This set of Network Theory Technical Interview Questions & Answers focuses on “Advanced Problems on Filters – 2”.

1. In a parallel RL circuit, 10 A current enters into the resistor R and 15 A current enters into the Inductor L. The total current I is _____________

a) 15.5 A

b) 25.05 A

c) 18.03 A

d) 30.15 A

View Answer

Explanation: Currents in resistance and inductance are out of phase by 90°.

Hence, I = \(I_1^2 + I_2^2\)

Or, I = [10

^{2}+ 15

^{2}]

^{0.5}

Or, I = \(\sqrt{100+225} = \sqrt{325}\)

= 18.03 A.

2. In the circuit given below, a dc circuit fed by a current source. With respect to terminals AB, Thevenin’s voltage and Thevenin’s resistance are ____________

a) V_{TH} = 5 V, R_{TH} = 0.75 Ω

b) V_{TH} = 7.14 V, R_{TH} = 2.14 Ω

c) V_{TH} = 7.5 V, R_{TH} = 2.5 Ω

d) V_{TH} = 5 V, R_{TH} = 1 Ω

View Answer

Explanation: V

_{TH}= \(\frac{5 X 10}{35}\) X 5 = 7.14 V

Also, R

_{TH}= \(\frac{5 X 15}{35}\) = 2.14 Ω.

3. In the circuit given below, the value of R is ____________

a) 12 Ω

b) 6 Ω

c) 3 Ω

d) 1.5 Ω

View Answer

Explanation: The resistance of parallel combination is given by,

R

_{eq}= \(\frac{40}{3}\) – 10 = 3.33 Ω

Or, \(\frac{1}{3.33} = \frac{1}{12} + \frac{1}{15} + \frac{1}{15}\)

Or, R = 6 Ω.

4. In the circuit given below, M = 1. The resonant frequency is _______________

a) 145.3 Hz

b) 0.1453 Hz

c) 1.453 Hz

d) 14.53 Hz

View Answer

Explanation: I

_{EQ}= L

_{1}+ L

_{2}+ 2M

L

_{EQ}= 5 + 5 + 2 × 1

= 10 + 2 = 12 H

∴ F

_{O}= \(\frac{1}{2π\sqrt{LC}}\)

= \(\frac{1}{2π\sqrt{12 × 0.1}}\)

= 0.1453 Hz.

5. A thermistor is used for ____________

a) Over voltage protection

b) Temperature alarm circuit

c) Automatic light control

d) Automatic sensor

View Answer

Explanation: The resistance of a thermistor decreases with increases in temperature. It is used to monitor the hot spot temperature of electric machines.

6. Two network functions are given below.

H_{1} = \(\frac{1}{s^2 + 2s + 1}\), H_{2} = \(\frac{1}{s^3+3s^2+3s+1}\)

The frequency response indicates that the filter is ___________

a) Low-pass

b) Band-pass

c) High-pass

d) Band reject

View Answer

Explanation: | H

_{1}|

^{2}= \(\frac{1}{[(jω)^2 + 2jω + 1] [(jω)^2 + 2 jω + 1]}\)

Similarly, | H

_{2}|

^{2}= \(\frac{1}{1 + ω^6}\)

Therefore at ω = 0, 1 and ∞, we have | H |

^{2}= 1, \(\frac{1}{2}\) and 0 respectively.

Hence, the filter is a Low-pass filter.

7. A particular band-pass function has a network function as H(s) = \(\frac{s}{s^2+2s+1}\) then, its quality factor Q is ___________

a) \(\frac{3}{4}\)

b) \(\frac{1}{2}\)

c) \(\frac{3}{2}\)

d) \(\frac{1}{4}\)

View Answer

Explanation: H(s) = \(\frac{Ks}{s^2+as+b}\)

Then, quality factor is given as \(\frac{\sqrt{b}}{a}\)

Here, b = 1, a = 2, K = 1

∴ Q = \(\frac{1}{2}\) = 0.5.

