So the first thing you need to know is that waves transfer energy without transferring matter. And there are two types transverse and longitudinal. Longitudinal is when the particles involved in the wave are oscillating parallel to the direction of energy transfer.
And of course they're made up of compressions and rarefactions e.g. sound waves. Transverse is the opposite particles oscillate perpendicular e.g. light or any EM for that matter electromagnetic waves. waves on a string, waves in water, so on and so forth.
So this is your standard wave, this could be time, it could also be distance as well, usually it's time. This axis here is displacement from the midpoint which is equilibrium, so the particles are when they're not oscillating. This here is lambda, that's wavelength, this here is amplitude, now it would be wavelength if this is distance.
If it's time on the x-axis then distance between one peak and the next we don't have wavelength but we have time period. Time period is the time taken for one complete wave to pass a point. I'll measure that in seconds. Frequency, number of complete waves passing a point every second. So therefore, if you want to find the frequency, then we just do one divided by the time period.
So our other equation is V equals F lambda. That's wave speed equals frequency times wavelength. Polarization.
Transverse waves can be polarized by a filter that's just made up of very small lines. This only lets. half of light be transmitted we say that's a posh word for just let through it absorbs the rest what we say is that it selects waves oscillating in a particular direction interference also known as superpositioning when the displacements of the individual waves sum at each point they add up on a piece of string this is what we call the first harmonic and this is when the wavelength is equal to two lots of the length of the string draw the second harmonic as well when the wavelength is equal to the length of the string so At a node, always destructive interference, no energy transferred at these points.
At an antinode, we have both constructive and destructive interference, but energy is transferred because the string is actually moving. Diffraction. So Young's double slit, he had a candle and he had a single slit and then a double slit, which then made the diffraction pattern. He needed the single slit to produce...
coherent sources at the double slit coherent what does that mean well it means basically in sync in phase but the proper definition is waves that have a constant phase difference we use a laser nowadays because that is coherent it's also monochromatic whereas the candle wasn't that means just one wavelength so if we draw a graph of what's going on here's our intensity here's our distance from the center fringe width or fringe spacing it's given the letter W and the Young double slit equation is W equals lambda D over S. S is the slit separation. That's the double slit, the spacing between the two slits there.
In reality, what does this look like? Well, it looks like bright spots with dark spots in between. We also call these maxima and that's where we get constructive interference. In other words, two waves arriving in phase, they reinforce each other as it were.
So making a super wave. So that's why we see a bright spot. Minima is where we get destructive interference, dark.
And for a maximum, the path difference, that's how much further one ray is traveling than the other, is equal to a multiple of the wavelength. For a minimum, path difference is equal to a whole number, take away a half times the wavelength. So one and a half, two and a half, et cetera.
Speaking of path difference and phase difference, phase difference is just how out of sync two bits on one wave or two waves are. So all we do is that we take the difference in the time divided by the time period or difference in distance divided by the whole wavelength. So it's just the bit divided by the lot times by two pi and that turns it into radians.
Single slit looks like this. A big central max falls away very quickly. Central max is twice as big than the other fringes.
Diffraction grating equation is n lambda equals d sine theta. where n is the order and d is the line spacing and we calculate that by doing one divided by lines per meter so you might get lines per millimeter change it into lines per meter and then do one divided by that to get d find the maximum order theta equals 90 degrees e.g you'll end up with something like n is equal to 3.7 max is 3. you can't have a 3.7 order at 90 degrees And last but not least we have refraction and the only equation you need to be concerned about is n1 sine theta 1 equals n2 sine theta 2. Here's our normal, it's always 90 degrees. Here's our n2, here's our n1.
So this could be water and air, don't know. It's worth remembering that air and is 1 for TIR to occur. Angle of incidence must be greater than critical angle.
and also the refractive index of this medium must be greater than the second medium otherwise it doesn't work. To find the critical angle all we do is make theta 2 90 degrees therefore n1 sine theta c because that's what we're talking about it's the angle of incidence is just equal to n2. TIR is when all light is reflected because we always get a partial reflection but not with TIR. First thing we need to talk about is average speed, it's distance over time. We say average speed because we don't know what's happening.
to the speed over the course of that distance. Here are graphs. We have a distance time graph. We could say displacement time graph. Gradient is equal to speed or velocity if it's displacement time.
