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VCE Stuff => VCE Science => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Physics => Topic started by: chid on November 08, 2008, 09:55:49 pm

Title: 'Maximum induced voltage'
Post by: chid on November 08, 2008, 09:55:49 pm: In VCAA 2006 Exam Question 8 (AS 1) required the calculation of the maximum induced voltage in a loop moving at a constant rate into a magnetic field.
Faraday's equation calculates the average EMF so don't you have to multiply the answer by root 2.

The solutions don't do this, so I must be wrong...but why?

Thanks.
Title: Re: 'Maximum induced voltage'
Post by: BiG DaN on November 08, 2008, 10:40:07 pm: im pretty sure ur only asked to do av emf now
Title: Re: 'Maximum induced voltage'
Post by: onlyfknhuman on November 08, 2008, 10:40:33 pm: You dont times it by root 2, because emf = delta flux / delta time is really average emf induced which in terms of the formula is the maximum.

the only formula for maximum voltage is emf = NBA2PIf which is not in the course.

When a voltage is given in RMS do you times it by sqroot 2. But when using e = blv or emf = N delta flux / delta time , noting else forget the whole sqr root concept if uc an use those. In terms of motors

YEAH its stupid how they asked for maximum...
Title: Re: 'Maximum induced voltage'
Post by: Mao on November 08, 2008, 11:01:51 pm: times average emf by $\frac{\pi}{2}$

$\frac{\pi}{2}\cdot \frac{1}{t_{\frac{1}{4}}} = \frac{\pi}{2}\cdot \frac{1}{\frac{1}{4f}} = \frac{\pi \cdot 4f}{2} = 2\pi f$

$\Phi_{max} = B\cdot A$

$\implies \mathcal{E}_{max}=nBA2\pi f = n\cdot \frac{\Phi_{max}}{t_{\frac{1}{4}}} \cdot \frac{\pi}{2}$

http://vcenotes.com/forum/index.php/topic,4476.0.html
Title: Re: 'Maximum induced voltage'
Post by: chid on November 08, 2008, 11:03:51 pm: Quote from: onlyfknhuman on November 08, 2008, 10:40:33 pm
You dont times it by root 2, because emf = delta flux / delta time is really average emf induced which in terms of the formula is the maximum.

the only formula for maximum voltage is NBA2pif which is not in the course.

When a voltage is given in RMS do you times it by sqroot 2. But when using e = blv or emf = N delta flux / delta time , noting else forget the whole sqr root concept if uc an use those. In terms of motors

YEAH its stupid how they asked for maximum...
But isn't NBA2pif the peak voltage, which must be divided by root 2 to get EMF average?
Title: Re: 'Maximum induced voltage'
Post by: onlyfknhuman on November 08, 2008, 11:11:51 pm: Quote from: chid on November 08, 2008, 11:03:51 pm
Quote from: onlyfknhuman on November 08, 2008, 10:40:33 pm
You dont times it by root 2, because emf = delta flux / delta time is really average emf induced which in terms of the formula is the maximum.

the only formula for maximum voltage is NBA2pif which is not in the course.

When a voltage is given in RMS do you times it by sqroot 2. But when using e = blv or emf = N delta flux / delta time , noting else forget the whole sqr root concept if uc an use those. In terms of motors

YEAH its stupid how they asked for maximum...
But isn't NBA2pif the peak voltage, which must be divided by root 2 to get EMF average?

Yes i think..

Mao is that even in the course?

Dispite it asking for maximum voltage it used the formula for average voltage
Title: Re: 'Maximum induced voltage'
Post by: Mao on November 08, 2008, 11:15:30 pm: Chid: RMS and this are very different things. in RMS, the ratio between peak and average is $\sqrt{2}$ , in this, the ratio between peak and average is $\frac{\pi}{2}$ .

however, as onlyfknhuman pointed out, the latter isn't even on the course [though it's not hard to derive, it just requires methods knowledge]

and for the sake of clarity:

$\frac{\pi}{2}\mathcal{E}_{ave} \equiv nBA2\pi f$ , these two will yield the same result.
Title: Re: 'Maximum induced voltage'
Post by: onlyfknhuman on November 08, 2008, 11:22:51 pm: Hrm why did they ask for the maximum induced voltage then odd... ?

And sorry, so just times by pi/2 for max voltage?
Title: Re: 'Maximum induced voltage'
Post by: chid on November 08, 2008, 11:24:24 pm: Quote from: Mao on November 08, 2008, 11:15:30 pm
Chid: RMS and this are very different things. in RMS, the ratio between peak and average is $\sqrt{2}$ , in this, the ratio between peak and average is $\frac{\pi}{2}$ .

however, as onlyfknhuman pointed out, the latter isn't even on the course [though it's not hard to derive, it just requires methods knowledge]

and for the sake of clarity:

$\frac{\pi}{2}\mathcal{E}_{ave} \equiv nBA2\pi f$ , these two will yield the same result.
Does that mean that VCAA in providing the average emf instead of the maximum are wrong? If they are then 2006 was a pretty bad year for them in Physics (remember the transistor amplifier stuff up on the mid year!)