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#1 2014-04-20 03:11:31

gourish
Member
Registered: 2013-05-28
Posts: 153

root mean square value

if current i=3 sin Δ t + 4 cos Δ t
then the root mean square value of current is....
can anybody tell me a way to answer this using either calculus or a rough graph?

"The man was just too bored so he invented maths for fun"
-some wise guy

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#2 2014-04-20 03:32:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: root mean square value

Hi;

Just a question. This delta function, is a Dirac delta function, an impulse function or just a straight difference operator?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2014-04-20 03:34:38

gourish
Member
Registered: 2013-05-28
Posts: 153

Re: root mean square value

actually i didn't find the omega symbol which is generally used for the angular frequency of a wave so i used so treat it as a constant....

"The man was just too bored so he invented maths for fun"
-some wise guy

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#4 2014-04-20 03:38:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: root mean square value

If it is a constant then why not use the continuous formula for RMS?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2014-04-20 03:46:10

gourish
Member
Registered: 2013-05-28
Posts: 153

Re: root mean square value

well it depends on the time "t" so it's not a constant value the current is a function of time... generally if current i was given by
i= I cos (omega)t i know that I is the maximum value of current and find the RMS as I/root(2) which is not the case for this function.... i seem bit silly but i feel differentiating might help but i am not sure about it...

"The man was just too bored so he invented maths for fun"
-some wise guy

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#6 2014-04-20 03:49:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: root mean square value

There are some formulas here,

http://en.wikipedia.org/wiki/Root_mean_square

which do you think applies?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2014-04-20 03:58:56

gourish
Member
Registered: 2013-05-28
Posts: 153

Re: root mean square value

well that's the problem i don't know it's a combination of both sine wave and cosine wave... if we could maybe make them turn into either a sine wave or cosine wave we will find the rms value... i differentiated the equation and found that the current is maximum at tan θ =3/4 and plugged in the values into the original equation i am guessing the rms value is 5/root(2) but i am not sure....

"The man was just too bored so he invented maths for fun"
-some wise guy

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#8 2014-04-20 04:02:41

gourish
Member
Registered: 2013-05-28
Posts: 153

Re: root mean square value

thanks bobbym... your link helped i used the rms total=sqroot {rms1^2+rms2^2} where rms1 is 3/root(2) and rms2 is 4/root(2) so i ended up with the same answer 5/root(2)...

"The man was just too bored so he invented maths for fun"
-some wise guy

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#9 2014-04-20 04:05:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: root mean square value

What did you get as a maxima?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2014-04-20 04:08:14

gourish
Member
Registered: 2013-05-28
Posts: 153

Re: root mean square value

well maxima was at tan θ =3/4 but the link that you gave had the required formula to find the actual rms of the equation so it's really necessary

"The man was just too bored so he invented maths for fun"
-some wise guy

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#11 2014-04-20 04:09:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: root mean square value

What did you maximize?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2014-04-20 04:35:48

bob bundy
Registered: 2010-06-20
Posts: 8,226

Re: root mean square value

This might help:

where tan alpha = 3/4

This uses the compound angle formula http://www.mathsrevision.net/advanced-l … e-formulae

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#13 2014-04-21 05:38:30

gourish
Member
Registered: 2013-05-28
Posts: 153

Re: root mean square value

bob bundy the same thing is achieved even by calculus and bobbym i differentiated the current with respect to time and set the resulting equation to zero and found tan theta = 3/4

"The man was just too bored so he invented maths for fun"
-some wise guy

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#14 2014-04-21 06:18:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: root mean square value

I am not following you. I am getting as maximum of a bit more than 5.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#15 2014-04-21 06:43:42

gourish
Member
Registered: 2013-05-28
Posts: 153

Re: root mean square value

well  i=3 sin Δ t + 4 cos Δ t differentiate this with respect to time (after all it's a wave which is variable in space with time) doing this i get diff(i) w.r.t.time  = 3cosΔt-4sinΔt

for maxima diff(i) w.r.t.time=0 so 3cosΔt-4sinΔt=0
which gives tanΔt=3/4 now we can put it back into the original equation to find the answer to my question which is what i did

"The man was just too bored so he invented maths for fun"
-some wise guy

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