) cosh^{-1}(f_{c}/f)

c) cosh^{-1}(f/f_{c})

d) 2 cosh^{-1}(f/f_{c})

### View Answer

^{-1}(f/f

_{c}).

8. The value of β in the attenuation band of constant k-low pass filter is?

a) 0

b) π

c) π/2

d) π/4

### View Answer

_{1}/4Z

_{2}< -1 i.e., f/f

_{c}< 1. So the value of β in the pass band of constant k-low pass filter is β= π.

9. The value of α in the attenuation band of constant k-low pass filter is?

a) α=2 cosh^{-1}(f_{c}/f)

b) α=cosh^{-1}(f/f_{c})

c) α=2 cosh^{-1}(f/f_{c})

d) α=cosh^{-1}(f_{c}/f)

### View Answer

^{-1}[Z

_{1}/4Z

_{2}] and Z

_{1}/4Z

_{2}= f/f

_{c}. On substituting we get α = 2 cosh

^{-1}(f/f

_{c}).

10. The value of α in the pass band of constant k-low pass filter is?

a) π

b) π/4

c) π/2

d) 0

### View Answer

_{1}/4Z

_{2}< 0. So α= π.

## Network Theory MCQ Set 5

1. The relation between α, β, ϒ is?

a) α = ϒ + jβ

b) ϒ = α + jβ

c) β = ϒ + jα

d) α = β + jϒ

### View Answer

2. If Z_{1}, Z_{2} are same type of reactance, then |Z_{1}/4 Z_{2}| is real, then the value of α is?

a) α = sinh^{-1}√( Z_{1}/4 Z_{2})

b) α = sinh^{-1}√( Z_{1}/Z_{2})

c) α = sinh^{-1}√( 4 Z_{1}/Z_{2})

d) α = sinh^{-1}√( Z_{1}/2 Z_{2})

### View Answer

_{1}, Z

_{2}are same type of reactance and |Z

_{1}/4 Z

_{2}| is real. |Z

_{1}/4 Z

_{2}| > 0. The value of α is α = sinh

^{-1}√(Z

_{1}/4 Z

_{2}).

3. If Z_{1}, Z_{2} are same type of reactance, then |Z_{1}/4 Z_{2}| is real, then?

a) |Z_{1}/4 Z_{2}|=0

b) |Z_{1}/4 Z_{2}| < 0

c) |Z_{1}/4 Z_{2}| > 0

d) | Z_{1}/4 Z_{2}|>= 0

### View Answer

_{1}and Z

_{2}are same type of reactances, then √(Z

_{1}/4 Z

_{2}) should be always positive implies that |Z

_{1}/4 Z

_{2}|>0.

4. Which of the following expression is true if Z_{1}, Z_{2} are same type of reactance?

a) sinhα/2 sinβ/2=0

b) coshα/2 sinβ/2=0

c) coshα/2 cosβ/2=0

d) sinhα/2 cosβ/2=0

### View Answer

_{1}, Z

_{2}are same type of reactance, then the real part of sinhϒ/2 = sinhα/2 cosβ/2 + jcoshα/2 sinβ/2 should be zero. So sinhα/2 cosβ/2=0.

5. Which of the following expression is true if Z_{1}, Z_{2} are same type of reactance?

a) sinhα/2 cosβ/2=x

b) coshα/2 cosβ/2=0

c) coshα/2 sinβ/2=x

d) sinhα/2 sinβ/2=0

### View Answer

_{1}, Z

_{2}are same type of reactance, then the imaginary part of sinhϒ/2 = sinhα/2 cosβ/2 + jcoshα/2 sinβ/2 should be some value. So coshα/2 sinβ/2=x.

6. The value of α if Z_{1}, Z_{2} are same type of reactance?

a) 0

b) π/2

c) π

d) 2π

### View Answer

_{1}, Z

_{2}are same type of reactance is α= 0.

7. The value of β if Z_{1}, Z_{2} are same type of reactance?

a) 2π

b) π

c) π/2

d) 0

### View Answer

_{1}, Z

_{2}are same type of reactances, then sinhα/2 cosβ/2=0 and coshα/2 sinβ/2=x. So the value of β is β= π.

8. If Z_{1}, Z_{2} are same type of reactance, and if α = 0, then the value of β is?

a) β=2 sin^{-1}(√(Z_{1}/4 Z_{2}))

b) β=2 sin^{-1}(√(4 Z_{1}/Z_{2}))

c) β=2 sin^{-1}(√(4 Z_{1}/Z_{2}))

d) β=2 sin^{-1}(√(Z_{1}/Z_{2}))

### View Answer

_{1}/4 Z

_{2}). But sine can have a maximum value of 1. Therefore the above solution is valid only for Z

_{1}/4 Z

_{2}, and having a maximum value of unity. It indicates the condition of pass band with zero attenuation and follows the condition as -1 < Z

_{1}/4 Z

_{2}<= 0. So β=2 sin

^{-1}(√(Z

_{1}/4 Z

_{2})).

9. If the value of β is π, and Z_{1}, Z_{2} are same type of reactance, then the value of β is?

a) α=2 cosh^{-1}√(Z_{1}/2 Z_{2})

b) α=2 cosh^{-1}√(Z_{1}/Z_{2})

c) α=2 cosh^{-1}√(4 Z_{1}/Z_{2})

d) α=2 cosh^{-1}√(Z_{1}/4 Z_{2})

### View Answer

_{1}/4 Z

_{2}). This solution is valid for negative Z

_{1}/4 Z

_{2}and having magnitude greater than or equal to unity. -α <= Z

_{1}/2 Z

_{2}<= -1. α=2 cosh

^{-1}√(Z

_{1}/4 Z

_{2}).

10. The relation between Z_{oπ}, Z_{1}, Z_{2}, Z_{oT} is?

a) Z_{oT} = Z_{1}Z_{2}/Z_{oπ}

b) Z_{oπ} = Z_{1}Z_{2}/Z_{oT}

c) Z_{oT} = Z_{1}Z_{1}/Z_{oπ}

d) Z_{oT} = Z_{2}Z_{2}/Z_{oπ}

### View Answer

_{oπ}= Z

_{1}Z

_{2}/Z

_{oT}.