Question

Can we please continue with the questions:

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:

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.

Answer 1

solution t. The instantaneous value of vollage es given by = 142sin (8TTE - 0.125 T) volts when t= 10ms. = 10x10 3 see V= 142 Sin (843.142 x 10 x103 - 0.125 X 3-142) V= 142 Sin (0.2513 – 0.3927). = 142 sin (-0.14) V=-142sin (0.14) =- 142 sin(8.02) = - 142 x 0.139 v=- 19.81 volts so when t=10ms; V- _19.81 Volts. g. when = 100 volts then ROO = 142 sin ( 8 TT+ - 0.125T) =142 sin ( 25:136- 0.3927) 1. 25.136+ - 0.3927 - sin)(100/162) - sint (0.704) -sin- (0.704) - 0.7810 rad = 44,740 25.136 t = 0.7810 + 0.3927 25. 136 t = 1.1735 t = 1.1737 = 0.0466 see 25.136 t = 46.69 ms

h. The maximum voltage is 142 v. Hence 142 = 142 sin ( 8 Tit - 0.125 TT) 1 = sin (8TTt - 0.125 IT) :. (8177 - 0.1257) = sint (1) = 90° = 1. 5708 rad. i 8Tt = 1.5708 0.125 TI - 1.9635 t = 0.07811 see t= 78.11 msec. i one cycle a waveform. when t = 0. v=142 sin (on 0.12511). = 142 sin (- 0.125 T1) = 12 sin (-0.3927) = 142x60.3826) Tv = – 54.32 volts]

The time period of ware es- T= 2T here was T = sec i. T= 0.25 see. = 250 msee 162v = 142 sin (STTA) = 142 sin (87t- 0.125TT) - 19.81 asomsed 500 msec - 54.32 -1428

This are the calculated values for given instantaneous values of voltage in the question.