Electromotive force

A typical reaction path requires the initial reactants to cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration. If charge separation is involved, this energy difference can result in an emf. See Bergmann et al. and Transition state.
Galvanic cell using a salt bridge
The equivalent circuit of a solar cell; parasitic resistances are ignored in the discussion of the text.
Solar cell voltage as a function of solar cell current delivered to a load for two light-induced currents IL; currents as a ratio with reverse saturation current I0. Compare with Fig. 1.4 in Nelson.

Electrical action produced by a non-electrical source, measured in volts.

- Electromotive force
A typical reaction path requires the initial reactants to cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration. If charge separation is involved, this energy difference can result in an emf. See Bergmann et al. and Transition state.

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Pole-mounted distribution transformer with center-tapped secondary winding used to provide "split-phase" power for residential and light commercial service, which in North America is typically rated 120/240 V.

Transformer

Passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits.

Passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits.

Pole-mounted distribution transformer with center-tapped secondary winding used to provide "split-phase" power for residential and light commercial service, which in North America is typically rated 120/240 V.
Ideal transformer connected with source VP on primary and load impedance ZL on secondary, where 0 < ZL < ∞.
Ideal transformer and induction law
Leakage flux of a transformer
Real transformer equivalent circuit
Instrument transformer, with polarity dot and X1 markings on low-voltage ("LV") side terminal
Power transformer overexcitation condition caused by decreased frequency; flux (green), iron core's magnetic characteristics (red) and magnetizing current (blue).
Laminated core transformer showing edge of laminations at top of photo
Interleaved E-I transformer laminations showing air gap and flux paths
Laminating the core greatly reduces eddy-current losses
Small toroidal core transformer
Windings are usually arranged concentrically to minimize flux leakage.
Cut view through transformer windings.
Legend: 
White: Air, liquid or other insulating medium 
Green spiral: Grain oriented silicon steel 
Black: Primary winding 
Red: Secondary winding
Cutaway view of liquid-immersed transformer. The conservator (reservoir) at top provides liquid-to-atmosphere isolation as coolant level and temperature changes. The walls and fins provide required heat dissipation.
Substation transformer undergoing testing.
An electrical substation in Melbourne, Australia
showing three of five 220 kV – 66 kV transformers, each with a capacity of 150 MVA
Camouflaged transformer in Langley City
Transformer at the Limestone Generating Station in Manitoba, Canada
Schematic of a large oil-filled power transformer 1. Tank 2. Lid
3. Conservator tank 4. Oil level indicator 5. Buchholz relay for detecting gas bubbles after an internal fault 6. Piping
7. Tap changer 8. Drive motor for tap changer 9. Drive shaft for tap changer
10. High voltage (HV) bushing
11. High voltage bushing current transformers
12. Low voltage (LV) bushing
13. Low voltage current transformers
14. Bushing voltage-transformer for metering
15. Core 16. Yoke of the core
17. Limbs connect the yokes and hold them up 18. Coils
19. Internal wiring between coils and tapchanger
20. Oil release valve
21. Vacuum valve
Faraday's experiment with induction between coils of wire
Induction coil, 1900, Bremerhaven, Germany
Faraday's ring transformer
Shell form transformer. Sketch used by Uppenborn to describe ZBD engineers' 1885 patents and earliest articles.
Core form, front; shell form, back. Earliest specimens of ZBD-designed high-efficiency constant-potential transformers manufactured at the Ganz factory in 1885.
The ZBD team consisted of Károly Zipernowsky, Ottó Bláthy and Miksa Déri
Stanley's 1886 design for adjustable gap open-core induction coils
"E" shaped plates for transformer cores developed by Westinghouse

A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's core, which induces a varying electromotive force across any other coils wound around the same core.

Batteries are sources of voltage in many electric circuits.

Voltage

Difference in electric potential between two points, which is defined as the work needed per unit of charge to move a test charge between the two points.

Difference in electric potential between two points, which is defined as the work needed per unit of charge to move a test charge between the two points.

Batteries are sources of voltage in many electric circuits.
The electric field around the rod exerts a force on the charged pith ball, in an electroscope
In a static field, the work is independent of the path
Working on high voltage power lines
Multimeter set to measure voltage

Electric potential differences between points can be caused by the build-up of electric charge (e.g., a capacitor), and from an electromotive force (e.g., electromagnetic induction in generator, inductors, and transformers).

A thermoelectric circuit composed of materials of different Seebeck coefficients (p-doped and n-doped semiconductors), configured as a thermoelectric generator. If the load resistor at the bottom is replaced with a voltmeter, the circuit then functions as a temperature-sensing thermocouple.

Thermoelectric effect

Direct conversion of temperature differences to electric voltage and vice versa via a thermocouple.

Direct conversion of temperature differences to electric voltage and vice versa via a thermocouple.

A thermoelectric circuit composed of materials of different Seebeck coefficients (p-doped and n-doped semiconductors), configured as a thermoelectric generator. If the load resistor at the bottom is replaced with a voltmeter, the circuit then functions as a temperature-sensing thermocouple.
The Seebeck circuit configured as a thermoelectric cooler

The Seebeck effect is a classic example of an electromotive force (EMF) and leads to measurable currents or voltages in the same way as any other EMF.

Some examples of closed surfaces (left) and open surfaces (right). Left: Surface of a sphere, surface of a torus, surface of a cube. Right: Disk surface, square surface, surface of a hemisphere. (The surface is blue, the boundary is red.)

Magnetic flux

Surface integral of the normal component of the magnetic field B over that surface.

Surface integral of the normal component of the magnetic field B over that surface.

