Question

# If the instantaneous value of a voltage in an AC circuit of the communication system (at...

If the instantaneous value of a voltage in an AC circuit of the communication system (at any time t seconds) is given by V= 142sin(8πt-0.125π) volts, determine:

a. The amplitude,

b. Periodic time (in ms)

c. Frequency

d. Phase angle in degrees

e. Voltage at t=0

f. Voltage at t=10ms

g.Time when voltage reaches 100volts

h. Time when voltage is maximum

i. Sketch one cycle of the waveform

j. Given that the voltage waveform can also be represented as V=Rsin(ωt+θ), use compound angle identities to resolve the resultant voltage waveform into its two component waveforms: asinωt and bcosωt.

k. In another circuit the voltage, V is made up of two components v1 = (A/3)Sin(t) and v2 = (A/2)Cos(t). Sketch the two component waveforms and the resulting waveform V= (A/3)Sin(t) + (A/2)Cos(t) on the same axes and estimate from your graph the equation of the combined waveform. Also analytically calculate, showing all your working, the parameters (R&θ) of the equation of the combined waveform if represented as V=Rsin(Ѡt+θ), giving θ in radians.

Solution:- 