HELP! Sine Waves

Discussion in 'Homework Help' started by Frano, Jun 9, 2008.

  1. Frano

    Thread Starter New Member

    Jun 9, 2008
    7
    0
    Hi,

    My text isn't great - can anyone help me with the following question?

    A waveform is represented by the following equation:

    e = 100 sin 314,28 t
    Determine:

    a) the maximum value of the emf
    b) the rms and average values
    c) the frequency of the suppy
    d) the instantaneous value of the emf @ 12 milliseconds after passsing through the zero positively
    e) the form factor

    Thanks​
     
  2. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Your sinusoidal wave can be generically represented as:

    e(t) = E_{max}Sin\left(2\pi ft\right)

    E_{max}

    E_{rms} = \frac{1}{\sqrt{2}}E_{max}

    E_{average} = \frac{2}{\pi}E_{max}

    Comparing your equation with the generic equation you can equate the following:

    314.28 = 2\pi f

    Rearrange to get the frequency f.

    Substitute the value 12e-3 for t in your orginal equation to get the instantaeous voltage.

    The form factor is calculated as:

    F_{F} = \frac{E_{rms}}{E_{average}}

    Have a go and post up you answers if you want someone here to check your calculations.

    Dave
     
    Last edited: Jun 9, 2008
  3. Frano

    Thread Starter New Member

    Jun 9, 2008
    7
    0
    Thanks Dave, I'm at work at the moment but I'll have a crack at it tonight and post my answers tomorrow. :)
     
  4. Frano

    Thread Starter New Member

    Jun 9, 2008
    7
    0
    a) from the generic equation Emax = 100

    b) Erms = 1/1.4142 x 100 = 70.71

    Eave = 2/3.1428 x 100 = 63.64

    e) Form factor = 70.71/63.64 = 1.11

    c) 314.28 = 2 x pi x f so f = 314.28/ 6.2856 = 50Hz What happens to the (t) from the generic equation (2 x pi x f x t)?

    d) I'm afraid you lost me here - I couldn't figure out where you got (12e - 3) from so I did my own thing...

    e @ 12 milliseconds = E(max) sin (2 x pi x f x t)
    = 100 sin (2 x 3.1428 x 50 x 0.012)
    = 100 sin (3.77136)
    = 100 x 0.065775
    = 6.5775

    Is this correct?

    Thanks.
     
  5. Wiaan1

    New Member

    Feb 23, 2009
    1
    0
    Q: The starting circuit of a motor has a coil with a resistance of 40 Ohm and an inductance of 0,25 henry connected in series with a capacitor of 20 microfarad. The supply is 250V, 50 Hz.

    Calculate:

    1.1) the inductive reactance
    1.2) the capacitive reactance
    1.3) the impedance
    1.4) the supply current
    1.5) the power factor
    1.6) the phase angle
     
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