Electricity

=Electricity=

On this page:

 * Electricity - definitions and analogies
 * The first rule of electric circuits: determine if it is series or parallel
 * The second and third rules of electric circuits: Kirchoff's laws

Electrons and electric charge - static electricity
[section still to be created]

Electricity - useful definitions and analogies
I = Q/t If the current is not constant this will give an average current over the time interval. For the instantaneous current, you would consider the gradient of the charge/time graph, i.e. dQ/dt. Amps are one of the seven SI base units, and are defined in terms of the magnetic forces acting between two wires carrying a current: One amp is "the constant current that will produce an attractive force of 2×10 –7 newtons per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum" (source: []). It is possible that in the next few years the definition of current will be changed so that it is defined in terms of the number of fundamental units of charge passing a given point in a second (i.e. the number of electrons per second) (source: []). ||= I ||= ampere ||= A ||= A (base unit) or Cs -1 || One m3 of water per second. || The flow of charge is analogous to the flow of water. ||
 * ~ Term ||~ Description ||~ Symbol ||~ Unit ||~ Unit symbol ||~ SI Unit ||~ Water analogy ||~ Explanation ||
 * **Current** || Is the transfer of charge from place to place. It is often referred to as the flow of charge. The size of the current is the rate at which charge is transferred per second, i.e. the flow of charge past a point per unit time.
 * Charge || Is an important property of nature. Objects with electric charge exert a force on each other: like charges repel, unlike (or opposite) charges attract. Electrons are said to have a negative charge, protons a positive charge. The charge on an electron is 1.6x10 -19 C.

1 coulomb (C) is a derived unit and is defined in relation to amps as the amount of charge passing a point when a steady current of 1A flows for 1s. 6x10 18 electrons would provide a (negative charge) of 1C.

Q=It

//Note: we should not talk of the flow of// current //- charge flows. Current __is__ the flow of charge//.

Note that charge can be positive or negative. Rub a glass rod on silk, and electrons are transferred from the glass to the silk so the rod becomes positively charged; Rub rubber on fur, electrons are transferred from the fur to the rubber and the rubber becomes negatively charged.

Also, a fundamental conservation law is that charge is conserved. In other words the amount of electricity in a closed system is conserved - e.g. when rubbing fur on rubber and the fur becomes charged by the same amount as the rubber (but positively). ||= Q ||= coulomb ||= C ||= C (derived unit) or As (in base units) || One m 3 of water || The water, like the charge is a physical thing. However we don't have any senses that directly detect charge. || V = //W///Q; units = J/C = V
 * emf || Is the amount of energy converted from other forms into electricity per unit of charge. The emf of a battery is 1V if each coulomb of charge (Q) leaving the battery has 1 joule (J) of electrical energy (//W//). Note, energy here is being given the symbol //W// (in italics), for "Work", but this should not be confused with the SI unit for Power (W).

Care is needed when referring to the voltage associated with a battery (or other source):

Strictly: the emf of the source refers to the energy produced by the battery in the absence of a load. i.e. the electrical energy per unit charge produced by the source before any losses caused by the internal resistance of the battery (or the potential difference across the terminals when there is no current).

This is to be distinguished from the terminal voltage, which is the potential difference across the terminals of the source. This is equal to the amount of electrical energy that the source is capable of delivering, per unit charge, when the source is connected to a circuit. The relationship between emf (E ), terminal voltage (V) and internal resistance (r) is:

E =V+Ir

When considering the effects of internal resistance in a circuit it can simply be treated as an additional resistor within the source with resistance of r ohms. ||= emf ||= volt ||= V ||= V (derived unit) or JC -1 || The gpe* given to the water by a pumping station (lifting the water to the top of the system) || In a pumped storage hydroelectric power station the water is pumped up to the top reservoir, storing the energy much like energy is stored in a battery. ||
 * Potential Difference || Measures the energy used up by a circuit element or elements. It is measured across an element. The p.d. between two points is the amount of energy converted from electrical energy to other forms when one unit of charge passes from one point to the other. The unit is V (J/C). ||= p.d. ||= volt ||= V ||= V (derived unit) or JC -1 ||   ||   ||
 * Resistance || Is the opposition to current flow. The resistance of a conductor is defined as V/I . Hence V=I R. Ohm's Law: Georg Simon Ohm, a German high school teacher of Mathematics and Physics, was able to use his school's well equipped physics lab to undertake experiments into electricity. In 1827 he published a book on the mathematics of electricity, which included what became known as Ohm's Law:

'Provided that temperature and other physical conditions remain constant, the current through a conductor is proportional to the potential difference across the conductor'.

i.e. that electric current is proportional to the potential difference across a conductor (other things equal):

I a V ||= R ||= Ohm ||= W ||= V/A || Narrow water pipes result in more resistance and slower flow of water. ||  ||
 * S || Siemens = 1/Ohm = conductance = I/V (opposite of resistance). ||=  ||=   ||=   ||=   ||   ||   ||
 * Resistivity (or specific electrical resistance) || By the analogy with water, it can be imagined that resistance will increase as the cross-sectional area of the wire decreases and as the length of the wire increases. This is in fact the case, and the constant of proportionality (which will vary from material to material) is the 'resistivity' of the material, r (rho):

||= Rho ||= r ||= W m || Vm/A || See description ||  ||
 * Power || The energy per second (e.g. converted to light and heat by a bulb). From the definition of Voltage (J/C) and Current (C/S) it can be seen that:

Power, P = VI = I 2 R = V 2 /R ||=  ||=   ||=   ||   ||   ||   ||
 * Capacitance || Any arrangement of two conductors separated from each other by an insulator will form a capacitor. A capacitor stores energy by keeping electric charge on their plates (or, they can be viewed as devices for storing charge). When a capacitor is charged one plate will have a negative charge, and the other an equal positive charge and a voltmeter connected across the capacitor will measure a potential difference. The ratio of the charge to potential difference (Q/V) will be fixed for a given capacitor, and this is called the capacitance. (Think of capacitance as the capacitors 'charge density' (//my term - I need to understand this in more detail//) - one capacitor may store the same positive and negative charge closer together than another capacitor, resulting a greater "force" or emf between them. It will therefore have a higher capacitance <- DOESN'T MAKE SENSE (inc V lowers capacitance). ||  ||   ||   ||   ||   ||   ||

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 * gravitational potential energy

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The First Rule of Electric Circuits: determine if it is series or parallel (and why we care)
Being able to distinguish series and parallel circuits (or the series and parallel parts of a circuit) is essential if the behaviour of a circuit is to be understood


 * Looking at simple series circuits:**

A __series circuit__ is a circuit which only has one path for the electricity to flow. There is only one wire, if you like, although it may be broken up with other circuit elements, like bulbs perhaps.

The photos below show a number of simple series circuits where bulbs are being connected with a battery (and in the last case, they are being connected to two batteries). The circuit diagrams for each circuit are shown immediately above each photo.



It is clear that the brightness of each bulb falls as the number of bulbs connected in series increases (pictures 1-1 to 1-3). You might even go so far as to say that the brightness of the bulbs in picture 1-2 is half that of the bulb in 1-1, and that the brightness of the bulbs in 1-3 is one third of that in 1-1?

Furthermore, if the number of batteries is increased at the same time as the number of bulbs it appears that the brightness remains the same, e.g. the brightness of the bulb in picture 1-1 (where a 6V battery is connected to one bulb) appears to be the same as the brightness each bulb in picture 1-4 (where two bulbs are connected in series to a 12V battery).

Well, when the bulb are bright, they must be giving off energy... That energy must come from somewhere, and that somewhere must be the battery. So the battery is providing energy (and this must be something to do with the markings on each battery of "6V"). This energy is somehow flowing round the wires to the bulb where it is used up... Knowing that electrons have electric charge, we might suppose that electrons are carrying the energy, so they somehow "flow" from the battery to the bulb. The electrons must then give up the energy in the bulb (as we see the energy being released as light (and perhaps also feel it as heat), but then the electrons must carry on, otherwise there would be a traffic jam and the "flow" would stop.... So the electrons must carry on along the wires until they get back to the battery (and they have made a complete "__circuit__"). We can test the last point by unplugging the lead on one side of the bulb and seeing that the electricity does not flow (the bulbs go out) if there is not a complete circuit for the electrons to flow around.
 * How can we think about what is happening?**

Well, from that thought experiment, we have in fact discovered much of what there is to know about electricity:

- Energy is provided by a power source (a battery, the mains, or a solar cell). We measure it in "__volts__" (V). The energy is given to electrons, which each have a charge, but as the charge on an electron is very small and inconvenient to count we measure the __charge__ on a large group of electrons in "__coulombs__" (C), so volts are the measure of energy given to each coulomb, making the SI units J/C or JC -1.