Velocity time graph, the gradient gives you acceleration. The area under the graph gives you distance traveled or displacement. But what about SUVAT? We use the SUVAT equations or Newton's equations of motion if the object is accelerating. If we're chucking something up or dropping something, doesn't matter, acceleration is. always 9.8 meters per second squared towards the ground so it might be minus if something's moving upwards.
Don't forget that for projectile motion if something's chucked horizontally then we use suvat vertically but then we just use speed equal systems over time horizontally because we assume there's no frictional forces. The path that an object takes in this case is a parabola or it's parabolic. Let's have a look at forces. Newton's first law is that an object's motion is constant if there's no external force acting on it. In other words velocity is constant.
Don't forget that could mean that the direction is changing while speed is staying the same, circular motion. We're not going into that here though. Second law is F equals MA, force equals mass times acceleration.
Don't forget that F is the resultant force doing the accelerating, and mass is the total mass being accelerated. Third law, to each action of force, there is an equal and opposite reaction. Weight is equal to MG, that's mass times gravitational field strength, 9.8 or 9.81.
For an object to be in equilibrium, that means constant motion. We're talking about Newton's first law there. We need no resultant force.
That means that forces are balanced. And also we have to have no resultant moment or torque. We'll talk about that a little bit later on as well. Air resistance and friction, this frictional force is increased with speed. If you've got a mass on a slope, then the force pulling parallel to the slope down the slope is equal to mg sine theta.
That's the component of the weight. All right, energy, here we go. Kinetic energy is half mv squared.
GPE is mgh. If we're given h, we pretty much know that we're gonna use GPE. If there's no energy lost when something falls, then we know mgh equals half mb squared and the m's cancel. But if the gp at the top does not equal the kinetic energy at the bottom, then energy is lost in the form of thermal energy or heat. And we can say that that's actually work done against frictional forces.
That leads us nicely on to work done. Work done is equal to force times distance, E equals Fd. I prefer E, some people use W, but it is energy as measured in joules. Remember that the force and distance need to be parallel.
So if they're not then you need to times by cos theta, theta being the angle between them. The power version of this, power developed, is P equals FV. We've just divided the whole equation by time. Okay materials, let's look at Hooke's law.
Force is equal to spring constant times extension F equals KE or F equals KX or F equals K delta RL. Doesn't matter which one you use. Here's the graph of force against extension.
The gradient gives you the spring constant and that's measured in newtons per meter. The area under the graph is equal to the energy stored, it's a triangle so therefore it's going to be half times force times extension. If we substitute in ke instead of f then we get half ke2. Stress or tensile stress measured in pascals is equal to force divided by area. Strain is the ratio of extension to original length.
The Young modulus is equal to stress over strain. So therefore the whole version is FL over AE. And if you draw a graph of stress against strain, then obviously our gradient is going to be equal to the young modulus. Let's look at that graph again. We've got three main points that we look at.
We have the limit of proportionality. That's when it starts to curve downwards. We have the elastic limit. Beyond that, it's not going to return. to its original length, it deforms plastically, and then the top of the curve is the ultimate tensile stress.
Don't forget that things can take a different route when they unload compared to loading and the area of the graph in between is equal to the energy lost between loading and unloading. Don't forget that if forces are balanced then no matter how many forces there are they will always make a closed loop if you add them up, that is top and tail them. If something's being accelerated upwards then the force needed is not only ma but it's mg plus ma because you need the force of mg just to keep it there floating as it were and then we need the extra force ma to make it accelerate upwards. Okay moments we know that moment is equal to force times distance don't forget that our definition is force times distance perpendicular from pivot to force's line of action so we might have to times by cos theta. If there are two unknown forces in the diagram then you take moments about one or in other words make it the pivot to remove it from the equation as well.
it were and then you can find out the other. The principle of moments is that for a system to be in equilibrium the sum of the clockwise moments must equal the sum of the anti-clockwise moments and we know there has to be no resultant force for complete equilibrium. For an object to topple the center of mass must be past the pivot so that the moment of the weight does pull it the wrong way as it were.
