This set of Network Theory Questions and Answers for Entrance exams focuses on “Classification of Pass Band and Stop Band”.

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

Explanation: We know that the propogation constant is a complex function and the real part of the complex propogation constant is a measure of the change in magnitude of the current or voltage in the network known as attenuation constant and imaginary part is a measure of the difference in phase between the input and output currents or voltages known as phase shift constant. ϒ = α + jβ.

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

Explanation: Z

_{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

Explanation: If Z

_{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

Explanation: If Z

_{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

Explanation: If Z

_{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

Explanation: As sinhα/2 cosβ/2=0 and coshα/2 sinβ/2=x, the value of α if Z

_{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

Explanation: The value of β if Z

_{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

Explanation: If α = 0, sin β/2 = x(√(Z

_{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

Explanation: If the value of β is π, cos β/2 = 0. So sin β/2 = ±1; cosh α/2 = x = √(Z

_{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

Explanation: The characteristic impedance of a symmetrical π-section can be expressed in terms of T. Z

_{oπ}= Z

_{1}Z

_{2}/Z

_{oT}.

**Sanfoundry Global Education & Learning Series – Network Theory.**

To practice all areas of Network Theory for Entrance exams, __here is complete set of 1000+ Multiple Choice Questions and Answers__.