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What is voltage

  1. Jul 24, 2014 #1
    Definition/Summary

    Voltage is electric potential difference, which is potential energy difference per charge: [itex]V\ =\ U/q[/itex]

    Energy per charge equals energy per time divided by charge per time, which is power divided by current (watts per amp): [itex]V\ =\ U/q\ =\ P/I[/itex]

    Since potential energy is just another name for work done (by a conservative force), voltage is also electric force "dot" displacement per charge, ie electric field "dot" displacement:[itex]V\ =\ \int{E}\cdot d{x}[/itex]

    The unit of voltage is the volt, [itex]V[/itex], also equal to the joule per coulomb, [itex]J/C[/itex].

    Equations

    Equations for DC and instantaneous equations for AC:

    [tex]V\ =\ IR[/tex]

    [tex]V\ =\ P/I\ =\ \sqrt{PR}[/tex]

    [tex]P\ =\ V^2/R\ =\ I^2R\ =\ VI[/tex]

    Average equations for AC:

    [tex]P_{average}\ =\ V_{rms}^2/R[/tex]

    [tex]P_{average}\ =\ V_{rms}I_{rms}cos\phi[/tex]

    [tex]P_{apparent} \ =\ V_{rms}I_{rms} \ =\ |P_{complex}|\ =\ \sqrt{P_{average}^2 + Q_{average}^2}[/tex]

    [tex]P_{average}\ =\ V_{rms}^2\cos\phi/|Z|[/tex]

    [tex]V_{average}\ =\ (2\sqrt{2}/\pi)V_{rms}\ =\ (2/\pi)V_{peak}[/tex]

    where [itex]\phi[/itex] is the phase difference between voltage and current, Z is the (complex) impedance, [itex]Q[/itex] is the reactive or imaginary power (involving no net transfer of energy), and [itex]V_{rms}\text{ and }I_{rms}[/itex] are the root-mean-square voltage and current, [itex]V_{peak}/\sqrt{2}\text{ and }I_{peak}/\sqrt{2}[/itex].

    Extended explanation

    Two ways of defining voltage:

    voltage = energy/charge = work/charge = force"dot"distance/charge = (from the Lorentz force) electric field"dot"distance, or dV = E.dr

    but also voltage = energy/charge = (energy/time)/(charge/time) = power/current, or V = P/I

    Volt:

    The volt is defined as the potential difference across a conductor when a current of one amp dissipates one watt of power.

    Kirchhoff's second rule: (syn. Kirchhoff's Law, KVL)

    The sum of potential differences around any loop is zero.

    So potential difference is "additive" for components in series: the total potential difference is the sum of the individual potential differences.

    Across a DC or AC resistance, [itex]V\ =\ IR[/itex]. Across an AC capacitor or inductor, [itex]V\ =\ IX[/itex], where [itex]X[/itex] is the reactance.

    For a general AC load, [itex]V_{rms}\ =\ I_{rms}|Z|[/itex], where the complex number [itex]Z\ =\ R+jX[/itex] is the impedance (purely real for a resistance and purely imaginary for a capacitor or inductor). If phase is important, we use [itex]V\ =\ IZ[/itex], where [itex]V[/itex] and [itex]I[/itex] are complex numbers also.


    Alternating current (AC):

    The "official" voltage delivered by electricity generators and marked on electrical equipment (such as 240V or 100V) is the root mean square voltage, [itex]V_{rms}[/itex], which is the peak voltage (amplitude) divided by √2.

    Voltage may be out of phase with current, by a phase difference (phase angle), [itex]\phi[/itex].

    Instantaneous power equals instantaneous voltage times instantaneous current: [itex]P\ =\ VI[/itex], but average power is [itex]V_{rms}I_{rms}\cos\phi[/itex], or the apparent power times the phase factor.

    AC power:

    AC power, [itex]P[/itex], usually means the power (true power, or real power) which transfers net energy (does net work), as opposed to the reactive power (imaginary power), [itex]Q[/itex], which transfers no net energy.

    Complex power is [itex]S\ =\ P\ +\ jQ[/itex].

    Electromotive force (emf):

    Electromotive force has different meanings for different authors (and is not a force anyway): see http://en.wikipedia.org/wiki/Electromotive_force#Terminology. Sometimes it means voltage. :wink:


    * This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!
     
  2. jcsd
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