The electrical work indicates how much electrical energy is converted into other forms of energy.

Formula symbol: W

Units: one watt-second (1st W.⋅ s), one joule (1 J)

Electrical work has to be done to move a charged body in an electrical field.

The electrical work indicates how much electrical energy is converted into other forms of energy.

Formula symbol: W

Units: one watt-second (1st W.⋅ s), one joule (1 J)

Electrical work has to be done to move a charged body in an electrical field. The work to move such a body is equal to the product of its charge and the voltage between the starting point and the endpoint:

W.= Q ⋅ U

Another equation is used for calculations in a circuit. The work in the electrical circuit is equal to the product of the electrical power and the time during which the power is expended:

W.= P⋅ t

Both calculation equations can be converted into one another.

In general, if you apply a force F to move a body along the path s, you do work on this body. Two differently charged bodies attract each other. If you want to pull them apart, you have to apply a force to move one of these bodies in the electrical field of the other body. With this shift,

## The electrical work in a plate capacitor

In some cases, the equation for electrical work is particularly easy to derive. This is possible if the force and the displacement path are directed in the same way. In addition, it is necessary that the electric field strength is constant over the entire path and thus the force is also constant. These conditions are very well met within a plate capacitor. The aim is to calculate the W= FD that has to be done to move a charged test specimen between two plates of a plate capacitor, the distance between which is d. Under the conditions mentioned, the following applies to this work:

W.= Fs

The force on a test specimen inside a plate capacitor is the product of its electrical charge and the electrical field strength in the capacitor:

F.= Q ⋅ E

This results in the following for the electrical:

W.= Q ⋅ E⋅ d

The following applies to the electric field strength E between the capacitor plates:

E.=Ud( U voltage between the plates)

If one uses this equation to replace the electric field strength E in the calculation formula for the electric work, the overall result is:

W.= Q ⋅ U

The electrical work in a current-carrying conductor

One can imagine a straight piece of a conductor like a plate capacitor with tiny plate surfaces. Since an electrical voltage is applied to a line wire and electrical charges flow in the conductor – that is, they are “shifted” – the voltage source performs electrical work on the charge carriers. This work is necessary, for example, to overcome the line resistance. Since it is not possible to “count” all charge carriers individually in a live conductor, the equation obtained using the plate capacitor is converted for calculations in electrical circuits.

The total charge flowing through a piece of the conductor is the product of the current I and time:

Q = I⋅ t

The following then applies to w=fd

W.= Q ⋅ U= I.⋅ t ⋅ U= P⋅ t

Electrical work is the product of electrical power and time. This equation applies provided that the power converted in the circuit is constant.

Note for calculations of electrical work

As a rule, either the power or voltage and current strength are specified on electrical components. For example, every light bulb is provided with a power rating. If you want to calculate the electrical work of an incandescent lamp, you only have to multiply this power figure by its operating time. A 100 W lamp that has been in operation for 12 hours, therefore, has an electrical work of

W.= P.⋅ t = 100 W ⋅ 12 H = 1200 W ⋅ h = 1.2 kW ⋅ h

performed.