Voltage
Voltage (sometimes also called electric or electrical tension) is the difference of electrical potential between two points of an electrical or electronic circuit, expressed in volts. It measures the potential energy of an electric field to cause an electric current in an electrical conductor. Depending on the difference of electrical potential it is called extra low voltage, low voltage, high voltage or extra high voltage.

# Explanation
Between two points in an electric field, such as exists in an electrical circuit, the difference in their electrical potentials is known as the electrical potential difference.  This difference is proportional to the force that tends to push electrons or other charge-carriers from one point to the other.  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 EMFa term which is still used in certain contexts.
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.
When using the term 'potential difference' or voltage, one must be clear about the two points between which the voltage is specified or measured. There are two ways in which the term is used. This can lead to some confusion.

## Voltage with respect to a common point
One way in which the term voltage is used is when specifying the voltage of a point in a circuit. When this is done, it is understood that the voltage is usually being specified or measured with respect to a stable and unchanging point in the circuit that is known as ground or common. This voltage is really a voltage difference, one of the two points being the reference point, which is ground.  A voltage can be positive or negative.  "High" or "low" voltage may refer to the magnitude (the absolute value relative to the reference point). Thus, a large negative voltage may be referred to as a high voltage.  Other authors may refer to a voltage that is more negative as being "lower."

## Voltage between two stated points
Another usage of the term "voltage" is in specifying how many volts are across an electrical device (such as a resistor). In this case, the "voltage," or, more accurately, the "voltage across the device," is really the first voltage taken, relative to ground, on one terminal of the device minus a second voltage taken, relative to ground, on the other terminal of the device. In practice, the voltage across a device can be measured directly and safely using a voltmeter that is isolated from ground, provided that the maximum voltage capability of the voltmeter is not exceeded.
Two points in an electric circuit that are connected by an "ideal conductor," that is, a conductor without resistance and not within a changing magnetic field, have a potential difference of zero. However, 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.

## Addition of voltages
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. The various voltages in a circuit can be computed using Kirchhoff's circuit laws.
When talking about alternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added as for direct current (DC), but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.

## Hydraulic analogy
If one imagines water circulating in a network of pipes, driven by pumps in the absence of gravity, as an analogy of an electrical circuit, 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 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. In relation to electric current, the larger the gradient (voltage or hydraulic) the greater the current (assuming resistance is constant).

## Mathematical definition
The electrical potential difference is defined as the amount of work needed to move a unit electric charge from the second point to the first, or equivalently, the amount of work that a 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:

# Useful formulae

## DC circuits
Where V = voltage/potential difference, I = current intensity, R = resistance, P = power/watts

## AC circuits
Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, =phasor angle between I and V

## AC conversions
Where Vpk=peak voltage, Vppk=peak-to-peak voltage, Vavg=average voltage over a half-cycle, Vrms=effective (root mean square) voltage, and we assumed a sinusoidal wave of the form   V_{pk} \sin(\omega t - k x) , with a period  T = 2\pi/\omega , and where the angle brackets (in the root-mean-square equation) denote a time average over an entire period.

## Total voltage
Voltage sources and drops in series:
Voltage sources and drops in parallel:
Where  n \!\  is the nth voltage source or drop

## Voltage drops
Across a resistor (Resistor R):
Across a capacitor (Capacitor C):
Across an inductor (Inductor L):
Where V=voltage, I=current, R=resistance, X=reactance.

# Measuring instruments
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 the resistor. 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.

# Safety
Electrical safety is discussed in the articles on High voltage and Electric shock.