10.4.1 Direct and alternating current

Direct current

1. In a direct current, written d.c., the charge flows in one direction only and never reverses.
2. A cell or a battery has a fixed positive terminal and a fixed negative terminal, so the potential difference it supplies always acts the same way round and the conventional current in the external circuit always passes from the positive terminal to the negative terminal.
3. Sources of direct current include a single cell, a battery of cells in series, a d.c. power pack on the bench, a solar cell, and the low potential difference output of a phone charger.
4. The size of a direct current can be changed, for example by adjusting a variable resistor, while its direction stays the same, so d.c. means one direction rather than one fixed value.
5. Because the direction never changes, a direct supply can drive components that only work one way round, such as an LED or a rechargeable cell being charged.
6. Reversing the connections to a d.c. supply reverses the current in the circuit, which is why the terminals are marked $+$ and $-$.

Alternating current

1. In an alternating current, written a.c., the direction of the current reverses repeatedly, many times every second.
2. The potential difference of the supply alternates, so the terminal that is positive relative to the other for one half of a cycle becomes negative for the next half, and the push on the charge reverses with it.
3. The delocalised electrons in the wire therefore oscillate backwards and forwards about a fixed position instead of drifting steadily one way round the circuit.
4. One complete cycle is a push in one direction followed by a push in the other, which returns the supply to the state it started from.
5. The mains supply that reaches the sockets in a house is alternating, and so is the output of a generator.
6. An alternating current still transfers energy, because the energy dissipated in a resistance depends on the size of the current and not on the direction in which that current happens to be flowing.
7. A mains heater therefore warms up during every half cycle, and it does not cool between one reversal and the next.

The UK mains supply

1. The mains supply in the United Kingdom is an alternating supply of about $230V$ with a frequency of $50Hz$.
2. The $230V$ figure describes the size of the alternating potential difference between the live wire and the neutral wire, and it is this potential difference that drives the current through an appliance.
3. The $50Hz$ figure is the frequency of the supply, meaning that the supply completes $50$ full cycles every second.
4. The current reverses twice in each cycle, so it changes direction $100$ times every second, which is far too fast to be seen as any flicker in a lamp.
5. The period $T$ is the time taken for one complete cycle, and it is linked to the frequency by $T=\frac{1}{f}$, with $T$ in seconds and $f$ in hertz.
6. A supply at $50Hz$ therefore has a period of $\frac{1}{50}=0.020s$, which is $20ms$.
7. The potential of the live wire alternates because the supply it is connected to alternates, and that reversal is passed unchanged along the cables to the socket.

Reading supply graphs

1. A graph of current against time, or of potential difference against time, shows at once which kind of supply is connected.
2. A direct supply gives a trace that stays on one side of the time axis, because the value keeps the same sign throughout.
3. A direct supply whose size varies gives a trace that changes height yet still never crosses the time axis.
4. An alternating supply gives a trace that rises above the time axis and falls below it in turn, crossing the axis at every reversal.
5. Each crossing of the time axis marks an instant when the current is momentarily zero and about to flow the other way.
6. The peak value is the greatest distance of the trace from the time axis, and it is reached twice in every cycle, once above the axis and once below it.
7. The period is read as the time from one peak to the next peak, or from one crossing of the axis to the second crossing after it, and the frequency then follows from $f=\frac{1}{T}$.
8. A flat trace lying exactly along the time axis means there is no current at all, so the switch is open or the supply is off.

Devices and their supply

1. A filament lamp and a heater work on either supply, because the heating effect depends on the size of the current through the resistance and not on its direction.
2. A kettle element connected to the mains therefore transfers energy at the same rate as it would on a direct supply of the same potential difference.
3. Many electronic devices need direct current, because their circuits contain components such as diodes and integrated circuits that only work with a fixed polarity.
4. A laptop, a phone and an LED lamp are supplied through an adapter that converts the alternating mains into direct current at a lower potential difference.
5. Charging a rechargeable cell also needs direct current, because the charging current has to be driven through the cell in one particular direction.
6. A torch running from cells is on direct current from the start, so no conversion is needed inside it.

