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voltage
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Definition/Summary
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Voltage is electric potential difference, which is potential energy difference per charge: 
Energy per charge equals energy per time divided by charge per time, which is power divided by current (watts per amp): 
Since potential energy is just another name for work done (by a conservative force), voltage is also electric force "dot" displacement per charge: 
The unit of voltage is the volt,  , also equal to the joule per coulomb,  . |
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Equations
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Equations for DC and instantaneous equations for AC:
Average equations for AC:
where  is the phase difference between voltage and current, Z is the (complex) impedance,  is the reactive or imaginary power (involving no net transfer of energy), and  are the root-mean-square voltage and current,  . |
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Breakdown
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Physics
> Electromagnetism
>> Currents & Circuits
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Extended explanation
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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:
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,  . Across an AC capacitor or inductor,  , where  is the reactance.
For a general AC load,  , where the complex number  is the impedance (purely real for a resistance and purely imaginary for a capacitor or inductor). If phase is important, we use  , where  and  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,  , which is the peak voltage (amplitude) divided by √2.
Voltage may be out of phase with current, by a phase difference (phase angle),  .
Instantaneous power equals instantaneous voltage times instantaneous current:  , but average power is  , or the apparent power times the phase factor.
AC power:
AC power,  , usually means the power (true power, or real power) which transfers net energy (does net work), as opposed to the reactive power (imaginary power),  , which transfers no net energy.
Complex power is  . 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.  |
Commentary
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moved I2R onto the correct line).
