Learning objectives.
By reading this article, you should be able to:
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Discuss the connection between current, voltage and power.
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Explain what magnetism is and how it is important.
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Know the components of an electricity supply and how transformers are used in this.
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Understand what resistors, capacitors and inductors are and how they can be connected together in circuits.
Key points.
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The movement of charge is electric current and is measured in amperes.
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Voltage is the electric potential per unit charge, measured in volts.
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DC is direct current, where the current (and voltage) is constant.
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AC is alternating current, where the current (and voltage) is alternating and not constant.
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In circuits, Ohm's law can be used to calculate voltage and current values.
Basic electricity is important to anaesthetists because all devices and machines used in anaesthetic practice use electricity. This paper is the first in a series of three in this subject. Electricity is a broad term that includes a variety of phenomena resulting from the flow (or presence) of electric charge. Charge is measured in coulombs (C), and 1 C contains 6.24 × 1018 electrons.
Electric current
The movement of charge is electric current and is measured in amperes. One coulomb of charge flowing for 1 s is an ampere. Therefore, current I=C s−1. Current was thought to flow from the most positive part of a circuit to the negative, but in fact the actual flow of the electrons is in the opposite direction. Current flowing through a wire causes many observable effects, for example heating, light and magnetism.
Voltage or volts
Voltage is the electric potential energy per unit charge, measured in joules per coulomb (volts V=J C−1). The difference in voltage measured when moving from Point A to Point B is equal to the work that would have to be done, per unit charge to move the charge from A to B. Voltage usually means the voltage difference between two points in a circuit.
A simple analogy to help understand voltage is the water pressure difference from a mountain reservoir and sea level. The water pressure difference corresponds to the voltage difference. The water pressure difference will drive water through a turbine. In a similar way, work can be done by the electric current driven by the voltage difference via the battery; for example, the current generated by the battery can light a bulb in a circuit.
Power
The power P, work done per second, in watts, J s−1 consumed by a circuit is.
V (J C−1) × I (C s−1).
Magnetism
Magnetism is the effect that is observed when the north and south ends of a bar magnet—the poles—attract or repel neighbouring ferromagnetic items. The opposite poles attract, and like poles repel.
A wire carrying an electric current also behaves like a magnet by inducing a magnetic field around it. Therefore, magnetic fields can be created using an electrical source, and these magnetic fields can be used to provide mechanical force, as in an electric motor. Conversely, if a wire is moved through the magnetic field, an electric current is induced in the wire proportional to its speed of movement. Mechanical force or movement can create electric current, as in a dynamo or a power station.
If the wire carrying the current is coiled, a more intense magnetic field is created. The close proximity of the coils to each other magnifies this effect in proportion to the number of coils. The coil can have an air core or an iron core, but the higher magnetic permeability of iron means that the flux density of such a coil will be greatly enhanced for a given magnetic field strength.
Alternating and direct voltage/current
Two types of current flow exist in electric circuits. The first is when the voltage source (or current) is at a constant level, and the flow of current is in a constant direction. This current flow is defined as direct current (DC). The other is alternating current (AC), where the signal (the voltage or the current) oscillates around zero in a rhythmical manner, as in a sine wave. Batteries supply DC, and the domestic mains uses AC. Both behave very differently in circuits.
Circuit components, capacitors, inductors and resistors
Resistors
Resistors are the simplest component. They are passive devices, normally having two terminals, and are used to reduce current flow. They have multiple uses. Their response is the same whether AC or DC is used.
Capacitors and inductors
The capacitor consists of two conductor plates separated by an insulator, which could be air or a solid material. An inductor consists of a number of turns of a wire conductor wound around a core of magnetic material. The capacitor and inductor behave very differently depending on whether AC or DC is used. If a constant (DC) voltage is applied across a capacitor, via a source resistance as shown in Fig. 1, the capacitor will charge up exponentially from zero to the DC value across it, and the current will decrease exponentially with a time constant of RC seconds (in Fig. 1, RC=1 s).
Fig. 1.
Capacitor charging circuit showing components and the corresponding current and voltage waveforms across the capacitor C (reproduced with permission from Magee and Tooley, The Physics, Clinical Measurement and Equipment of Anaesthetic Practice).
