Voltage

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Image:High voltage warning.svg Voltage is an electric potential difference between two points; it is measured in volts. Voltage is named in honor of the Italian physicist Alessandro Volta (1745–1827), who invented the voltaic pile, the first chemical battery.

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Explanation

Electrical potential difference can be thought of as the ability to move electrical charge through a resistance. At a time in physics when the word force was used loosely, the potential difference was named the electromotive force or emf - a term which is still used in certain contexts.

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Electrical potential difference ("voltage")

Between two points in an electric field, such as exists in an electrical circuit, the potential difference is equal to the difference in their electrical potentials. This difference is proportional to the electrostatic force that tends to push electrons or other charge-carriers from one point to the other. Potential difference, electrical potential and electromotive force are measured in volts, leading to the commonly used term voltage and the symbol V (sometimes <math>\mathcal{E}</math> is used for voltage).

Voltage is additive in the following sense: the voltage between A and C is the sum of the voltage between A and B and the voltage between B and C. Two points in an electric circuit which are connected by an ideal conductor, without resistance and without the presence of a changing magnetic field, have a potential difference of zero. But other pairs of points may also have a potential difference of zero. If two such points are connected with a conductor, no current will flow through the connection. The various voltages in a circuit can be computed using Kirchhoff's circuit laws.

Voltage is a property of an electric field, not individual electrons. An electron moving across a voltage difference experiences a net change in energy, often measured in electron-volts. This effect is analogous to a mass falling through a given height difference in a gravitational field.

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Hydraulic analogy

If one thinks of an electrical circuit in analogy to water circulating in a network of pipes, driven by pumps in the absence of gravity, then the potential difference corresponds to the fluid pressure difference between two points. If there is a pressure difference between two points, then water flowing from the first point to the second will be able to do work, such as driving a turbine.

This hydraulic analogy (see separate article for full details) is a useful method of teaching a range of electrical concepts. In a hydraulic system, the work done to move water is equal to the pressure multiplied by the volume of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to 'electrical pressure' (an old term for voltage) multiplied by the quantity of electrical charge moved. Voltage is a convenient way of quantifying the ability to do work.

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Technical definition

The electrical potential difference is defined as the amount of work per charge needed to move electric charge from the second point to the first, or equivalently, the amount of work that unit charge flowing from the first point to the second can perform. The potential difference between two points a and b is the line integral of the electric field E:

<math>V_a - V_b = \int _a ^b \mathbf{E}\cdot d\mathbf{l}</math>
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Useful formulae

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DC circuits

<math> V = \sqrt{PR} </math>
<math> V = \frac{P}{I} </math>
<math> V = IR \!\ </math>

Where V=voltage, I=current, R=resistance, P=power

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AC circuits

<math> V = \frac{P}{I\cos\theta}</math>
<math> V = \frac{\sqrt{PZ}}{\sqrt{\cos\theta}} \!\ </math>
<math> V = \frac{IR}{\cos\theta}</math>

Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, θ=phasor angle

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AC conversions

<math> V_{avg} = .637V_{pk} \!\ </math>
<math> V_{rms} = .707V_{pk} \!\ </math>
<math> V_{rms} = .354V_{ppk}\!\ </math>
<math> V_{avg} = .319V_{ppk} \!\ </math>
<math> V_{avg} = 0.9V_{rms} \!\ </math>
<math> 2V_{pk} = V_{ppk} \!\ </math>

Where Vpk=peak voltage, Vppk=peak-to-peak voltage, Vavg=average voltage, Vrms=effective voltage

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Total voltage

Voltage sources and drops in series:

<math> V_T = V_1 + V_2 + V_3 + ... \!\ </math>

Voltage sources and drops in parallel:

<math> V_T = V_1 = V_2 = V_3 = ... \!\ </math>
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Voltage drops

Across a resistor (Resistor n):

<math> V_n = IR_n \!\ </math>

Across a capacitor (Capacitor n):

<math> V_n = IX_n \!\ </math>

Across an inductor (Inductor n):

<math> V_n = IX_n \!\ </math>

Where V=voltage, I=current, R=resistance, X=reactance

<math> V_n = IR_n = IX_n \!\ </math>
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Measuring instruments

Image:Digital Multimeter Aka.jpg Instruments for measuring potential differences include the voltmeter, the potentiometer (measurement device), and the oscilloscope. The voltmeter works by measuring the current through a fixed resistor, which, according to Ohm's Law, is proportional to the potential difference across it. The potentiometer works by balancing the unknown voltage against a known voltage in a bridge circuit. The cathode-ray oscilloscope works by amplifying the potential difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the potential difference.

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See also

cs:Elektrické napětí da:Elektrisk spænding de:Elektrische Spannung eo:Tensio es:Diferencia de potencial fi:Jännite fr:Tension he:מתח חשמלי it:Tensione elettrica ja:電圧 la:Tensio electrica lt:Įtampa nl:Elektrische spanning no:Elektrisk spenning nn:Elektrisk spenning pl:Napięcie elektryczne pt:Tensão elétrica ru:Напряжение (электрическое) sr:Напон sk:Elektrické napätie sl:Električna napetost sv:Elektrisk spänning ta:மின்னழுத்தம் zh:電壓

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