10.4.2 Live, neutral and earth wires; safety

The three-core cable

1. An appliance with a metal case is joined to the mains by a three-core cable, which holds three separately insulated copper cores inside one tough outer sheath.
2. The live wire is insulated in brown. It carries the alternating supply into the appliance, so it is the core that delivers the energy pathway from the mains to the appliance.
3. The neutral wire is insulated in blue. It completes the circuit by carrying the current back out of the appliance towards the supply, and it is joined to earth at the local substation.
4. Charge flows in along one of these two cores and out along the other, swapping over many times each second because the mains supply alternates.
5. The earth wire is insulated in green and yellow stripes. It is a safety wire, connecting the metal case of the appliance to the earth, and it carries no current at all while the appliance is working normally.
6. The striped colouring of the earth core is deliberately unlike the plain colours of the other two, so it cannot be mistaken for a core that carries current in normal use.
7. The cores are copper because copper has a low resistance, while the insulation round each core and the outer sheath are insulators that keep the cores apart and keep them out of reach of the user.

Wiring a plug

1. In a three-pin plug the earth pin is the longest and sits at the top, so it is the first connection made as the plug goes in and the last broken as it comes out.
2. With the earth pin uppermost and the open back of the plug facing the person wiring it, the live terminal is on the right and the neutral terminal is on the left.
3. The brown core goes to the live terminal, which is the terminal joined to the fuse, the blue core goes to the neutral terminal, and the green and yellow core goes to the earth pin.
4. The pins are brass because it conducts well and resists corrosion, while the casing and the pin sleeves are plastic because plastic is an electrical insulator.
5. The cable grip clamps the outer sheath of the cable rather than the individual cores, so that any pull on the cable is taken by the sheath and never reaches the terminals.
6. If the cores themselves took the strain, a tug on the cable could drag the live core out of its terminal and leave a bare live conductor loose inside the plug, where it could touch the case or the other cores.
7. The outer sheath must reach inside the cable grip, and each core is stripped back only far enough for its bare copper to sit fully inside the terminal, so that no bare metal is left exposed.
8. Each terminal screw is tightened firmly, because a loose connection has a higher resistance and so heats up when current passes through it.

How a fuse protects

1. A fuse is a short length of thin wire, usually sealed inside a ceramic cartridge, fitted in the live wire inside the plug.
2. The fuse wire is made thinner than the rest of the circuit so that it has the greatest resistance in the path and heats up the fastest, since the energy dissipated each second in a resistance rises with the square of the current through $P=I^{2}R$.
3. A common fault is the insulation on the live core wearing through inside the appliance, so that the bare live conductor comes into contact with the metal case.
4. From that moment the fault follows a fixed sequence.
   1. The metal case becomes live, because it is now joined directly to the live wire and sits at the same potential as it.
   2. The case is also joined to the earth by the earth wire, so a complete path now exists from the live wire, through the case, along the earth wire, and out to earth.
   3. That path is made of thick copper and has a very low resistance, so a very large current flows along it.
   4. The whole of this large current has to pass through the fuse, because the fuse is in the live wire ahead of the fault.
   5. The thin fuse wire heats up rapidly, reaches its melting point and melts, which is what is meant by the fuse blowing.
   6. A gap opens in the live wire, so the circuit is broken and the current stops.
   7. The appliance is now cut off from the live supply, so the case is no longer live and anyone who touches it is not given a shock.
5. Breaking the circuit also stops the large fault current from overheating the cable and the appliance, which removes a serious fire risk.
6. A blown fuse cannot be reset, so it has to be replaced, and the fault must be traced and repaired first or the replacement will blow as soon as the appliance is switched on.
7. The earth wire by itself would not make the appliance safe, because the fault current would simply keep flowing; it is the fuse melting that disconnects the supply.

Circuit breakers

1. A circuit breaker is an automatic switch that does the same job as a fuse, opening the circuit when the current through it rises above the value it is set for.
2. The current passes through an electromagnet inside the breaker, and a large current makes that electromagnet strong enough to pull a catch and force a pair of contacts apart.
3. Because nothing has to melt, a circuit breaker opens the circuit in a small fraction of a second, while a fuse wire must first heat all the way to its melting point, so the breaker cuts off the supply sooner and less energy is transferred during the fault.
4. A circuit breaker is reset by pressing a switch once the fault has been repaired, so no replacement part is needed, although it costs more than a cartridge fuse.
5. A residual current device works differently again, comparing the current in the live wire with the current in the neutral wire.
6. If current is leaking out of the circuit, for example through a person to earth, the two currents are no longer equal and the device trips, so it responds to a current far too small to melt a fuse and acts quickly enough to protect a person.

