What is rms value: Definition and 20 Discussions

In mathematics and its applications, the root mean square of a set of numbers



{\displaystyle x_{i}}
(abbreviated as RMS, RMS or rms and denoted in formulas as either



{\displaystyle x_{\mathrm {RMS} }}



{\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



{\displaystyle M_{2}}
) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted



{\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.

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  1. PhysicsTest

    Phase currents of Trapezoidal switching

    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...
  2. JamesBennettBeta

    Engineering Power and RMS Value of a Signal

    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...
  3. Frigus

    B What is the RMS value in this context?

    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...
  4. M

    RMS value secondary voltage electronic halogen transformer

    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"...
  5. I

    Find the RMS value of current I

    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...
  6. CassiopeiaA

    RMS value & noise measurements

    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.
  7. Q

    Question about rms value of a sine wave

    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?
  8. N

    Determine the rms value for the given function

    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...
  9. I

    RMS value of a fully rectified clamped sinusoid.

    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...
  10. L

    Calculating RMS Value for Unequal Peak Amplitudes

    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 :)
  11. Twinflower

    Finding RMS value of strange column function

    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...
  12. Y

    Rms value of the half-wave rectified sinusoidal wave

    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...
  13. K

    Intensity of an electromagnetic wave, given only rms value of magnetic field

    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...
  14. R

    Calculating RMS Value of i=1/3sin3t

    [b]1. find the rms value of i=1/3sin3t between t=0 and t=1/10 [b]2. not sure of the method or the formula i may need [b]3. Any help appreciated
  15. E

    Determine the rms value of the electric field of the transmitted beam

    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...
  16. T

    Phasor Voltage and Voltage RMS value

    What's the difference between the two? RMS is divided by square root of 2?
  17. D

    Deriving RMS value from sinusoidal waveform.

    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...
  18. K

    Why Are Mean and RMS Values Close to 30 in Dynamic Signal Analysis?

    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...
  19. D

    Capacitor: RMS value or double RMS value?

    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.
  20. B

    Discover the Analytical Calculation for RMS Voltage from v(t) = Vm cos(wt+theta)

    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?