This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Constant-K Low Pass Filter”.

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

Explanation: Z

_{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

Explanation: The constant k, T or π type filter is also known as the prototype because other more complex networks can be derived from it. From the given figure, the value of Z

_{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

Explanation: From the prototype T section and prototype π section shown in figures, we get the value of Z

_{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

Explanation: Z

_{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

Explanation: We got Z

_{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

Explanation: Z

_{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

Explanation: The value of α in the pass band of constant k-low pass filter is α= 2 cosh

^{-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

Explanation: We know that in the attenuation band, Z

_{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

Explanation: α = 2 cosh

^{-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

Explanation: We know that in the pass band, the condition is -1 < Z

_{1}/4Z

_{2}< 0. So α= π.

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

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