Double insulation

1. An appliance with double insulation has two separate layers of insulation between its live parts and anything a user can touch.
2. The first layer is the plastic insulation around the cores and the internal wiring, and the second is an outer casing made entirely of insulating plastic.
3. Because the outer case is an electrical insulator, no part of it can become live even if a live wire works loose inside, so there is nothing that needs connecting to earth.
4. A double-insulated appliance is therefore supplied by a two-core cable carrying only live and neutral, with no earth core, and it is marked with a symbol of one square inside another.
5. A hair dryer, a vacuum cleaner, a plastic-cased electric drill and a food mixer are usually double insulated.
6. An appliance with exposed metal that a user can touch, such as a metal toaster, an electric kettle, a cooker or a washing machine, must be earthed instead, because that metal could otherwise become live.

Switching the live wire

1. The fuse and the appliance's on and off switch are always fitted in the live wire, never in the neutral wire.
2. Opening a switch anywhere in the loop stops the current, so a switch in the neutral wire would still appear to turn the appliance off.
3. A switch in the neutral wire would nonetheless leave every internal part of the appliance connected to the live wire, so those parts would stay at the live potential and could give a shock to anyone who opened the appliance.
4. A switch in the live wire disconnects the appliance from the live side of the supply, which isolates the internal parts.
5. The same argument applies to the fuse. A fuse in the neutral wire would melt and stop the current, but the appliance would still be joined to the live wire, so a faulty case could remain live.
6. A fuse in the live wire cuts the appliance off from the supply as it melts, and that is what makes the case safe to touch afterwards.

10.4.3 Mains wire potential differences and dangers

Potentials on the wires

1. A potential difference is always measured between two points, so a single value quoted for one mains wire means the potential difference between that wire and the earth.
2. The earth is taken as the zero of potential, so earth potential is $0V$ and every other mains value is quoted relative to it.
3. The live wire is at an alternating potential of about $230V$ relative to earth, swinging one way and then the other $50$ times each second.
4. The neutral wire stays close to $0V$, because it is connected to the earth at the local substation.
5. The earth wire is at $0V$, since it is joined directly to the ground through a buried metal rod or through the earth conductor of the supply cable.
6. The potential difference across a working appliance is the difference between the two supply wires, about $230V-0V=230V$, and it is this potential difference that drives the current through the appliance.
7. Because the neutral and earth wires both sit near $0V$, there is almost no potential difference between them and a person standing on the ground, which is why the danger lies in the live wire.

Getting a shock

1. A person standing on the ground is in electrical contact with the earth, so their body sits at about $0V$.
2. If that person touches the live wire, the point of contact is raised to about $230V$ while their feet remain at $0V$.
3. A potential difference of about $230V$ therefore acts across the body, from the hand to the feet.
4. The human body is an electrical conductor, because body fluids contain dissolved ions that are free to move, so charge can pass through it.
5. That potential difference drives a current through the person and on into the ground, and this current through the body is an electric shock.
6. The size of the current follows from $I=\frac{V}{R}$, where $V$ is about $230V$ and $R$ is the total resistance of the whole path, including the skin at both points of contact.
7. It is the current that does the damage. It interferes with the electrical signals that control the heart and the muscles, and it dissipates energy in the tissue, which causes burns where the resistance is greatest.
8. A current whose path crosses the chest is the most dangerous of all, because it passes through the heart.

