Basic Engineering Mathematics, Fifth Edition

(Amelia) #1

204 Basic Engineering Mathematics



  1. v=300sin( 200 πt− 0. 412 )V

  2. A sinusoidal voltage has a maximum value of
    120V and a frequency of 50Hz. At timet=0,
    the voltage is (a) zero and (b) 50V. Express
    the instantaneous voltage v in the form
    v=Asin(ωt±α).

  3. An alternating current has a periodic time of
    25ms and a maximum value of 20A. When
    time=0, currenti=−10 amperes. Express
    the currentiin the formi=Asin(ωt±α).

  4. Anoscillatingmechanismhasamaximumdis-
    placement of 3.2m and a frequency of 50Hz.
    At timet=0 the displacement is 150cm.
    Express the displacement in the general form
    Asin(ωt±α)
    7. The current in an a.c. circuit at any timet
    seconds is given by
    i=5sin( 100 πt− 0. 432 )amperes
    Determine the
    (a) amplitude, frequency, periodic time and
    phase angle (in degrees),
    (b) value of current att=0,
    (c) value of current att=8ms,
    (d) time when the current is first a maximum,
    (e) time when the current first reaches 3A.
    Also,
    (f ) sketch one cycle of the waveform show-
    ing relevant points.

Free download pdf