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voltage

 Definition/Summary Voltage is electric potential difference, which is potential energy difference per charge: $V\ =\ U/q$ Energy per charge equals energy per time divided by charge per time, which is power divided by current (watts per amp): $V\ =\ U/q\ =\ P/I$ 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:$V\ =\ \int{E}\cdot d{x}$ The unit of voltage is the volt, $V$, also equal to the joule per coulomb, $J/C$.

 Equations Equations for DC and instantaneous equations for AC: $$V\ =\ IR$$ $$V\ =\ P/I\ =\ \sqrt{PR}$$ $$P\ =\ V^2/R\ =\ I^2R\ =\ VI$$ Average equations for AC: $$P_{average}\ =\ V_{rms}^2/R$$ $$P_{average}\ =\ V_{rms}I_{rms}cos\phi$$ $$P_{apparent} \ =\ V_{rms}I_{rms} \ =\ |P_{complex}|\ =\ \sqrt{P_{average}^2 + Q_{average}^2}$$ $$P_{average}\ =\ V_{rms}^2\cos\phi/|Z|$$ $$V_{average}\ =\ (2\sqrt{2}/\pi)V_{rms}\ =\ (2/\pi)V_{peak}$$ where $\phi$ is the phase difference between voltage and current, Z is the (complex) impedance, $Q$ is the reactive or imaginary power (involving no net transfer of energy), and $V_{rms}\text{ and }I_{rms}$ are the root-mean-square voltage and current, $V_{peak}/\sqrt{2}\text{ and }I_{peak}/\sqrt{2}$.

 Scientists Alessandro Volta (1745-1827)

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 Breakdown Physics > Electromagnetism >> Electronics

 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, $V\ =\ IR$. Across an AC capacitor or inductor, $V\ =\ IX$, where $X$ is the reactance. For a general AC load, $V_{rms}\ =\ I_{rms}|Z|$, where the complex number $Z\ =\ R+jX$ is the impedance (purely real for a resistance and purely imaginary for a capacitor or inductor). If phase is important, we use $V\ =\ IZ$, where $V$ and $I$ 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, $V_{rms}$, which is the peak voltage (amplitude) divided by √2. Voltage may be out of phase with current, by a phase difference (phase angle), $\phi$. Instantaneous power equals instantaneous voltage times instantaneous current: $P\ =\ VI$, but average power is $V_{rms}I_{rms}\cos\phi$, or the apparent power times the phase factor. AC power: AC power, $P$, usually means the power (true power, or real power) which transfers net energy (does net work), as opposed to the reactive power (imaginary power), $Q$, which transfers no net energy. Complex power is $S\ =\ P\ +\ jQ$.Electromotive force (emf): Electromotive force has different meanings for different authors (and is not a force anyway): see http://en.wikipedia.org/wiki/Electro...ce#Terminology. Sometimes it means voltage.