What makes a shock worse

1. Damp or sweaty skin lowers the resistance of the contact, because water carrying dissolved salts conducts far better than dry skin.
2. A smaller resistance gives a larger current for the same $230V$, from $I=\frac{V}{R}$, so wet hands can turn a survivable shock into a fatal one.
3. Bare feet on a damp floor make a good connection to the earth, which lowers the resistance of the return part of the path and raises the current again.
4. Dry shoes with rubber soles put a large resistance in series with the body, so the current driven by the same potential difference is much smaller.
5. A large area of contact, such as gripping a live conductor in the whole hand, gives a lower resistance than a brief touch with one fingertip.
6. The longer the contact lasts, the more energy is transferred into the body, which is why a protective device that cuts off the supply quickly reduces the harm done.
7. For these reasons mains sockets are not fitted in bathrooms, the supply is switched off at the consumer unit before any wiring is worked on, and an appliance is unplugged before it is opened.

Live wire when switched off

1. Switching an appliance off opens its switch, which puts a gap in the circuit so that no charge can flow round the loop.
2. Breaking the circuit stops the current, but it does not change the potential of the live wire on the supply side of the switch.
3. That length of live wire is still joined through the socket and the house wiring back to the substation, so it stays at about $230V$ relative to earth.
4. Anyone who touches it while standing on the ground still has about $230V$ across them, so a current is driven through them to earth and they receive a shock.
5. The current can flow because the person completes a new circuit from the live wire through their body to the earth, and that new path does not pass through the appliance's switch at all.
6. The appliance is only made safe by unplugging it, or by switching off the whole circuit at the consumer unit so that the house wiring is isolated from the supply.
7. A lamp with a broken switch or a damaged flex is dangerous for the same reason, because the live conductor inside it remains at about $230V$ whether the lamp is lit or not.

Short circuits

1. A short circuit is an unintended connection of very low resistance that lets charge bypass the path it was meant to follow.
2. It happens when the insulation between the live and neutral cores wears through, when a cable is crushed or pierced by a nail, or when water bridges two terminals.
3. The current then no longer passes through the appliance, so nearly all of the resistance is taken out of the circuit and only the small resistance of the wires is left.
4. From $I=\frac{V}{R}$, the same $230V$ across a very small resistance drives an extremely large current.
5. The rate at which energy is dissipated in that wire is $P=I^{2}R$, and because the current is squared, an enormous power is transferred in the cable even though its resistance is small.
6. The cable heats up within a fraction of a second, the insulation softens and melts, and the cable or the material around it can catch fire.
7. The very large current is also what makes the protective device act, since it melts the fuse or trips the circuit breaker in the live wire and disconnects the supply before the cable is destroyed.

Birds on overhead lines

1. A bird perched on a single overhead line is touching only one conductor.
2. Both feet rest on the same wire, and the short length of thick wire between them has an extremely small resistance, so there is almost no potential difference between one foot and the other.
3. With almost no potential difference across it, almost no current is driven through the bird, so it is unharmed even on a line at a very high potential.
4. The bird is also not connected to the earth, so there is no complete path from the line to any point at $0V$.
5. If the bird touched a second line, or an earthed pylon, at the same time, a large potential difference would appear across it and a large current would flow through it.
6. The contrast with a person is the connection to earth: standing on the ground holds the feet at $0V$, so touching a live conductor puts the whole supply potential difference across the body.

10.4.4 Power ratings and energy use

Reading a power rating

1. Every mains appliance carries a data plate giving the supply it is designed for, $230V$ at $50Hz$ in the United Kingdom, and its power rating in watts or kilowatts.
2. The power rating is the energy the appliance transfers each second while it is working normally, so a rating of $2000W$ means $2000J$ every second.
3. Ratings are quoted either way round, since $1kW=1000W$, so $2000W$ and $2.0kW$ are the same rating.
4. Typical UK figures are an electric shower at $9.0kW$, a kettle at $3.0kW$, a hair dryer at $2.0kW$, a laptop at $65W$, a fridge at $100W$ and an LED lamp at $8W$.
5. A larger power rating means energy is transferred faster, not that more energy is used in total, because the total energy also depends on how long the appliance runs.
6. A fridge with a small rating runs for many hours a day, while a kettle with a large rating runs for only a few minutes, so the fridge can easily use more energy over a day.
7. Some appliances switch themselves on and off, so the rating gives the power while the appliance is actually working rather than an average over the day.

