rms

(noun)

Root mean square: a statistical measure of the magnitude of a varying quantity.

Related Terms

Examples of rms in the following topics:

  • Root Mean Square Values

    • The root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity.
    • Now using the definition above, let's calculate the rms voltage and rms current.
    • If we are concerned with the time averaged result and the relevant variables are expressed as their rms values.

  • Vapor Pressure of Nonelectrolyte Solutions

    • In this equation, $p^{\star}_{\rm A}$ is the vapor pressure of the pure solvent and $x_{\rm A}$ is the mole fraction of the solvent.

  • RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram

    • By combining Ohm's law (Irms=Vrms/Z; Irms and Vrms are rms current and voltage) and the expression for impedance Z, from:
    • Therefore, the rms current will be Vrms/XL, and the current lags the voltage by almost 90∘.
    • Therefore, the rms current will be given as Vrms/XC, and the current leads the voltage by almost 90∘.

  • Power

    • Power delivered to an RLC series AC circuit is dissipated by the resistance in the circuit, and is given as $P_{avg} = I_{rms} V_{rms} cos\phi$.

  • Answers to Chapter 6 Questions

    • We calculate the net present value of 43,126.54 rm below:
    • $NPV=-2,000\euro \left( 4.00\text{ rm}/ \euro\right)+\frac{?
    • \euro \left( 4.25\text{ rm}/ \euro \right) }{(1+0.04)^1}+\frac{?
    • \euro \left( 4.50\text{ rm}/ \euro \right) }{(1+0.04)^2}+\frac{?
    • \euro \left( 5.00\text{ rm}/ \euro \right) }{(1+0.04)^3}$

  • Root-Mean-Square Speed

    • The root-mean-square speed measures the average speed of particles in a gas, defined as $v_{rms}=\sqrt{\frac{3RT}{M}}$ .
    • It is represented by the equation: $v_{rms}=\sqrt{\frac{3RT}{M}}$, where vrms is the root-mean-square of the velocity, Mm is the molar mass of the gas in kilograms per mole, R is the molar gas constant, and T is the temperature in Kelvin.

  • Speed Distribution of Molecules

    • The distribution has a long tail because some molecules may go several times the rms speed.
    • The most probable speed vp (at the peak of the curve) is less than the rms speed vrms.
    • The most likely speed v_p is less than the rms speed v_rms.
    • Although very high speeds are possible, only a tiny fraction of the molecules have speeds that are an order of magnitude greater than v_rms.

  • Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams

    • The rms current Irms through an inductor L is given by a version of Ohm's law: $I_{rms} = \frac{V_{rms}}{X_L}$ where Vrms is the rms voltage across the inductor and $X_L = 2\pi \nu L$ with $\nu$ the frequency of the AC voltage source in hertz.

  • Avogador's Number

  • Exercises

    • Answer: $mg = kx$ , so $x = mg/k = .1 {\rm kg}~ 9.8 {\rm \frac{m}{s^2}}/ 15.8 {\rm \frac{N}{m}} = .06 {\rm m} = 6 {\rm cm}$ .
    • Answer: $\gamma _ {\rm critical} = 2 \omega _0 = 2 \times 2 \pi \times 2 {\rm s^{-1}} \approx 25 {\rm s^{-1}}$ .
    • Answer: $\sqrt{\frac{1}{LC}} = \omega _0 = 2 \pi f_0 = \frac{2 \pi}{1 \rm{sec}}$$C = \frac{1}{L (2 \pi)^2} \approx 1 \rm Farad$ .
    • Therefore $C = \frac{1}{L (2 \pi)^2} \approx 1 \rm Farad$ .