204 Basic Engineering Mathematics
- v=300sin( 200 πt− 0. 412 )V
- 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). - 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). - 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.