volt

SI coherent derived unit with special name and symbol

Name

Symbol

Derived quantity

Expressed in terms of SI base units

volt

potential difference,
electromotive force

kg m² s⁻³ A^-1

Definition

The volt, symbol V, is the SI coherent derived unit of electric potential, electric potential difference(voltage), and electromotive force.

One volt is defined as the difference in electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points.

One volt is also equal to the potential difference between two parallel, infinite planes spaced one metre apart that create an electric field of one newton per coulomb. Additionally, it is the potential difference between two points that will impart one joule of energy per coulomb of charge that passes through it.

The volt is named after the Italian physicist Alessandro Volta (1745 – 1827).

Voltage

Voltage is the difference in electric potential between two points. An electric potential difference between two points can be caused by:

electric charge,
electric current through a magnetic field,
time-varying magnetic fields,
a combination of the above.

The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points.

$V = \dfrac{E}{Q}$

Using SI coherent units,

$1\ \text{V} = 1\ \dfrac{\text{J}}{\text{C}}$

Ohm’s law

Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points. The proportionality constant is the resistance of the conductor:

$I = \dfrac {V}{R}$

Using SI coherent units:

I is the current through the conductor, measured in amperes, symbol A,
V is the voltage across the conductor, measured in volts, symbol V,
R is the resistance of the conductor, measured in ohms, symbol Ω.

Joule’s first law

Joule’s first law states that the power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the current passing through it:

$P \propto I^{2}R$

Using SI coherent units, the proportionality constant is 1:

$P = I^{2}R$

where:

P is the rate of heat generation, or power, measured in watts, symbol W,
I is the current passing through the conductor, measured in amperes, symbol A,
R is the resistance of the conductor, measured in ohms, symbol Ω.

Substituting Ohm’s law gives:

$P = IV = I^{2}R = \dfrac{V^{2}}{R}$

Power transmission

Electrical power, generated in power stations, is distributed via transmission cables.

Using SI coherent units, the electric current passing through a power transmission cable is equal to the power transmitted divided by the transmission voltage:

$I = \dfrac{P_{\rm {t}}}{V}$

where:

I is the electric current, measured in amperes, symbol A,
P_t is the power transmitted, measured in watts, symbol W,
V is the transmission voltage, measured in volts, symbol V.

From Joule’s first law, it can be seen that some power will always be lost when it is transmitted by electricity through a conductor of finite resistance. The power lost due to Joule heating can be calculated as a ratio of the original power:

$\dfrac{P_{\rm {w}}} {P_{\rm {t}}} = \dfrac{I^2 R} {P_{\rm {t}}}$

where:

P_w is the power lost due to Joule heating, measured in watts, symbol W,
P_t is the original generated power, measured in watts, symbol W,
I is the electric current, measured in amperes, symbol A,
R is the resistance of the transmission cable, measured in ohms, symbol Ω.

For a given transmission power, the use of a higher voltage, and a lower current, leads to more efficient transmission of power.

For example, for a 25 Ω transmission cable, carrying 100 MW:

Voltage in V	Current in A	Power loss in W	Power loss ratio
250 000	400	4.0 × 10⁶	4.0 %
200 000	500	6.25 × 10⁶	6.25 %
125 000	800	1.6 × 10⁷	16.0 %
100 000	1000	2.5 × 10⁷	25.0 %

For this reason, power is often transmitted at hundreds of kilovolts, before being stepped down to 110 V – 230 V for domestic use.

Kirchhoff’s voltage law

Kirchhoff’s voltage law, also known as Kirchhoff’s second law, states that the directed sum of the potential differences, or voltages, around any closed loop is zero.

Measurement

A voltmeter can be used to measure the voltage, or potential difference, between two points in a system. A reference potential, such as the ground of the system, is commonly used as one of the two points.