rms current

(noun)

the root mean square of the current, Irms=I0/√2 , where I0 is the peak current, in an AC system

Related Terms

Examples of rms current in the following topics:

  • 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:
    • We also learned the phase relationships among the voltages across resistor, capacitor and inductor: when a sinusoidal voltage is applied, the current lags the voltage by a 90º phase in a circuit with an inductor, while the current leads the voltage by 90∘ in a circuit with a capacitor.
    • 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∘.

  • Root Mean Square Values

    • Unlike direct current (DC), where the currents and voltages are constant, AC currents and voltages vary over time.
    • 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.
    • Here, I is the current at time t, and I0=V0/R is the peak current.
    • 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.

  • Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams

    • The voltage across a capacitor lags the current.
    • We say that the current and voltage are in phase.
    • Since an AC voltage is applied, there is an rms current, but it is limited by the capacitor.
    • This is considered to be an effective resistance of the capacitor to AC, and so the rms current Irms in the circuit containing only a capacitor C is given by another version of Ohm's law to be $I_{rms} = \frac{V_{rms}}{X_C}$, where Vrms is the rms voltage.
    • Since the voltage across a capacitor lags the current, the phasor representing the current and voltage would be give as in .

  • Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams

    • The graph shows voltage and current as functions of time.
    • The current then becomes negative, again following the voltage.
    • Current lags behind voltage, since inductors oppose change in current.
    • Changing current induces an emf .
    • 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.

  • Resonance in RLC Circuits

    • where Irms and Vrms are rms current and voltage, respectively.
    • A variable capacitor is often used to adjust the resonance frequency to receive a desired frequency and to reject others. is a graph of current as a function of frequency, illustrating a resonant peak in Irms at $\nu_0 = f_0$.
    • A graph of current versus frequency for two RLC series circuits differing only in the amount of resistance.

  • Humans and Electric Hazards

    • A shock hazard occurs when electric current passes through a person.
    • A person can feel at least 1 mA (rms) of AC current at 60 Hz and at least 5 mA of DC current.
    • The current may, if it is high enough, cause tissue damage or fibrillation, which leads to cardiac arrest. 60 mA of AC (rms, 60 Hz) or 300-500 mA of DC can cause fibrillation.The potential severity of the shock depends on paths through the body that the currents take.
    • Current: The higher the current, the more likely it is lethal.
    • Since current is proportional to voltage when resistance is fixed (Ohm's law), high voltage is an indirect risk for producing higher currents.

  • Phase Angle and Power Factor

    • Impedance is an AC (alternating current) analogue to resistance in a DC circuit.
    • (We will represent instantaneous current as i(t). )
    • we notice that voltage $v(t)$ and current $i(t)$ has a phase difference of $\phi$.
    • Because voltage and current are out of phase, power dissipated by the circuit is not equal to: (peak voltage) times (peak current).
    • It can be shown that the average power is IrmsVrmscosϕ, where Irms and Vrms are the root mean square (rms) averages of the current and voltage, respectively.

  • Power

    • Power delivered to an RLC series AC circuit is dissipated by the resistance in the circuit, and is given as $P_{avg} = I_{rms} V_{rms} cos\phi$.
    • As seen in previous Atoms, voltage and current are out of phase in an RLC circuit.
    • There is a phase angle ϕ between the source voltage V and the current I, given as
    • I(t) and V(t) are current and voltage at time t).
    • \phi is the phase angle, equal to the phase difference between the voltage and current.

  • 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.

  • Answers to Chapter 6 Questions

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