### Voltages, currents and circuits

**Voltages** and currents can be pictured as electrical pressure. The analogy is often used with water in a pipe; voltage is analogous to the pressure of the water. Voltage is the same thing as **potential difference**. This term arises because the voltage is the potential to do work.

Voltage is, strictly, always measured between two objects; the potential difference between the two points. However, it is conventional to define the earth as at zero volts. Then we can talk about the **voltage** of a single point or conductor, with the implied addition “with respect to earth”.

**Current** is the flow of electricity. A voltage will always try to drive a current. The size current that is driven depends on the resistance of the circuit. If the voltage occurs across an air gap, for instance, a negligible amount of current will flow until the voltage is so high that the air breaks down. If the voltage occurs across a conductor, a current will flow.

In metals, the current is carried by **electrons**, fundamental particles carrying one negative **charge** each. In passing, note electrons move so slowly that, generally, no one electron will actually flow all the way round a circuit. A good analogy is a string of ping-pong balls in a pipe. When you push the end ball, all the balls move (a current flows) but no one ball moves the whole length.

It is necessary to have a complete **circuit** for electricity to flow. If your pipe has a closed end, you can push the ping-pong balls as hard as you want, and they may squash a bit but there will be no flow. To have a flow you must make the pipe into a continuous loop.

Although it so happens that in **metals** the current is carried by electrons, this is not fundamental to the nature of current. Any charged object which can be made to move can carry a current. When air breaks down under high voltage, the current is partly carried by** ions** (molecules of air that have had electrons stripped off them), and in electrolysis, the current is carried by ions in solution.

**Power** is the product of voltage and current. In the electricity industry, we tend to keep the voltage more-or-less constant and let the change in power be accommodated by changes in the current.

The relationship** “power = voltage times current”** applies no matter what units you use for measuring the various quantities, provided the units are consistent with each other. The simplest units to use are **volts**, **amps** and **watts.**

**The power is transmitted through the transmission and distribution networks and used by the consumer at the far end. To transmit a given power, you can have a high voltage and a low current or vice versa.**

However, current causes** heating**. Simplistically, this is because the electrons, as they move along the wire, keep banging into the atoms that make up the wire, and these collisions cause heating. The heating increases as the** square** of the current.

Therefore, to transfer a given amount of power, if you use low volts and high current you will waste a lot more of the power in heating the wires than if you use high volts and low current. That is why bulk transfer of power is done at **high voltages**.

### DC and AC

In a **direct current** (dc) circuit, the voltage and the current continue in the same direction all the time. Battery-operated electronics, car electrics, and main-line railways south of the Thames are all examples of dc circuits.

Most power transmission is, however, done with** alternating currents** (ac). The **frequency** in this country (and elsewhere including those bits of the world influenced by the British) is 50 hertz (Hz). America uses 60 Hz. One **hertz** is one** cycle per second**. One cycle consists of the voltage and current starting from zero, rising smoothly to a maximum in one direction, falling back though zero to the same value in the opposite direction, and returning to zero. Mains electricity does this 50 times each second, so each cycle lasts a fiftieth of a second or twenty milliseconds.

Nowadays, dc is used in power systems only where it is necessary to transmit power over very long distances indeed, or where you want to connect two different ac systems but you don’t want to have to keep them **synchronised** (e.g. Britain and France).

With ac, most of the concepts used to describe dc still apply, but need small modifications. Voltage and current still mean basically the same thing. However, because the voltage (or current) are continuously changing but you want to describe it with a single value, you have to define which voltage or current you mean. You could define the voltage as the** maximum value** reached by the voltage in either direction. That is called the** amplitude**. However, it is more usual to define a different quantity, called the **“rms”** voltage or current. Rms stands for **“root mean square”**. For practical purposes in the electricity industry, it is just a constant fraction of the amplitude: rms = 0.71 x amplitude, amplitude = 1.41 x rms. (The factor 1.41 is the square root of 2.) Rms is used because an alternating current usually has the same effect as a direct current when its rms values is the same as the direct current.

Values in electricity supply are always expressed in rms quantities. Thus** 400 kV** is the rms value. The amplitude (that is, the maximum voltage) is bigger, 566 kV.

**Frequencies and harmonics**

Although electricity supply is basically conducted at 50 Hz, in any practical power system, small amounts of current and voltage at other frequencies always creep in. These frequencies are usually exact multiples of the power frequency and are known as** harmonics**. Thus** second harmonic** is 100 Hz,** third harmonic** is 150 Hz, etc. (Note that musicians count their harmonics differently to electrical engineers!).

