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​

 

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​

Your sinusoidal wave can be generically represented as:

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

a) the maximum value of the emf

\(E_{max}\)

b) the rms and average values

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

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

c) the frequency of the suppy

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

\(314.28 = 2\pi f\)

Rearrange to get the frequency f.

d) the instantaneous value of the emf @ 12 milliseconds after passsing through the zero positively

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

e) the form factor

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

 

Thanks Dave, I'm at work at the moment but I'll have a crack at it tonight and post my answers tomorrow.

 

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.

 

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