Voltage

The term voltage is commonly used as shorthand for the scientific quantity better described as voltage difference. In this introduction, the term "voltage" is used to mean a specific value (not a difference), and is denoted by the symbol V. The SI unit for voltage is the volt (symbol: V). Note that "sloping vee" (V) and "upright vee" (V) have related but different meanings.

The voltage difference between two points "A" and "B", inside a solid electrical conductor, is denoted by (V_A − V_B). This voltage difference (V_A − V_B) is the electrical driving force that drives a conventional electric current in the direction A to B. It is also true that voltage difference is what is measured on an "ideal voltmeter". Well-constructed real voltmeters approximate well to ideal voltmeters.

Exact modern and historic definitions of voltage difference exist, but some historic forms of definition are not now regarded as strictly correct. It is universally accepted that, in conduction processes as they occur in metals and most other solids, electric currents consist exclusively (or almost exclusively) of the flow of electrons in the direction B to A. This movement of electrons is controlled by differences in a so-called "total local thermodynamic potential" often denoted by µ. This parameter µ is often called the "local Fermi level", and is sometimes called the "(local) electrochemical potential of an electron" or the "total (local) chemical potential of an electron". The modern definition of voltage difference (V_A − V_B) is in terms of differences in µ:

$(V_{\mathrm {A} }-V_{\mathrm {B} })=\;-({\mu }_{\mathrm {A} }-{\mu }_{\mathrm {B} })/e$ ,

where e is the elementary positive charge. It is sometimes convenient to choose point "B" so that it can be a convenient reference zero for V, and put µ_B=0 and V_B=0. It is common to choose point "B" to be in a conductor solidly connected (by a very-low-resistance path) to the local "Earth" or "Ground".

A common misapprehension is to assume that difference in voltage is always equal to difference in electric potential (i.e. electrostatic potential). This is often untrue, because differences in "chemical effects" (e.g., as between conductors made from different materials) also contribute to differences in µ, and hence to differences in voltage. Some textbooks (especially physics textbooks) give historic definitions of voltage that are not strictly compatible with the modern definition. However, the difference in value between a "voltage difference" and the related "electric potential difference" is always small (at most a few volts, often less), and in many contexts it is commonplace to disregard the distinction. Nonetheless, in some contexts, such as the theory of contact potential differences, the distinction is vital.

Explanation

Between two points in an electric field, such as that created in an electrical circuit, the difference in their electrical potentials is known as a difference in electric potential. 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. Voltage is usually represented in equations by the symbols V, U, or E. (E is often preferred in academic writing, because it avoids the confusion between V and the SI symbol for the volt, which is also V.)

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.

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 between two stated points

Another usage of the term "voltage" is in specifying how many volts are dropped across an electrical device (such as a resistor). In this case, the "voltage," or, more accurately, the "voltage drop 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 drop 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 voltage difference of zero. However, other pairs of points may also have a voltage 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:

V_{a}-V_{b}=\int _{a}^{b}\mathbf {E} \cdot d\mathbf {l} .

Useful formulae

DC circuits

V={\sqrt {PR}}

V=IR

where V = potential difference (volts), I = current intensity (amps), R = resistance (ohms), P = power (watts).

AC circuits

V={\frac {P}{I\;\cos \phi }}

V={\frac {\sqrt {P\;Z}}{\sqrt {\cos \phi }}}\!\

V={\frac {I\;R}{\cos \phi }}

Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, φ=phase difference between I and V

AC conversions

V_{avg}=.637\,V_{pk}={\frac {2}{\pi }}V_{pk}={\frac {\omega }{\pi }}\int _{0}^{\pi /\omega }V_{pk}\sin(\omega t-kx){\rm {d}}x\!\

V_{rms}=.707\,V_{pk}={\frac {1}{\sqrt {2}}}V_{pk}=V_{pk}{\sqrt {\langle \sin ^{2}(\omega t-kx)\rangle }}\!\

V_{pk}=0.5\,V_{ppk}\!\

V_{avg}=.319\,V_{ppk}\!\

V_{rms}=.354\,V_{ppk}={\frac {1}{2{\sqrt {2}}}}V_{ppk}\!\

V_{avg}=0.900\,V_{rms}={\frac {2{\sqrt {2}}}{\pi }}V_{rms}\!\

Where V_pk=peak voltage, V_ppk=peak-to-peak voltage, V_avg=average voltage over a half-cycle, V_rms=effective (root mean square) voltage, and we assumed a sinusoidal wave of the form $V_{pk}\sin(\omega t-kx)$ , 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:

V_{T}=V_{1}+V_{2}+V_{3}+...+V_{n}\!\

Voltage sources and drops in parallel:

V_{T}=V_{1}=V_{2}=V_{3}=...=V_{n}\!\

Where $n\!\$ is the nth voltage source or drop

Voltage drops

Across a resistor (Resistor R):

V_{R}=IR_{R}\!\

Across a capacitor (Capacitor C):

V_{C}=IX_{C}\!\

Across an inductor (Inductor L):

V_{L}=IX_{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 (note that even low voltage, e. g. of 50 Volts, can lead to a lethal electric shock) and Electric shock.

References

External links