Scalers and vectors, scalers just have magnitude like area, distance, energy and power whereas vectors have magnitude and direction. like force, acceleration, velocity, and displacement. Momentum is equal to mv, so that means the unit is kilogram meters per second, or newton seconds.
How does it link to force? Well, force is equal to delta mv, that's change in momentum divided by time. In word form, force is equal to the rate of change of momentum. This is the equation that shows that the longer a collision takes, the less the force felt. And that's how crumple zones and airbags work, they increase the collision time, In other words, increase the time that it takes for you to lose your momentum so you feel less force.
If you have a force-time graph there's really only one thing you can do with it and that is find the area under the graph that gives you the impulse, that's the change in momentum. Principle of conservation of momentum is total momentum is conserved, absent that means so long as there are no external forces. A couple of examples, if we have two objects colliding then we know that the momentum of A plus the momentum of B must equal.
the momentum of both of them if they couple together. Then if we have a recoil situation, like a bullet being fired from a gun, then we know that there's no momentum before and no momentum afterwards, so that must mean that the momentum of the gun going backwards must be equal to the momentum of the bullet going forwards. Okay, technically we should stick a minus in front of one of them because one of them's gonna have a negative velocity, but when it comes to recoil, we don't care about that too much. Let's think about braking distance. Braking distance.
quadruples if you double your speed because kinetic energy is half mv squared so if you double your v then you have four times the kinetic energy. Other things that can affect braking distance are the road condition, weather and tyre condition. What about thinking distance?
Speed again drugs distractions and tiredness. And we have a couple there's two equal forces that means that there's no acceleration but it does turn or start to turn. If you have something that's traveling at a constant velocity but mass is being churned out as it were like a fluid like water in a hose then we rejig the rate of change in momentum equation so that we have F equals delta m over t times v and so that's kilograms per second times meters per second units are really helpful for these kind of questions but if you have density area and speed then the force is going to be equal to rho a v squared note that you might see that called momentum carried per second but that's effectively force and if we have a force or any vector Then we can find the components of the resultant vector by times in by cos theta or sine theta.
Turn through the angle times by cos, turn away from the angle times by sine. And we have two types of collision. We have elastic collisions and inelastic collisions. For elastic collisions total kinetic energy is conserved and it's not in inelastic collisions.
But don't forget that total energy is conserved in both. Total energy is always conserved. So let's first look at the types of particles that we have, that is things that make up matter. We split particles into two main groups, hadrons and leptons. Leptons are fundamental particles, examples are electron, positron and neutrinos.
However we can split hadrons in two again, into baryons and mesons. Baryons and mesons are made of quarks, and quarks are fundamental particles, as far as we know. Baryons have three quarks, and mesons have two quarks, always a quark and an antiquark. and the quarks are held together by the strong nuclear force. Examples are the neutron and proton, and the main meson we deal with is the pion, but there are others.
Conservation rules, we know that baryons have a baryon number and leptons have a lepton number. So let's talk about the four forces that we're concerned with in physics, specifically in the area of quantum electrodynamics. Electromagnetic force, the gauge boson, or the exchange particle for that is the virtual photon. Strong nuclear force, the gauge boson is the pion, sometimes you'll see the gluon. Weak is W plus or W minus, we don't really deal with Z zero.
And the cousin that we all ignore is gravity, because we don't really understand it as well, and even though we haven't found it, we call the exchange particle the graviton. Okay, let's talk about strong nuclear force, it keeps a nucleus together. Of course, the electrostatic repulsion of the protons in the nucleus means that the EM force is always trying to explode a nucleus. So that means that we must have another force keeping it together, and that's the strong nuclear force, and that affects neutrons and protons.
What's stopping the strong nuclear force from imploding a nucleus then? Well, What we say is when the nucleons get too close together, to 0.5 femtometers, the strong nuclear force flips from being attractive to repulsive. And the range of attraction for the strong nuclear force is about three to four femtometers.
Okay, so we know that mass and energy are interchangeable. The equation that links the two is the equation for rest energy of a particle, and that's E equals MC squared. Mass is converted into energy in annihilation.