Current drawn by appliances

1. The current an appliance draws from the mains follows from the power equation $P=IV$, where $P$ is in watts, $I$ is in amperes and $V$ is in volts.
2. Rearranging for the current gives $I=\frac{P}{V}$, and for a UK mains appliance the potential difference used is $V=230V$.
3. Because the supply potential difference is fixed, the current is decided by the power rating alone: the larger the rating, the larger the current.
4. A $2.0kW$ hair dryer therefore draws a far larger current than a $65W$ laptop charger plugged into the same socket.
5. The current matters because it decides how thick the flex must be, how warm the flex becomes in use, and which fuse should be fitted in the plug.
6. A power in kilowatts must be converted to watts before substituting, so $2.0kW$ becomes $2000W$, otherwise the current comes out $1000$ times too small.

Choosing a fuse

1. A fuse is chosen so that it carries the appliance's normal working current without melting, yet melts quickly if a fault makes the current much larger.
2. The standard cartridge fuses fitted in a UK plug are rated at $3A$, $5A$ and $13A$.
3. The working current is found first from $I=\frac{P}{V}$, and the fuse chosen is then the smallest standard rating above that working current.
4. A fuse rated below the working current would melt every time the appliance was switched on, so the appliance would never work.
5. A fuse rated far above the working current is also unsafe, because a fault current could flow for a long time, overheating the flex and starting a fire before the fuse melted.
6. A $2.0kW$ hair dryer drawing $8.7A$ therefore takes a $13A$ fuse, while a $460W$ television drawing $2.0A$ takes a $3A$ fuse.
7. A $3.0kW$ kettle draws $\frac{3000}{230}=13A$, which sits right at the limit of the standard range, so it is fitted with the $13A$ fuse because no larger plug fuse is made.

The kilowatt-hour

1. The joule is an inconveniently small unit for household energy, since a single kettle boiling transfers a few hundred thousand joules and a whole house uses a few thousand million in a quarter.
2. Domestic energy is therefore measured in kilowatt-hours, and one kilowatt-hour is the energy transferred by an appliance of power $1kW$ working for $1hour$.
3. Energy in kilowatt-hours is found from $E=P\times t$ with the power $P$ in kilowatts and the time $t$ in hours, which is the same equation as $E=Pt$ in joules and seconds but with larger units.
4. Converting to joules uses $1kW=1000W$ and $1hour=3600s$, so $1kWh=1000\times 3600=3.6\times 10^{6}J$.
5. A time given in minutes is converted to hours by dividing by $60$, so $12minutes=\frac{12}{60}=0.20h$.
6. The electricity meter in a house counts kilowatt-hours, and one kilowatt-hour is what a bill calls a unit of electricity.

Cost of electricity

1. The cost of running an appliance is the energy it transfers multiplied by the price of one unit, so cost $=$ energy in $kWh$ $\times$ price per $kWh$.
2. The price is quoted in pence per kilowatt-hour, for example $27p$ per unit, and multiplying by an energy in kilowatt-hours gives a cost in pence.
3. Dividing a cost in pence by $100$ converts it to pounds, so $1458p$ is £14.58\pounds14.58£14.58.
4. Two appliances at the same price per unit can be compared directly by their energy in kilowatt-hours, since the price cancels out of the comparison.
5. A standing charge on a bill is a fixed daily amount that does not depend on the energy used, so it is added after the energy cost has been worked out.
6. Reducing a cost means reducing the energy, which can be done by lowering the power rating, shortening the time of use, or both.

Comparing appliances

1. Comparing two appliances means comparing the energy each transfers over the time it is actually used, not their power ratings alone.
2. A filament lamp rated at $60W$ and an LED lamp rated at $8W$ give out a similar amount of light, so the LED does the same useful job for a much smaller power.
3. Left on for $1000h$, the filament lamp transfers $E=0.060\times 1000=60kWh$ while the LED lamp transfers $E=0.008\times 1000=8kWh$.
4. The saving of $52kWh$ is worth $52\times 27=1404p$, which is £14.04\pounds14.04£14.04 over the life of one lamp.
5. Time can outweigh power completely: a $100W$ fridge running all day transfers $0.100\times 24=2.4kWh$, while a $3.0kW$ kettle used for $10minutes$ transfers only $3.0\times \frac{10}{60}=0.50kWh$.
6. The fridge, with a rating $30$ times smaller, therefore uses nearly five times as much energy in a day as the kettle.