- One "coulomb" is made up of 6x10 18 electrons, and the charge flows around a complete "circuit", and the number passing any point in one second is the flow of charge, or the "current" (I ). The SI units of current are therefore C/s or Cs -1. C/s are also called "amps" (unit: ampere).

- The energy carried by the coulombs or charge is given off when the electrons meet something (like a bulb) which must have something different about it compared to the circuit wires (to explain the different behaviour). If we look at the bulb very closely we can see that the filament of the bulb is made up of a very thin coil of wire. The thinness (and in fact the material) of the wire (compared to the wires of the circuit) makes it difficult for the electrons to get through, which means they have to make an effort, or give up their energy. So the filament of the bulb resists the flow of current, and the filament wires are said to have higher "resistance" (R) than the circuit wires. Resistance is measured in Ohms (W ).


 * In summary:**
 * The emf or voltage (V) of the battery is measured in volts (V) with SI units J/C, where the C is the unit of charge (coulombs);
 * The current (I ) is measured in amps (A) with SI units C/s.
 * The Resistance (R) is measured in Ohms (<span style="font-family: Symbol,sans-serif;">W )

So what does the behaviour of the bulbs tell us about V, <span style="font-family: Georgia,serif;">I and R in a series circuit?

Well, the current (<span style="font-family: Georgia,serif;">I ) anywhere in a series circuit must be the same as there is only one path for the charge to flow. Think of it like loads of cars going round a racetrack, if they can't overtake, eventually the speed of all of them will be determined by the slowest car, so they will all have to travel at that speed. In picture 1-1 the bulb is very bright, so it must get all the energy (all of the battery's 6V). In picture 1-2, the bulbs are half as bright, so the energy is being shared between them (3V each), and in 1-3 they are less bright still, so again the energy from the battery (6V) is being shared between them: 2V each. Less energy to each bulb, so less bright - makes sense.

The energy transferred from electricity to light and heat in the bulb is called the "potential drop" (pd) across the bulb, and is measured in volts (i.e. the energy transferred from electric to other forms per second across part of a circuit).

Finally, what does the behaviour of the bulbs tell us about resistance: as the number of bulbs increases in each of 1-1 to 1-3 the overall length of very thin wire along which the charge flows increases (as there are more bulbs). That might suggest that the resistance is increasing, so perhaps the current will be lower in 1-3 than 1-2, and lower in 1-2 than 1-1? But park that thought for the moment and lets look at parallel circuits.


 * Looking at simple parallel circuits:**

A __parallel circuit__ is a circuit with //more than// one path for the electricity to flow.

The photos below show a number of simple parallel circuits with just bulbs and a battery (at least 2-2 and 2-3 do; 2-1 is the same as 1-1 above). The circuit diagrams for each circuit are shown immediately above each photo.



.

So what can we understand from these circuits. The behaviour is certainly very difficult from that of the series circuits. Here the bulbs are each clearly as bright as each other. So adding a second or third bulb //in parallel// does not reduce the brightness of the bulbs. The energy being delivered to each bulb must be the same if they have the same brightness. This would suggest that the potential drop (pd) across each bulb is the same. This makes sense as if you look at the circuit diagrams, each bulb is connected directly to the battery, which is supplying 6V. So it makes sense that each bulb has a 6V potential drop across it.

What about the current and resistance. Well, there is the same amount of resistive material in 2-3 as 1-3, i.e. 3 bulbs with the thin wire filaments. The difference is that in 2-3 the thin wires are each providing an additional path for the current, whereas in 1-3 the current had to pass through each bit of thin wire in turn. An analogy with water is very helpful to understand this. Imagine a bath full of water (the battery). If there is one plug hole (filament bulb), the water (charge) will flow out at a certain rate (however long the pipe is - i.e. whether you have one or three bulbs in series). But what if there are three plug holes - it will be much easier for the water to flow out and it will flow out faster. So although each battery has a high resistance, having two in parallel provides less resistance than one as there are now two paths for the current rather than one.