That's when a particle and its corresponding antiparticle collide and they're destroyed and the rest energy is converted into photons. So we can say that E equals mc squared plus half mv squared. That's the kinetic energy of the particles going in. And we have two lots of HF coming out. The opposite is pair production.
That's when a photon turns into two particles. Again, a particle and its corresponding antiparticle. Of course, the photon must have at least the same amount of energy as the rest energy of the particles. So again, E equals mc squared.
But if the photon has more than the minimum amount of energy, then the leftover energy is turned into kinetic energy of the particles afterwards. Okay, let's talk about ionising radiation. Alpha, beta, gamma. Call them ionising radiation because all of these can give electrons enough energy to escape an atom or molecule, therefore ionising them. An alpha particle is a helium nucleus, two protons and two neutrons.
It's highly ionising, mostly because it's very heavy, but it's weakly penetrating. It's stopped by a piece of paper or a few centimetres of air. Beta particle is a fast moving electron.
Don't worry, I'll fix my mistake in a second. Then it has medium ionizing and penetrating ability, stopped by a few millimeters of aluminum. Gamma is just a high energy EM ray or photon, and that's emitted from an energetic nucleus. Photons don't have charge, so they can't change the nucleus in any way when they're emitted. It's weakly ionizing, but it's highly penetrative.
It can't be stopped really, but the intensity can be reduced by concrete and lead. Okay, here are the decay equations for alpha and beta. We know that alpha is four and two, beta is zero and minus one, because it's got the opposite charge to a proton, and so therefore it's just mass then, isn't it?
Don't forget that for beta decay, we must have an anti-electron neutrino produced as well to make sure that lepton number is conserved. Here's a Feynman diagram for beta minus decay. We have a neutron turning into a proton, and the W minus boson takes the negative charge away, as it were, to produce an electron and an anti-electron neutrino.
A neutron is up, down, down. Proton is up, up, down. So therefore we can say that actually it's a down quark turning into an up quark.
You can see either one on a Feynman diagram for this. Okay, conservation rules, what has to be conserved? Charge, lepton number, and baryon number, Q, L, and P. They're always conserved.
Strangeness, however, is only conserved in strong interactions. Incidentally, any interaction that involves leptons has to be a weak interaction. It's good to be reminded about what a muon is. It's effectively a heavy electron. And a reminder that lepton number wise, electrons and neutrinos have a lepton number of plus one because the electron is the OG lepton, as it were.
Positron has a lepton number of minus one. Okay, let's go back a little bit. Isotopes, what are they? Well, they're the same element, that means the same number of protons, or same atomic number, but with a different number of neutrons, so that means they have a different relative atomic mass, like carbon-12 and carbon-14 here.
Specific charge is the charge to mass ratio, so we calculate it by doing charge to volume by mass. So the unit is coulombs per kilogram, generally a very big number, because the masses of these particles are tiny. Worth remembering that one electron volt is the same number as the charge of electron, because one electron volt is the energy in joules that an electron has when accelerated through a PD of one volt. So that means that one electron volt is 1.6 times 10 to the minus 19 joules. Quite often we deal with mega electron volts and so if we have to convert that into joules it's 1.6 times 10 to the minus 13. Yes you can figure that out but it's useful as a shortcut.
Okay so let's go on to some quantum then. What is the photoelectric effect? It's when photons of sufficient energy are absorbed by electrons on the surface of a metal therefore liberating them. They escape. The equation is E k max is equal to h f minus phi.
H f being the energy of the photon that goes in. Phi being the work function that's the minimum energy needed to liberate electrons and so taking one away from the other gives you the kinetic energy left when an electron has escaped. Here's the graph the y-intercept is minus phi. The x-intercept is the threshold frequency that's the minimum frequency needed for electrons to be liberated.
If the frequency is less than that, you won't see any electrons liberated. And in that case, EKmax is equal to zero, so HF0 equals phi. Okay, so what did the photoelectric effect prove? Well, it proved that light has a particle nature, not just wave nature, due to the one-to-one interactions between photons and electrons.
And it's one-to-one because if it were only a wave, then increasing the intensity of light would have increased the EK of the electrons. liberated but it doesn't. All it does is increase the number of electrons that are emitted per second because there are more photons. Okay so here's a circuit that we can use to measure the kinetic energy of these electrons. We have a variable PD applied across these two plates.
