Given v1 = 20 cos(wt + 10°) and v2 = -60 sin(wt + 10°) the phase difference %3D between the two sinusoids is :*
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- Find the phase relation for the following pairs of sinusoids, (which leads and lags which by how much). Draw the phasor diagram e1= -20sqrt2 sin(377t + 200°) V e2 = -10sqrt2 sin(377t - 285°) V1) Two alternating voltages are given by: v1 = 120 sin (ωt) volts and v2 =200 sin (ωt −π/4) volts. Obtain sinusoidal expressions for v1 −v2 (a) by plotting waveforms, and (b) by resolution of phasors.Two alternating voltages are given by v1 = 15sinωt volts and v2 = 25 sin (ωt – π/6) volts. Plot both functions on the same axes and hence determine a sinusoidal expression for the resultant vr = v1 + v2. Check your answer using an analytical method. Your manager has asked you to analyse the variation in in results between the two methods
- Find the phase relation for the following pairs of sinusoids, (which leads and lags which by how much). Draw each phasor diagrams (a) i1 = -3cos(377t-π/4)A i2 = -3cos(377t-2π/3)A (b) v = 12√2 sin(50πt+390°)V i = 1.2 sin(50πt+100°)A (c) v = -3cos(377t-π/4)V i = 1.2sin(50πt+100°)ASuppose that v1(t)=100 cos(ωt) and v2(t)=100 sin(ωt). Use phasors to reduce the sum vs(t) = v1(t) + v2(t) to a single term of the form Vm cos(ωt+θ). Draw a phasor diagram, showing V1, V2 and Vs .State the phase relationships between each pair of these phasors.The signal V1=100 cos(500t - 30°) and the signal V2=20 sin (500t +45°) compared in phase would be a) V1 15° ahead of V2 b) V1 75° behind V2 c) V2 15° ahead of V1 d) None of the above
- Find the phase relations for the following pairs of sinusoids. Sketch the curve e and i anddetermine which one LAGS and LEADS.a. v = 60 sin(377 t + 50°) V ; i = 3 sin(754t − 10°)A b. v = 6.4 sin(7.1 πt + 30°) V ; i = 7.3 sin(7.1 πt − 10°)A c. v = 42.3 sin(400 t + 60°) V ; i = −4.1 sin(400t − 50°)ASuppose we are to convert the phasor current I(jw) to the sinusoidal current i(t). Which of the following statements is/are true? The magnitude of the phasor current I(jw) is equal to the amplitude of the sinusoidal current i(t). The magnitude of the phasor current I(jw) is equal to the effective value of the sinusoidal current i(t). The angle of the phasor current I(jw) is equal to the phase shift of the sinusoidal current i(t). a. 2 and 3 b. 1 and 3 c. 2 only d. 1 onlyIf a current 5.0 A lags the applied voltage 230 V by an angle ϕ, it can be resolved into two components, OA in phase with the voltage and OB lagging by 90°. If the phasor diagram in to a circuit possessing resistance and inductance in series, OA and OB must not be labelled and respectively. It has become the practice to say that the power factor is laggingwhen the current lags the supply voltage, and leading when the current leads the supply voltage. This means that the supply voltage is regarded as the reference quantity. (a) A 30 μ F capacitor is connected across the applied voltage, 50 Hz supply. Calculate the reactance of 30 μ F capacitor connected across applied voltage (b) the reactance of the capacitor; (c) the current.
- Find the sinusoidal expression for the current iS for the system shown below: i1 = 6 mA sin(377t +180°) i2 = 8 mA sin (377t) i3 =2i2 A) iS=18 mA sin (377t) B) is = 16 mA sin (377t) C) is= 12.726 mA (sin 377t +20∘∘)Read A 70-Vac source has the following waveform. Determine:a. Vpkb. Vpk-pkc. Vrmsd. Periode. Frequencyf. Angular Velocityg. Phase Angleh. equation of the waveform (in time domain)i. the instantaneous voltage when t = 120 msj. the angle (1st occurrence) after t = 0 when the voltage is +80 Vk. the time (2nd occurrence) after t = 0 when the voltage is –10 VAnswers:a. 98.9949 Vb. 197.9899 Vc. 70 Vd. 100 mse. 10 Hzf. 20π rad/secg. 125.0876°h. v(t) = 98.9949sin(20πt + 125.0876°)i. -29.0880 Vj. 0.99959°k. 63.643 ms Give the solution for J and K ONLY ans (0.99959 degrees and 63.643 ms respectively)Suppose that v1(t) = 90 cos(ωt-15) and v2(t) = 50 sin (ωt-60). Use phasors to reduce the difference vs(t) = v1(t) –v2(t) to a single term of the form Vmcos(ωt+θ). State the phase relationships between each pair of these phasors.