Some examples of closed surfaces (left) and open surfaces (right). Left: Surface of a sphere, surface of a torus, surface of a cube. Right: Disk surface, square surface, surface of a hemisphere. (The surface is blue, the boundary is red.)
For an open surface Σ, the electromotive force along the surface boundary, ∂Σ, is a combination of the boundary's motion, with velocity v, through a magnetic field B (illustrated by the generic F field in the diagram) and the induced electric field caused by the changing magnetic field.
Area defined by an electric coil with three turns.

For example, a change in the magnetic flux passing through a loop of conductive wire will cause an electromotive force, and therefore an electric current, in the loop.

U.S. NRC image of a modern steam turbine generator (STG).

Electric generator

Device that converts motive power into electric power for use in an external circuit.

Device that converts motive power into electric power for use in an external circuit.

U.S. NRC image of a modern steam turbine generator (STG).
Early Ganz Generator in Zwevegem, West Flanders, Belgium
The Faraday disk was the first electric generator. The horseshoe-shaped magnet (A) created a magnetic field through the disk (D). When the disk was turned, this induced an electric current radially outward from the center toward the rim. The current flowed out through the sliding spring contact m, through the external circuit, and back into the center of the disk through the axle.
Hippolyte Pixii's dynamo. The commutator is located on the shaft below the spinning magnet.
This large belt-driven high-current dynamo produced 310 amperes at 7 volts. Dynamos are no longer used due to the size and complexity of the commutator needed for high power applications.
Ferranti alternating current generator, c. 1900.
A small early 1900s 75 kVA direct-driven power station AC alternator, with a separate belt-driven exciter generator.
The Athlone Power Station in Cape Town, South Africa
Hydroelectric power station at Gabčíkovo Dam, Slovakia
Hydroelectric power station at Glen Canyon Dam, Page, Arizona
Mobile electric generator
Protesters at Occupy Wall Street using bicycles connected to a motor and one-way diode to charge batteries for their electronics

The principle, later called Faraday's law, is that an electromotive force is generated in an electrical conductor which encircles a varying magnetic flux.

Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G).

Faraday's law of induction

Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G).
A diagram of Faraday's iron ring apparatus. The changing magnetic flux of the left coil induces a current in the right coil.
Faraday's disk, the first electric generator, a type of homopolar generator.
Alternating electric current flows through the solenoid on the left, producing a changing magnetic field. This field causes, by electromagnetic induction, an electric current to flow in the wire loop on the right.
Faraday's homopolar generator. The disc rotates with angular rate {{mvar|ω}}, sweeping the conducting radius circularly in the static magnetic field {{math|B}} (which direction is along the disk surface normal). The magnetic Lorentz force {{math|v × B}} drives a current along the conducting radius to the conducting rim, and from there the circuit completes through the lower brush and the axle supporting the disc. This device generates an emf and a current, although the shape of the "circuit" is constant and thus the flux through the circuit does not change with time.
A wire (solid red lines) connects to two touching metal plates (silver) to form a circuit. The whole system sits in a uniform magnetic field, normal to the page. If the abstract path {{math|∂Σ}} follows the primary path of current flow (marked in red), then the magnetic flux through this path changes dramatically as the plates are rotated, yet the emf is almost zero. After Feynman Lectures on Physics {{Rp|ch17}}

Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic induction.

Various cells and batteries (top left to bottom right): two AA, one D, one handheld ham radio battery, two 9-volt (PP3), two AAA, one C, one camcorder battery, one cordless phone battery

Electric battery

Source of electric power consisting of one or more electrochemical cells with external connections for powering electrical devices.

Source of electric power consisting of one or more electrochemical cells with external connections for powering electrical devices.

Various cells and batteries (top left to bottom right): two AA, one D, one handheld ham radio battery, two 9-volt (PP3), two AAA, one C, one camcorder battery, one cordless phone battery
A voltaic cell for demonstration purposes. In this example the two half-cells are linked by a salt bridge that permits the transfer of ions.
From top to bottom: a large 4.5-volt 3R12 battery, a D Cell, a C cell, an AA cell, an AAA cell, an AAAA cell, an A23 battery, a 9-volt PP3 battery, and a pair of button cells (CR2032 and LR44)
Line art drawing of a dry cell: 1. brass cap, 2. plastic seal, 3. expansion space, 4. porous cardboard, 5. zinc can, 6. carbon rod, 7. chemical mixture
A device to check battery voltage
An analog camcorder [lithium ion] battery
Battery after explosion
Leak-damaged alkaline battery

Each half-cell has an electromotive force (emf, measured in volts) relative to a standard.

Josephson voltage standard chip developed by the National Bureau of Standards as a standard volt

Volt

Josephson voltage standard chip developed by the National Bureau of Standards as a standard volt
A multimeter can be used to measure the voltage between two positions.
1.5 V C-cell batteries
Alessandro Volta
Group photograph of Hermann Helmholtz, his wife (seated) and academic friends Hugo Kronecker (left), Thomas Corwin Mendenhall (right), Henry Villard (center) during the International Electrical Congress

The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force.

Alessandro Volta

Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and the discoverer of methane.

Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and the discoverer of methane.

Volta battery, at the Tempio Voltiano museum, Como
A voltaic pile
Volta explains the principle of the "electric column" to Napoleon in 1801
Front page of De vi attractiva ignis electrici

In this way he discovered the electrochemical series, and the law that the electromotive force (emf) of a galvanic cell, consisting of a pair of metal electrodes separated by electrolyte, is the difference between their two electrode potentials (thus, two identical electrodes and a common electrolyte give zero net emf).

T equivalent circuit of mutually coupled inductors

Inductance

Tendency of an electrical conductor to oppose a change in the electric current flowing through it.

Tendency of an electrical conductor to oppose a change in the electric current flowing through it.

T equivalent circuit of mutually coupled inductors
π equivalent circuit of coupled inductors

From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction.