In mathematics and its applications, the root mean square of a set of numbers
x
i
{\displaystyle x_{i}}
(abbreviated as RMS, RMS or rms and denoted in formulas as either
x
R
M
S
{\displaystyle x_{\mathrm {RMS} }}
or
R
M
S
x
{\displaystyle \mathrm {RMS} _{x}}
) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set.
The RMS is also known as the quadratic mean (denoted
M
2
{\displaystyle M_{2}}
) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted
f
R
M
S
{\displaystyle f_{\mathrm {RMS} }}
) can be defined in terms of an integral of the squares of the instantaneous values during a cycle.
For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load.
In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data.
For trapezoidal switching or 180 degree switching these are the waveforms when i referred to the website
180 switching
when i calculated the RMS value of the phase voltage it is Vp = 0.4714Vs
so assuming the
Vs = supply voltage = 20V
and each phase - phase resistance as per the data sheet is...
I need to calculate the power and RMS value of some equations. The problem is, I found two methods to do that and don't know which is the right method.
I have few equations to find the power and RMS value, but here is one equation.
$$x( t) \ =\ 7\cos\left( 20t+\frac{\pi }{2}\right),$$
Method...
In this text they are saying that rms value is square root of average value of i² but i am not able to relate this thing to equations they have given.
It feels to me that the equations tell something different from the text.
From text I interpret that if we add each and every value of i² from 0...
I am trying to derive a scaling factor for an analog voltmeter for the purpose of measuring the secondary voltage of an electronic halogen transformer (EHT).
http://www.ledbenchmark.com/faq/Transformers-Output-and-Compatibility.html
The output voltage of these things is a "high frequency"...
Homework Statement
In the network of sinusoidal current, as shown in the figure, the current i2
is phase delayed for the angle of 3π/4 behind the current i.
In the moments in which the current i2 is minimal,
current value of current i1 is sqrt(2) A. This value is two times lower than the...
I am confused about very fundamental question.
Why does the rms value of number of electrons collected from a signal(like in photoconductor) gives you the noise in that signal.
Sorry if this sounds like a dumb question, but why is the effective value of a sine wave 0.707, as opposed to 0.637 which is the value generated by finding the definite integral over the domain [0,∏] divided length of the domain?
Homework Statement
Determine the rms value of v(t) = 15 + 10cos(20πt)
Homework Equations
Vrms = √(1/T*∫T0v2dt
The Attempt at a Solution
√(10*∫0.10[15+10cos(20πt)]2dt
Unless, I'm much mistaken I should be able to plug the equation into the formula I have given above. I used...
so i have a question about calculating the RMS value of a fully rectified clamped sinusoid.
Assumptions:
The top of the waveform = U
It is clamped at 0.5 U
I can calculate the RMS value by adding the 3 components of the wave, ei. @ 0.5U ω = π/6 & 5π/6 which forms a block and two side...
If I have a wave that looks pretty much sinusoidal but the peak positive amplitide is greater than the peak negative applitude how do I calcualte the rms vlaue - is it still the peak positive amplitude divided by root 2?
Thanks :)
Homework Statement
This is the given function:
Homework Equations
The RMS equation goes like this:
\sqrt(\frac{\int(f(t)^2 dt)}{b - a})
The Attempt at a Solution
The first part of the exercise was to find the mean value.
This is A/4.
The RMS value should be higher...
Homework Statement
I know the rms of a half wave is half the peak value. But the peak value is not given to me. Instead, the V(t) function of 4cos(20pi(x)) is given. Also the period T = 100ms
Homework Equations
vrms = vpeak/2
But the peak is not given!
The Attempt at a Solution...
Homework Statement
Hi, here is the problem I'm having trouble with:
The rms value of the magnitude of the magnetic field in an electromagnetic wave is Brms = 0.137 T. The intensity of this wave is approximately...
Homework Equations
E = cB
I = (ErmsBrms) / \mu0
The Attempt at a...
Homework Statement
A beam of polarized light has an average intensity of 13.2 W/m2 and is sent through a polarizer. The transmission axis makes an angle of 27.5° with respect to the direction of polarization. Determine the rms value of the electric field of the transmitted beam...
I'm having a problem with that integration part.
The average value of i^2 in one cycle = (sum of all i^2 in that period)/(that period).
To derive (sum of all i^2 in that period) we use integration, but that gives the area, how can the area be a substitution for this?...they are different...
Homework Statement
comment on nature and meaning of results in terms of analysis of dynamic signals.
(why do i see these results and what should we do to increase the accuracy of these two values)Homework Equations
y=30+(2cos(6*pi*t))
both mean value and rms value come out to be very close...
Hi! I have the following question:
A capacitor is connected to a transformer(sine wave) with 5v of output voltage(RMS). What final voltage is applied to the capacitor plates? And should I consider the current applied to the capacitor equal to RMS value or double RMS value? Thanks.
The question is "starting from v(t) = Vm cos(wt+theta), show analytically that the RMS value of v(t) is v(t)=Vm/sqrt(2) for any w or theta."
I'm not really sure how to begin this. Do I start by taking the integral?