rms voltage

(noun)

the root mean square of the voltage, Vrms=V0/√2 , where V0 is the peak voltage, in an AC system

Related Terms

Examples of rms voltage in the following topics:

  • Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams

    • The graph shows voltage and current as functions of time.
    • (b) starts with voltage at a maximum.
    • When the voltage becomes negative at point a, the current begins to decrease; it becomes zero at point b, where voltage is its most negative.
    • Hence, when a sinusoidal voltage is applied to an inductor, the voltage leads the current by one-fourth of a cycle, or by a 90º phase angle.
    • 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.

  • Root Mean Square Values

    • The root mean square (RMS) voltage or current is the time-averaged voltage or current in an AC system.
    • 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.
    • V is the voltage at time t, V0 is the peak voltage, and f is the frequency in hertz.
    • 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.

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

    • In previous Atoms we learned how an RLC series circuit, as shown in , responds to an AC voltage source.
    • 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∘.

  • Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams

    • The voltage across a capacitor lags the current.
    • When a capacitor is connected to an alternating voltage, the maximum voltage is proportional to the maximum current, but the maximum voltage does not occur at the same time as the maximum current.
    • 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 .

  • Resonance in RLC Circuits

    • To study the resonance in an RLC circuit, as illustrated below, we can see how the circuit behaves as a function of the frequency of the driving voltage source.
    • where Irms and Vrms are rms current and voltage, respectively.
    • This is also the natural frequency at which the circuit would oscillate if not driven by the voltage source.
    • The driving AC voltage source has a fixed amplitude V0.
    • An RLC series circuit with an AC voltage source. f is the frequency of the source.

  • Phase Angle and Power Factor

    • In a series RC circuit connected to an AC voltage source, voltage and current maintain a phase difference.
    • On the other hand, because the total voltage should be equal to the sum of voltages on the resistor and capacitor, so we have:
    • 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.

  • Humans and Electric Hazards

    • A short circuit is a low-resistance path between terminals of a voltage source.
    • Such an undesired contact with a high voltage is called a short.
    • A person can feel at least 1 mA (rms) of AC current at 60 Hz and at least 5 mA of DC current.
    • Since current is proportional to voltage when resistance is fixed (Ohm's law), high voltage is an indirect risk for producing higher currents.
    • Very high voltage (over about 600 volts): This poses an additional risk beyond the simple ability of high voltage to cause high current at a fixed resistance.

  • 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: $\gamma _ {\rm critical} = 2 \omega _0 = 2 \times 2 \pi \times 2 {\rm s^{-1}} \approx 25 {\rm s^{-1}}$ .
    • where $q$ is the charge on the capacitor, $L$ is the inductance of the coil, $R$ is the resistance, $C$ the capacitance, and $V$ is the applied voltage.
    • 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 $C = \frac{1}{L (2 \pi)^2} \approx 1 \rm Farad$ .

  • EMF and Terminal Voltage

    • The output, or terminal voltage of a voltage source such as a battery, depends on its electromotive force and its internal resistance.
    • presents a schematic representation of a voltage source.
    • The voltage output of a device is measured across its terminals and is called its terminal voltage V.
    • Terminal voltage is given by the equation:
    • The larger the current, the smaller the terminal voltage.