FOURIER SERIES MCQ

Objective Questions

Short notes

Objective questions (Answers are given below)

1. A given function f (t) can be represented by
   a Fourier series if it
   (a) is periodic
   (b) is single valued
   (c) has a finite number of maxima and
   minima in any one period
   (d) all of the above.
2. In a Fourier series expansion of a periodic
   function, the coefficient a0 represents its
   (a) net area per cycle
   (b) d.c value (c) average value over half cycle (d) average a.c value per cycle

3. If in the Fourier series of a periodic function,
   the coefficient a0 is zero, it means that the
   function has
   (a) odd symmetry
   (b) even quarter-wave symmetry
   (c) odd quarter-wave symmetry
   (d) any of the above.
4. A periodic function f (t) is said to possess
   odd quarter-wave symmetry if
   (a) f (t) = f (–t)
   (b) f (–t) = –f (t)
   (c) f (t) = –f (t + T/2)
   (a) both (b) and (c).
5. If the average value of a periodic function
   over one period is zero and it consists of
   only odd harmonics then it must be
   possessing _ symmetry.
   (a) half-wave
   (b) even quarter-wave
   (c) odd quarter-wave
   (d) odd.
6. If in the Fourier series of a periodic function,
   the coefficient a0 = 0 and an = 0, then it must
   be having _ symmetry.
   (a) odd
   (b) odd quarter-wave
   (c) even
   (d) either (a) or (b).
7. In the case of a periodic function possessing
   half-wave symmetry, which Fourier
   coefficient is zero ?
   (a) an (b) bn
   (c) a0 (d) none of above.
8. A periodic function has zero average value
   over a cycle and its Fourier series consists of
   only odd cosine terms. What is the symmetry
   possessed by this function.
   (a) even
   (b) odd
   (c) even quarter-wave
   (d) odd quarter-wave
9. Which of the following periodic function
   possesses even symmetry ?
   (a) cos 3t (b) sin t
   (c) t . cos 50 t (d) (t + t2 + t5).

10. If the Fourier coefficient bn of a periodic
    function is zero, then it must possess __
    symmetry.
    (a) even
    (b) even quarter-wave
    (c) odd
    (d) either (a) and (b).
11. A complex voltage waveform is given by
    V = 120 sin ωt + 36(3ωt + π / 2) + 12 sin
    (5ωt + π). It has a time period of T seconds.
    The percentage fifth harmonic contents in the
    waveform is
    (a) 12 (b) 10
    (c) 36 (d) 5
12. In the waveform of Q. 11 above, the phase
    displacement of the third harmonic represents
    a time interval of _ seconds.
    (a) T/12 (b) T/3
    (c) 3T (d) T/36
13. When the negative half-cycle of a complex
    waveform is reversed, it becomes identical to
    its positive half-cycle. This feature indicates
    that the complex waveform is composed of
    (a) fundamental
    (b) odd harmonics
    (c) even harmonics
    (d) both (a) and (b)
    (e) both (a) and (c)
14. A periodic waveform possessing half-wave
    symmetry has no
    (a) even harmonics
    (b) odd harmonics
    (c) sine terms
    (d) cosine terms
15. The Fourier series of a wave form possessing
    even quarter-wave symmetry has only
    (a) even harmonics
    (b) odd cosine terms
    (c) odd sine terms
    (d) both (b) and (c).
16. The Fourier series of a waveform possessing
    odd quarter-wave symmetry contains only
    (a) even harmonics
    (b) odd cosine terms
    (c) odd cosine terms
    (d) none of above

1. (d) 2. (b) 3. (d) 4. (d) 5. (a) 6. (d) 7. (c) 8. (c) 9. (a) 10. (d) 11.(b) 12. (a) 13. (d) 14. (a) 15. (b) 16. (c)