The electricity industry tries to keep harmonics as low as possible and generally in the transmission system they are less than 1%. Harmonics tend to be lowest in the transmission system and get larger in distribution circuits and larger still in homes. The third harmonic (150 Hz) tends to be the most significant.

The term** “power frequencies”** is often used to cover both 50 Hz and the first few harmonics. They can also be described as “extremely low frequency” or ELF, which is defined as frequencies from 30 to 300 Hz.

### Phases

Ideally, in an ac circuit, the voltage and the current are exactly** in phase**, that is they pass through zero at the same instant in time, reach their maximums together, etc. In practice, they are rarely exactly in phase: there is a **phase difference**, expressed in **degrees**. Another way expressing the phase difference is as the **power factor**. A power factor of unity is equivalent to zero phase difference. Consumers tend to be charged extra by their supply company if their power factor gets too far away from unity. Some phase differences, however, are introduced not by the customer but by the circuits the electricity is transmitted over.

The fact that the voltage and current may not be perfectly in phase introduces some subtleties to calculating power. This leads to the terms **“real power”** and **“reactive power”**, and the quantities **“MVA”** and **“MVAR”**. When we move from dc to ac we also have to expand the idea of **resistance** to include its ac partners, reactance and** impedance**.

With ac just as with dc, you still need a complete circuit for current to flow. Many ac circuits are just like dc circuits in having two wires (“out” and “back”, or “go” and “return”). However, the power system uses three wires instead of two. This is known as** “three-phase”** electricity, and is more efficient in that it requires only one-and-a-half times the number of wires (three instead of two) to transmit three times as much power.

The three phases carry voltages and currents which are nominally **120 degrees** out of phase with each other. They are often called after colours as convenient labels, usually **red**, **yellow** and** blue**.

When the three phases are not exactly the same voltage and are not exactly 120 degrees out of phases (which in practice is all of the time, because of the nature of the loads supplied), it would be perfectly possible to describe the system by the three individual voltages and their phases. However, electrical engineers tend to use a different way to describe the same thing. This is the system of **“positive-phase-sequence voltage”**, **“negative-phase-sequence voltage”** and** “zero-phase-sequence voltage”** (abbreviated **pps**,** nps** and **zps**. The “phase” is often left out, hence e.g. **“zero-sequence voltage”**). This has the advantage that the negative and zero-sequence voltages are usually small, and when the three phases are at exactly 120 degrees, they disappear altogether.

Three-phase electricity leads to another subtlety in voltages. The voltage between any two of the three phases is 1.73 (the square root of three) times larger than the voltage between any one phase and earth. You therefore have to decide whether to give voltages **between phases** or** phase-to-earth**. The electricity industry almost always gives phase-to-phase voltages. Thus 400 kV is 400 kV phase-to-phase and only 231 kV phase-to-earth. The exception is the final distribution voltage, which can be given either way. 230 V is phase-to-earth and 400 V is phase-to-phase. Note that strictly, prior to harmonisation with Europe, these voltages used to be 240 V and 415 V.

Some orders of magnitude:

- A 400 kV National Grid circuit may carry 1 kA in each of its three phases, thus transmitting a power of 700 MW.
- A 132 kV distribution circuit may carry 300 A in each of its three phases, thus transmitting a power of 70 MW.
- An 11 kV distribution circuit may carry 150 A in each of its three phases, thus transmitting a power of 3 MW.
- A 400 V final distribution circuit may carry 200 A in each of its three phases, thus transmitting a power of 150 kW.

(Remember, these voltages are phase-to-phase voltages, **the phase-to-earth voltages are 1.73 times lower.** Thus (400 kV/1.73) x 1kA x 3 = 700 MW.)

### Converting and storing electricity

Voltages are changed by a** transformer**. Transformers are very efficient – in the high nineties of percent – thus power flows through a transformer with very little being absorbed. A **substation** is simply one or more transformers plus their associated** switchgear** etc.

For practical purposes, ac electricity cannot be stored in large quantities. Small amounts of electrical energy are stored in fields, e.g. in a transformer and in the region round a transmission line. With ac, the only way of storing large amounts of electricity over significant periods of time is to convert the electrical energy into some other form of energy that can be stored (e.g. gravitational potential energy in a **pumped storage system**, chemical energy in a **battery**). Electric power flows through the transmission and distribution systems, but is not stored anywhere within them in the conventional sense.