8. The filter which passes all frequencies above fc by attenuating significantly, all frequencies above f_{c} is _______________

a) Low-pass

b) High-pass

c) Band-pass

d) Band-stop

View Answer

Explanation: A high-pass filter is one which passes all frequencies above f

_{c}by attenuating significantly, all frequencies below f

_{c}.

9. For a Band Pass Filter, the slope of the filter is given as 80dB/decade. The order of the Band Pass Filter is __________

a) 10

b) 8

c) 4

d) 6

View Answer

Explanation: The Bode plot is a logarithmic plot which helps in fitting a large scale of values into a small scale by the application of logarithm. Plotting the slope 80dB/decade on the Bode plot, we get n=8. Hence the order of the Band Pass Filter is 8.

10. In which of the filter circuits given below, will the bandwidth be equal to the critical frequency?

a) Low-pass

b) High-pass

c) Band-pass

d) Band-stop

View Answer

Explanation: Bandwidth can be calculated by considering,

Largest positive value – Smallest Positive Value

Here, in case of the Low-pass filter only, the largest positive value will of course be the critical frequency, beyond which frequencies have to be blocked. Hence, the bandwidth in a Low-pass filter equals the critical frequency.

11. For providing a Roll-off greater than 60dB/decade/pole, filters with which characteristics are useful?

a) Butterworth

b) Chebyshev

c) Bessel

d) Butterworth & Bessel

View Answer

Explanation: Roll off is a term commonly refers to the steepness of the transmission function with respect to the frequency. For a Chebyshev filter, the Roll-off value greater than 60. This characteristic feature is useful when a rapid roll-off is required because it provides a Roll-off rate more than 60. On the other hand, both Butterworth and Bessel have the Roll-off rate less than or equal to 60 dB/decade/pole.

12. A Low-pass filter circuit has a cut-off frequency of 50 kHz. The bandwidth of the filter is ______________

a) 24.6 kHz

b) 50 kHz

c) 61.5 kHz

d) 36.9 kHz

View Answer

Explanation: The bandwidth is defined as the highest cut-off frequency to the lowest cut-off frequency. Here the lowest cut-off frequency is Zero.

For a Low-pass filter therefore, Cut-off Frequency = Bandwidth of the filter

∴ Bandwidth = 50 kHz.

13. Given a system function H(s) = \(\frac{1}{s+10}\). Let us consider a signal sin 10t. Then the steady state response is ___________

a) 1

b) 2

c) 0

d) 5

View Answer

Explanation: H(s) = \(\frac{V(s)}{J(s)}\)

= \(\frac{1}{s+10}\)

V(s) = \(\frac{1}{s+10}\) . J(s)

J(s) = L (sin 10t) = \(\frac{10}{s^2+100}\)

V (s) = \(\frac{1}{s^2+100} . \frac{10}{s+10}\)

V

_{SS}= lim

_{s→0} sV(s)

= 0.

14. Current I = – 1 + \(\sqrt{2}\) (sin (ωt + 60°)) A is passed through three meters. The respective readings will be?

a) \(\sqrt{2}\) A, \(\sqrt{2}\) A and 1 A

b) 1 A, \(\sqrt{2}\) A and 1 A

c) – 1 A, \(\sqrt{2}\) A and \(\sqrt{2}\) A

d) -1 A, 1 A and 1 A

View Answer

Explanation: We know that a PMMC instrument reads only DC value and since it is a centre zero type, so it will give – 1.

So, rms = \(\sqrt{1^2 + (\frac{\sqrt{2}}{\sqrt{2}})^2} = \sqrt{2}\) A

Moving iron also reads rms value, so its reading will also be \(\sqrt{2}\) A.

15. For a Band Pass Filter, the slope of the filter is given as 40dB/decade. The order of the Band Pass Filter is __________

a) 2

b) 3

c) 4

d) 6

View Answer

Explanation: The Bode plot is a logarithmic plot which helps in fitting a large scale of values into a small scale by the application of logarithm. Plotting the slope 40dB/decade on the Bode plot, we get n=4. Hence order of the Band Pass Filter is 4.

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