**In summary**
Notes: (1) Think of people running the hurdles in the Olympics. In a 100m race they will use all their energy getting to the finish, but they will also use all their energy in a 200m race. So they must decide at the start of the 200m race to spend less energy per hurdle than they would if it was a 100m race, but in both cases they use up all the energy by the end of the race. This is analogous to the splitting (or sharing) of voltage over the elements in a series circuit - the energy must be used up by the end, but not before, so shared in proportion to the resistances. (2) Remember that in a parallel circuit the combined resistance of all the parallel elements must be less than the resistance of the element with the lowest resistance. (3) In a parallel circuit remember that MORE current will flow along the path with lower resistance, so the current splits in inverse proportion to the resistances.
 * ~ **Simple Series and Parallel circuits** ||~ Series circuits ||~ Parallel circuits ||
 * **Volts (pd)** ||= Shared across elements in the circuit (1) ||= Same everywhere ||
 * **Current** ||= Same everywhere ||= Splits along each path (3) ||
 * **Resistance** ||= Adding bulbs (or any element with resistance) increases the resistance of the whole circuit ||= Adding bulbs (or any element with resistance) reduces the resistance of the whole circuit (2) ||


 * Therefore if we want to determine what will happen is an electric circuit we first need to determine if the circuit components are arranged in series or parallel, as the resistance of circuit elements varies depending on how they are arranged (in series or in parallel) and this will result in different current flow and potential drops.**

//Thinking about emf//

//It can be confusing that the electrons "know" how much energy to give up to the first bulb in a series circuit when there may or may not be more bulbs which it hasn't yet got to, so can't know about yet. One way to think about this is to think of all the electrons being connected together, so that as one starts to move they all move (like carriages on a train), in this way the movement of any single electron is determined by the whole train. In addition, the energy would be transferred around the circuit much faster than any one electron actually moves (which is in fact the case - electrons "drift" round really slowly e.g. cm/s). Another way to think about emf is to think of marbles running down a frictionless track. The source voltage (emf) is how high the starting point of the track is, and the end point must be at the same height (as the marbles must get back to the battery (and will do on a frictionless track).//

//In the diagram above a one bulb circuit can be seen as analogous to the frictionless marble run with one "bump" in it. Here the gpe of the ball at A is analogous to the emf of the battery. The larger the emf the higher the battery, and the faster the ball with move through the bulb (the current is analogous to the average speed of the ball to get from A to C, so the "current" would be higher if the ball starts higher). Note that the ball will always have enough energy to get back to the battery (C) no matter how many bumps (bulbs) you put in. The two bulb circuit is an example of this. The emf (initial height) is the same as before, so the ball moves with the same velocity, but as it has further to travel its average speed will be lower - this is analogous to the lower current due to the higher resistance in the circuit), however it will still get to F.//

//There is however no analogy here for the pd of the bulb. In (1) it would be nice to think of t////he pd of the bulb as equal to the gpe lost as the ball rises up the "bump" of the battery, however the pd across 1-2 should be equal to the emf, so that doesn't work. Similarly, with the two bulb example, the pd across 3-5 should be the same as the pd across 1-2, and there is no clear analogy for that.//

Note: Diodes and LEDs - to remember which way round to connect them:
 * Circuit symbols**
 * In a circuit diagram the current (conventional) direction goes in the direction of the arrow. (Or, alternately, the electrons must flow towards the "bar" that looks like the posivite terminal of a battery).
 * In practice, LEDs have different length leads - the short one is the negative (cathode), which is connected to the negative terminal of the battery.

Note: Capacitors - some capacitors will have one terminal marked as either positive or negative - these must be connected the right way round. This means that the positive terminal of the capacitor must be connected to the point with the highest potential (the positive terminal of the battery, for example), and negative to negative.

Kirchoff's first law:

 * **//The sum of the currents into a junction must equal the sum of the currents out.//**

This follows from the principle of conservation of charge.

Kirchoff's second law:

 * **//In any closed loop in a circuit the sum of the emfs must equal the sum of the potential drops.//**

This follows from the principle of conservation of energy.