# Fourier Series Analysis using Circuits MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Series Analysis using Circuits”.

1. The Fourier series of the given signal is _______________

a) -4/π sin x
b) 4/π sin x
c) 4/π cos x
d) -4/π cos x

2. For the circuit given below, the effective inductance of the circuit across the terminal AB, is ___________

a) 9 H
b) 21 H
c) 11 H
d) 6 H

3. Given x (t) = [2 + e-3t] u (t). The final value of x(t) is ___________
a) 2
b) 3
c) e-3t
d) 0

4. For the circuit given below, the inductance measured across the terminals 1 and 2 was 15 H with open terminals 3 and 4. It was 30 H when terminals 3 and 4 were short-circuited. Both the inductors are having inductances 2H. The coefficient of coupling is ______________

a) 1
b) 0.707
c) 0.5
d) Inderminate due to insufficient data

5. Q meter operator is the principle of __________
a) Series resonance
b) Current resonance
c) Self-inductance
d) Eddy currents

6. The impedance seen by the source in the circuit is given by __________

a) (0.54 + j0.313) Ω
b) (4 – j2) Ω
c) (4.54 – j1.69) Ω
d) (4 + j2) Ω

7. In the circuit given below, the resonant frequency is ________________

a) \frac{1}{2π\sqrt{3}} Hz
b) \frac{1}{4π\sqrt{3}} Hz
c) \frac{1}{4π\sqrt{2}} Hz
d) \frac{1}{π\sqrt{2}} Hz

8. The probability cumulative distribution function must be monotone as well as ___________
a) Increasing
b) Decreasing
c) Non-increasing
d) Non-decreasing

9. In the circuit given below, the capacitor is initially having a charge of 10 C. 1 second after the switch is closed, the current in the circuit is ________

a) 14.7 A
b) 18.5 A
c) 40.0 A
d) 50.0 A

10. The Fourier transform of a rectangular function is ___________
a) Another rectangular pulse
b) Triangular pulse
c) Sinc function
d) Impulse

11. A coil of inductance 10 H, resistance 40 Ω is connected as shown in the figure. After the switch S has been in connection with point 1 for a very long time, it is moved to point 2 at t=0. For the value of R obtained, the time taken for 95 % of the stored energy dissipated is close to?

a) 0.10 s
b) 0.15 s
c) 0.50 s
d) 1.0 s

12. Convolution is used to find ____________
a) Impulse of an LTI system
b) Frequency response of an LTI system
c) Time response of an LTI system
d) Phase response of an LTI system

13. The property of Fourier Transform which states that the compression in time domain is equivalent to expansion in the frequency domain is ___________
a) Duality
b) Scaling
c) Time scaling
d) Frequency shifting

14. The function which has its Fourier transform, Laplace transform, and Z transform unity is __________
a) Gaussian
b) Impulse
c) Sinc
d) Pulse

15. N(t) = 2, 0≤t<4;
t2, t≥4;
The Laplace transform of M (t) is ___________
a) 2s–e−4s(2s3–8s2–14s)
b) 2s+e−4s(2s3–8s2–14s)
c) 2s–e−4s(2s3+8s2+14s)
d) 2s+e−4s(2s3+8s2+14s)

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