(adsbygoogle = window.adsbygoogle || []).push({}); A simple single-phase generator has coils of 200 turns. The coil is 14cm long and 9cm wide. The magnetic field in the generator is 0.15T. The generator coil is turned at a rate of 3000rpm.

Calculate the emf produced by this generator.

[tex]

\begin{array}{c} \\

\frac{{d\theta }}{{dt}} = 3000rpm = 100\pi {\rm{ rad/sec}} \\

\varepsilon = - N\frac{d}{{dt}}(AB\cos \theta ) \\

= \frac{{d\theta }}{{dt}}NAB\sin \theta \\

= (100\pi )(200)(0.09)(0.14)(0.15)\sin (100\pi t) \\

= 37.8\pi \sin (100\pi t) \\

\end{array}

[/tex]

Now it asks for 'the emf', which is a bit hard to give as a numerical answer, since the emf varies with time. I looked at the answer, and they give an average emf.

So i proceeded as follows:

[tex]

\varepsilon _{{\rm{av}}} = \frac{{\varepsilon _{\max } }}{{\sqrt 2 }} = \frac{{37.8\pi }}{{\sqrt 2 }} = 83.97V

[/tex]

Now the book does it differently. They find the change in flux over a 90 degree turn (and i think are assuming that the rate of change of flux is constant), and then find the change in time.

[tex]

\begin{array}{c}

\Phi _B = AB\cos \theta \\

\Phi _i = 0.00189\cos \frac{\pi }{2} = 0 \\

\Phi _f = 0.00189\cos 0 = 0.00189 \\

\Delta \Phi _B = 0.00189 \\

\Delta t = 0.005 \\

\varepsilon = - N\frac{{\Delta \Phi _B }}{{\Delta t}} = 75.6V \\

\end{array}

[/tex]

Which way is the correct way?

Thanks in advance,

Dan.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find the change in flux

**Physics Forums | Science Articles, Homework Help, Discussion**