390 23. The rms value of an AC voltage is defined by H v²(t)df where I' is the period of the waveform (a) A voltage is given by v(r) = l'cos (eor). Show that v. and is inde- Chapter 11: Symbolic Math pendent of ex. (The relationship between the period 7 and the radian fre- quency co is T = (b) A voltage is given by v(1) = 2.5 cos(350r) + 3 V. Determine v
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- Q2. For the Periodic Waveforms shown in the Figure, determine for each : Frequency, Average Value over half a cycle, RMS Value, Form Factor, and Peak Factor. 100 75 Voltage (V 50 25 20 40 Time (ms) 10 30 -100(b) An engineer is required to analyse a sinusoidal waveform for the voltage and current using oscilloscope. The voltage waveform produced Root Mean Square (RMS) value at 75 V with positive-going zero crossing at 30°. While the RMS value of current is 66.71 A with negative-going zero crossing at 0.349 rad. Assume the frequeney of both waveforms is 50 Hz. (i) Sketch the voltage and current waveform in the same axis by showing the important point. (ii) Determine instantaneous voltage when t = 8ms . (iii) Determine phase relationship between voltage and current waveform.Shown in the figure below is an "RC" circuit drive by an AC power source. The AC power source has an RMS voltage of Vps (RMS) = 11.58 Volts and is running at a frequency of f = 1.326e+04 Hz. resistor has a resistance of R = 3750 2 and the capacitor has an capacitance of C = 3.17e-09 Farads. Vps R ww Write the FORMULA for the total impedance of the circuit Ztot = Write the FORMULA for the phase of the total impedance of the circuit tot = Determine the numerical value of Ztot = Determine the numerical value of Pztot= Determine the current through the circuit: • I(PEAK) = • I(RMS) = Determine the voltage across the resistor: Amps Amps S2 C degrees
- The voltage waveform during the first half cycle are from t = 0 to t = 0.01 increases linearly from 50 to 100 V and during the remaining half cycle from -50 to –100 V. Determine the rms value of the voltage.Given the RMS value of the following voltage waveform is sqrt(8/3) , determine the maximum value, B, of the waveform.Shown in the figure below is an "RL" circuit drive by an AC power source. The AC power source has an RMS voltage of Vps (RMS) = 9.84 Volts and is running at a frequency of f = 8.585e+04 Hz. The resistor has a resistance of R = 2170 and the inductor has an inductance of L = 3.54e-03 Henries. Vps R ww Write the FORMULA for the total impedance of the circuit Ztot = Determine the numerical value of Ztot = 2890.5 Determine the numerical value of $z= = 41 Determine the current through the circuit: • I(PEAK) = 4.81E-3 • I(RMS) = 3.404E-3 Determine the voltage across the resistor: • VR(PEAK) = 7.387 • VR(RMS) = 5.22 ✔✔ Amps ✔Amps Write the FORMULA for the phase of the total impedance of the circuit z... = | tan-1 2701 R x Volts X Volts Determine the voltage across the inductor: • VL(PEAK) = 9.184 • VL(RMS) = 6.49 ✔ Volts Volts L R²+ WL- ✔ degrees 2 If a second circuit were connected in parallel with the inductor, this circuit would be considered as: O a low-pass filter O a capacitive switcher…
- A voltage wave of 250 kHz has a Vmax-5 V and Vmin=-35 V. The duty cycle of this wave is 0.875. This voltage waveform has been applied across a 2.5 µH inductor for a very long time so that steady state has been achieved. Diagrams of the wave parameters and circuit are shown in this figure: L What is the average voltage of this wave? Average voltage = 35 V Voltage (arb, unit) 1.25 Minimum current: -3.5€ Amps 1 0.75 0.5 0.25 0 4.25 05 Have you integrated the wave over full cycle? 4.75 4 -1.25 Vmax 0.5 Vmin What is the average current flowing through the inductor? Average current = 3.56 A 15 Period/s On average, there is no power consumed by the inductor. Have you considered this? What are the maximum and minimum currents that flow through the inductor? Maximum current: 0.50 Amps D= 25 TH TH Have you used the relationship for current and voltage in an inductor? Have you considered the slope of the current wave?49. The sinusoidal waveform is the fundamental type of waveform used in AC and is commercially distributed. True False 51. Peak factor of a signal is the ratio of the peak or maximum value to the RMS (root-median-square) value. True False 52. Periodic signals are signals that recur at a irregular time interval True FalseAn alternating voltage is given by: v=75 sin(200TTt-0.25) volts. Find the following: I. (a). The amplitude (b). The peak-to-peak value (c). The rms value (d). The periodic time (e). The frequency (f). The phase angle (in degrees and minutes) relative to 75 sin 200tt
- A harmonic analysis of the current drawn by a CFL yields the following data. Find the rms value of current and the wwwwwwww total harmonic distortion (THD). Harmonics rms Current (A) 1357a 0.15 0.12 0.08 0.03 0.02For the below sinusoidal voltage trace displayed by the CRO, the time/cm switch is on 0.2ms/cm and the volt/cm switch is on 1 V/cm. a) the frequency will be Hz b) the r.m.s value will be In CRO the beam can also be shifted vertically by applving a suitable DC voltage to theConsider the characteristics of alternating current (ac). Find the false statement below. A. Alternating Current is any current that periodically changes direction. B. The graph of an ac source shows the relationship between magnitude and time. C. The frequency of an ac signal refers to the noise on the signal. D. The period of an ac signal is the reciprocal of the frequency. O A. O B O D