The steady-state current (i.e. DC) through an inductor, as connected as shown in Fig. 2, will be limited only by the resistance of its coil, but a change of current produces a change in the magnetic field around the coil, which in turn generates a voltage in the coil with the opposite polarity to the driving voltage, which opposes the change in current. It therefore slows down any change of current. Fig. 2 shows that when DC voltage is applied to the inductor, the effect is the opposite to that which occurs with a capacitor. The time constant in this case is L/R seconds.
Fig. 2.
Inductor circuit showing components and the corresponding voltage and current waveforms (reproduced with permission from Magee and Tooley, The Physics, Clinical Measurement and Equipment of Anaesthetic Practice).
In an AC circuit (a similar circuit to Fig. 1, with the battery replaced by an AC source), the voltage across the capacitor is constantly changing direction, and the current and voltage never reach steady-state conditions. The current through a capacitor is proportional to the rate of change of voltage, so when a sinusoidal voltage waveform is applied (starting at zero), the current is at a maximum at the start of the cycle. As the capacitor charges up, the current decreases and the voltage increases. The minimum of the voltage cycle is the peak of the current waveform where the rate of change approaches zero. The current waveform peaks before the voltage 1, and therefore, the voltage lags the current by a quarter of the whole 360 degrees cycle (i.e. 90 degrees).
Because current is proportional to the rate of change of voltage, the current increases with frequency. The resistance to current flowing is inversely proportional to frequency and is called reactance. It is calculated as XC=1/(2fC)Ω, where f is the frequency of the supply waveform in hertz.
The current and voltage relationships with an inductor are different, and in this case the voltage peak occurs before the current peak and so the voltage leads the current by 90 degrees. The inductive resistance or reactance is XL=2fLΩ, where L is the inductance in henry.
Basic electrical circuit rules
Ohm's law states that the current I in amperes flowing through a conductor of resistance R measured in ohms () is proportional to the voltage V in volts. For a constant voltage, V=IR. This law gives the basis of solving most basic electrical circuits. The current goes through a component when a voltage is supplied across it. A simple circuit showing a battery (voltage) across a resistor is shown in Fig. 3. If the battery voltage is 9 V and the resistance is 1 M, then the current through the circuit will be 9/(1 × 106) A, which is 9 μA.
Fig. 3.
Simple circuit with battery of 9 V and resistor of 1 M (reproduced with permission from Magee and Tooley, The Physics, Clinical Measurement and Equipment of Anaesthetic Practice).
If the resistor in the circuit is replaced by two resistors connected to each other in series, then the total resistance is the sum of the two resistors. The current through each one is the same. Two or more resistors in series form the basics of voltage dividers, used in, for example, bridge circuits. The voltage reduction across one resistor is IR. Resistors in parallel behave differently. Here, the reciprocal of the total resistance is the sum of the reciprocals of the two (or more resistors) added together. The effect of putting resistors in parallel is to reduce the total resistance to below the value of the lowest resistor.
Transformers
Transformers are used extensively in power generation. A transformer consists of two separate (or more) coils (inductors) normally placed either side of an iron core. The transformer diagram and circuit diagram are shown in Fig. 4. The alternating voltage in the primary circuit causes a changing current, which induces magnetic flux in the iron core. This magnetic field to which this flux belongs induces a voltage in the secondary coil.
Fig. 4.
Diagram of a transformer showing turns around an iron core. Also shown is the circuit diagram of a voltage supplied to the transformer of 230 V RMS being stepped down to 23 V RMS (reproduced with permission from Magee and Tooley, The Physics, Clinical Measurement and Equipment of Anaesthetic Practice).
There is no direct electrical connection between the input and output coils of the transformer. The output circuit is therefore isolated from a DC component at the input, which is important to isolate the patient from the circuit for safety. If DC is applied to the input, no DC voltage will appear at the output.
Transformers are used for stepping down the domestic mains supply to safe voltages, isolating patient circuits and also in electronic filters. The power available on the primary side of the transformer will be similar to the secondary, so if the voltage is stepped down by a certain ratio, then the current must be stepped up by the same amount. The amount of stepping down (or up) is dependent on the ratio of the turns. In Fig. 4, if the primary has 1,000 turns and the secondary has 100 turns, then the voltage will be reduced 10 times. If the secondary had 10,000 turns, then the voltage would be increased 10 times. By adjusting the number of coils on the primary and secondary winding, it is possible to step up or step down the voltage between the input and the output. The equations are simply Vs/Vp=Ns/Np and NpIp=NsIs, where V is the voltage, I is the current, s is the secondary and p is the primary.
