root mean square value

gourish · 2014-04-20 03:11:31

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?

bobbym · 2014-04-20 03:32:54

Hi;

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

gourish · 2014-04-20 03:34:38

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....

bobbym · 2014-04-20 03:38:07

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

gourish · 2014-04-20 03:46:10

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...

bobbym · 2014-04-20 03:49:02

There are some formulas here,

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

which do you think applies?

gourish · 2014-04-20 03:58:56

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....

gourish · 2014-04-20 04:02:41

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)...

bobbym · 2014-04-20 04:05:49

What did you get as a maxima?

gourish · 2014-04-20 04:08:14

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

bobbym · 2014-04-20 04:09:18

What did you maximize?

Bob · 2014-04-20 04:35:48

This might help:

where tan alpha = 3/4

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

Bob

gourish · 2014-04-21 05:38:30

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

bobbym · 2014-04-21 06:18:55

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

gourish · 2014-04-21 06:43:42

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

Math Is Fun Forum

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

root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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

Re: root mean square value

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