# 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
158
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