Electricity supply
The domestic ‘mains’ supply in the UK uses AC at 50 Hz (cycles per second). This frequency is also used in many other parts of the world. The USA and some other countries use 60 Hz. These frequencies are used, as they are efficient frequencies for transmission from power generation to the users and minimise the effect of leakage currents attributable to capacitance, which is discussed later. But by unfortunate coincidence, these frequencies fall into the range that is the most dangerous for the human body. The peak voltage of the mains is ±325 V, but normally the voltage is given as the root mean square (RMS) of the waveform. This RMS is the value that would give the same heating effect (a resistor or electric fire) if the same value of DC voltage were supplied. For example, if 325 V peak (230 V RMS) was applied to an electric fire, then the same amount of heat would be obtained from if 230 V DC were to be applied to the same electric fire. For comparison, the RMS voltage in the USA is 110 V.
The mains is initially generated in a power station, and the power generated (volts × amps) is enough to supply a number of hospitals and consumers. The voltage and the potential to do work must be transmitted to the user, and this transmission is usually done by overhead pylons or sometimes by underground cables. Both types of cables will be designed to carry current, but the higher the current is, the greater power is lost to heat (I2R). It is desirable to keep the current as low as possible to reduce this transmission heat loss, and it can be done by making the voltage as high as possible. However, this higher voltage carries more of a risk to patients' safety. There is therefore a trade-off between safety and power economics. The transmission voltage is normally greater than 11 kV. However, the high voltage cables need to be kept as far away as possible from the earth, or ground, to prevent arcing; this reason is why tall pylons are used.
The mains arrives at a domestic substation and is transformed down to (in the UK) 230 V RMS by a transformer. At the substation (see Fig. 5), one connection of the transformer is firmly bound to the earth at the ‘star’ point, which forms the start of the ‘neutral’ lead. The connection on the other output of the transformer is called the ‘live’ lead, and this connection is at 230 V RMS. These two leads (live and neutral) are taken to the individual outlets or mains sockets. The earth connection of the mains socket, forming the third lead of the socket, is connected back to the star point separately, although sometimes in older installations this can be earthed locally. In this way, only one of the socket points is live, and the other is at near-zero potential. This is all demonstrated in Fig. 5. The neutral connection at the equipment is not exactly zero because of the resistance of the long-length cables (see figure) supplying the mains equipment.
Fig. 5.
Diagram of the domestic mains supply supplying class 1 equipment. The equipment has a load of 230 Ω, so the normal current would be 1 A. The case of the equipment is earthed. The leakage current by capacitance is shown by C. See text for details. Reproduced with permission from Magee and Tooley, The Physics, Clinical Measurement and Equipment of Anaesthetic Practice.
Declaration of interest
The author declares that he has no conflicts of interest.
Biography
Mark A. Tooley BSc MSc PhD CEng CSci FInstP FIET FIPEM FRCP FREng is a consultant clinical scientist (medical physics) and consultant in healthcare technologies and was previously head of medical physics and bioengineering at the Royal United Hospitals in Bath. He is an honorary professor at the University of Bath and visiting professor at the University of the West of England. Professor Tooley is past president of the Institute of Physics and Engineering in Medicine, was a specialist scientific advisor for NHS England and is currently a digital clinical advisor for the West of England Academic Health Science Network and a member of the Medical Technology Advisory Committee of the National Institute for Health and Care Excellence (NICE). He taught for many years on physics in anaesthesia, EEG and electricity courses for anaesthetists. His interests are in depth of anaesthesia, biosignals and clinical measurement.
Matrix codes: 1A03, 2A04, 3J00
MCQs
The associated MCQs (to support CME/CPD activity) will be accessible at www.bjaed.org/cme/home by subscribers to BJA Education.
Further reading
- 1.Magee P., Tooley M. 2nd Edn. Oxford University Press; Oxford: 2011. The Physics, Clinical Measurement and Equipment of Anaesthetic Practice. For more information on this topic, please refer to. [Google Scholar]