[Catalist] Average emf induced in a coil formulae

[Roy Skinner]

A lot of students are confused by all the different formulae on voltage.
Peak voltage only gets reached for a fraction of a second and average
voltage is found for only one flux change that has been made. RMS is very
similar to Standard Deviation in maths where you have as many negative
deviations from the mean as positive so square them all average the squares
then divide by 2 the square root back again. RMS is useful because it gives
the value of constant DC voltage that would give the same power as the
varying AC voltage. Household supplies actually hit 340 volts peak but we
say they are 240 RMS because this would be the constant DC value that would
give you the same power output.
Roy

-----Original Message-----
From: Catalist [mailto:catalist-bounces at lists.stawa.net] On Behalf Of
Elizabeth Kirby
Sent: Saturday, 17 September 2016 10:15 PM
To: <p.delacey at physics.org> <p.delacey at physics.org>;
<catalist at lists.stawa.net> <catalist at lists.stawa.net>
Subject: Re: [Catalist] Average emf induced in a coil formulae

Thank you for this response, Peter. Most people have responded similarly.
What I do find disconcerting is that the worked solutions for the new STAWA
book for the Problem Set on Induction, I think it's set 11, questions 18 to
21, uses Faraday's Law and the time for a quarter turn and according to the
solutions, it is the max emf that has been calculated. Subsequent parts of
the question asking for the RMS value then uses that emf and divides it by
square root of 2. It just seems contradictory. Instead of the new book using
the new formula when the frequency of the coil is given, it still shows the
'old' method.
Kind regards
Elizabeth

Sent from my iPhone

> On 17 Sep 2016, at 13:35, P. de Lacey <p.delacey at physics.org> wrote:
> 
> Hi Elizabeth,
> If students are using the formula Emf(av) = 4NABf they need to 
> understand clearly what they are calculating and how it differs from 
> Emf(rms) or Emf(max) The formula Emf(av) = 4NABf gives the average e.m.f.
of a fully-rectified sine wave. (This is not the same as Emf(rms).) Its
relationship to Emf(max) is Emf(max)= (pi/2)Emf(av), which reduces to the
formula Emf(max) = NAB2(pi)f.
> Average voltage is not a useful value when dealing with (sinusoidal) a.c.
because the average value over a full cycle is zero. Peak and r.m.s. values
are more useful, so students should, preferably, use these.
> Best regards,
> Peter de Lacey
> 
> 
>> On 14/09/16 06:28, Elizabeth Kirby wrote:
>> Esteemed Catalistians
>> Could someone in the realm of Yr 12 Physics clarify for me whether or 
>> not students can still use the formula Emf (av.) = 4NABf, when they 
>> are given the frequency of rotation of a coil - provided they explain 
>> that there are 4 flux changes per rotation? This formula gives the 
>> same result as Faraday's Law if one calculates the time for a quarter 
>> turn and one uses that quarter time as the time for a flux change. 
>> The new formula Emf (max) = NAB2 pi f, does not give the same answer 
>> even when one adjusts with the V peak and V RMS formula.
>> Urgent help required with this please.
>> Kind regards
>> Elizabeth
>> 
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