### Fields

A** field **is a very general concept in physics for a region of space where a quantity exists with a specific value at each point in the region. You can have a field of almost anything that varies over space:** temperature**, for instance, as well as the more common **gravitational **and **electric and magnetic fields**.

The term “field” is, however, only in common use for things which are capable of exerting a** force**. In formal terms, the field is defined by the force it exerts on an object placed in it. Thus, formally, the gravitational field is the force exerted on unit mass, the electric field is the force exerted on unit electric charge, and the magnetic field can be defined in terms of the force exerted on unit magnetic charge. (In fact, magnetic charge is probably a figment of the physicist’s imagination, but it has its uses as a concept, albeit one which almost certainly doesn’t actually exist.)

In practice, it is more helpful to think of both electric and magnetic fields as the regions round electrical conductors in which effects can be felt or measured. Electric fields can be measured because they exert a force on charges; magnetic fields can be measured because they exert a force on moving charges, ie a current.

**Electric fields** are produced by **voltages**, irrespective of how much current is flowing and indeed whether any current is flowing at all. **Magnetic fields** are produced by** currents**, irrespective of the voltage.

The field at any point is produced by all the sources round it. If one single source is dominant, the field will have a simple shape. If there are several significant sources, the field can be quite complicated.

The fields vary in time in the same way as the voltage or current which produces them. Thus, dc circuits produce dc fields (in the same direction all the time) and 50 Hz circuits produce fields which change direction.

If we have a single ac source or a single-phase circuit, the field at any point simply oscillates backwards and forwards along a straight line. This is known as** linear polarisation**. If we have more than one source, e.g. a three-phase circuit, the field no longer has to oscillate along a straight line. It actually traces out an** ellipse**. This is known as **“elliptical polarisation”**. The extreme case is **circular polarisation**.

More on elliptical polarisation

The earth has a **natural** electric and magnetic field. These are both static or dc fields. Any fields produced by the power system are superimposed on top of these natural fields. 50 Hz magnetic fields are often (but not always) smaller than the earth’s field (which is about 50 µT). When the 50 Hz magnetic field is smaller than the static field, it has no effect on the average field over time; it simply makes the field slightly bigger during half the cycle and slightly smaller during the other half.

### Radiation

Although electric fields are produced by voltage and magnetic fields by currents, once they have been produced, they can interact with each other. An alternating magnetic field** induces** an electric field. The interaction is described by **Maxwell’s equations**.

Maxwell’s equations are very simple to write down but harder to solve. For the present purposes, however, it is enough to know that at high frequencies, Maxwell’s equations work in such a way that the electric and the magnetic field always come coupled together as** radiation**. They are at right angles to each other, and propagate at the speed of light.

In principle, this coupling occurs at any frequency. In practice, it is strongest at high frequencies, and gets progressively weaker at lower frequencies. At 50 Hz, the coupling is so weak that radiation is negligible, and effectively the electric and magnetic fields are separate entities which can be produced independently. Thus it is incorrect to speak of “radiation” at 50 Hz.

One way of distinguishing high frequencies where radiation does occur from low frequencies where it does not is to think about the **wavelength**. The **wavelength** is the distance between two successive cycles of the wave. It is always related to the frequency by the formula **wavelength = speed of light / frequency**. The **speed of light** is 3×10^{8} metres per second. For 50 Hz, the wavelength is very long, **6,000 km**. **Radio waves** have wavelengths e.g. 1500 m, microwaves e.g. 12 cm, visible light e.g. a millionth of a metre, x-rays e.g. a billionth of a metre.

The criterion for radiation is whether you are within roughly one wavelength of the source. If you are less than a wavelength, radiation will be small. If you are more than a wavelength, radiation will be significant. These two regimes are called the **“near field” **region and the** “far field” **region. At 50 Hz we are always within one wavelength, 6000 km, of the source, so we are always in the near-field region and radiation is always negligible.

An alternative term for fields in the region where radiation is negligible is** “quasi-static fields”**.

A physicist will always speak of **“electric fields”**,** “magnetic fields”**, or **“electromagnetic radiation”**. When we use the abbreviation “EMFs”, we mean** “electric and magnetic fields”**. The term “electromagnetic fields” is not one that has a very clear meaning but usually includes both electric fields and magnetic fields.