We shine light on one of them specifically the anode and that will make electrons cross the gap and then they will flow around the circuit producing a current. What we do is increase the PD in the opposite direction as it were until the current goes to zero. That means that the electrons are no longer crossing the gap, so we know that their kinetic energy has been counteracted, as it were, by the energy supplied by the battery.
We call this PD the stopping potential, and we know that any voltage is energy divided by charge, and it's the same here. So we can say that EKmax is equal to E, charge of an electron, times the stopping potential for VS. A de Broglie wavelength is the wavelength that a particle can have. And the wave nature of particles was proven with electrons being fired at a graphite film and we see circular fringes on a phosphorescent screen behind. And that's because the electrons are diffracting around the carbon atoms and producing maxima and minima on the screen just like light.
Here's the pattern for it. Note that the intensity doesn't really go to zero. De Broglie wavelength is equal to Plex constant over momentum or or H over P or H over MV. Quite often we'll be given the energy of electrons but we'll have to find out the momentum in order to put it into the equation. So we find that by doing E equals half MV squared times the whole thing by M and that gives you ME equals half P squared.
Rearranging we get momentum P equals root two M times the energy. Okay, fluorescent tube. What we have is a tube with a cathode on one end and an anode on the other end. The cathode is heated with a current Electrons are emitted by thermionic emission. They're attracted to the anode on the other side, and they bash into low-pressure mercury gas atoms on the way, raising their electrons to higher energy levels.
We'll talk about energy levels in a bit. As these electrons de-excite, they emit UV photons, not visible light. And then these UV photons are absorbed by the electrons in the coating.
And then when these de-excite, they emit visible light. And then finally energy levels running out of space here so I apologize for the crampness of this bit electrons can be promoted or excited to higher energy levels through two ways either they can absorb a photon of energy exactly equal to the difference in energy levels or a free electron can come along and collide with it and impart some of its energy to the electron making it go up to a higher energy level. We have the ionization level if enough energy is given to an electron then it will escape an atom or molecule completely.
We have absorption and emission spectra. Emission spectrum we can get from the sun because light is just being emitted from it or any other light. Absorption spectrum is when we have a gas and shine all wavelengths through it and see what's transmitted, what's absorbed, and then we can tell what kind of elements are present. So let's draw the simplest circuit that we can. We have a battery or a cell or power supply.
Don't get your knickers in a twist if somebody uses battery instead of cell. Okay, so what does one of these do? Well, it provides an EMF.
That's short for electromotive force. It's more of an A-level term. At GCSE, all you need to know is that a battery gives electrons or charge energy. And the battery says that it's six volts, so that means that it's giving six joules of energy to every coulomb of electrons or charge that passes through it.
And don't forget we deal with coulombs instead of individual electrons of charge because, well, coulombs are much easier numbers to deal with, much like moles. We have a resistor and we have an ammeter that's in series with the rest of the circuit. We put it in series because it measures rate of flow of charge. The symbol for current is i and unit is amps a. So any rate is something divided by time and so current is charge divided by time or Q over T.
Some people prefer Q equals IT. But if you remember that it's the rate of flow of charge, then you know it's going to be that divided by T. So we know that the battery is supplying six volts, six joules of energy to each coulomb of electrons.
But where is that energy going? Well it's going to the resistor and the resistor converts electrical energy into thermal energy. No I can't be bothered to think in terms of energy stores and pathways because that's just confusing. Symbol is R and the unit is omega for ohms. Voltmeters always go across a component that is in parallel to it because it measures potential difference, also known as voltage.
We know the volts. The potential before the resistor is plus 6 volts, the potential afterwards is 0 volts, so therefore the PD must be 6 volts. That's what the voltmeter should say.
And we know the PD has to be 6 volts because all of that 6 volts from the battery has to be 0 volts. to be used up in the circuit somewhere. And there's nothing else in the circuit apart from the resistor using it. So the equations for PD, voltage or potential in general, V is equal to energy divided by charge, joules per coulomb if you will. And of course, Ohm's law, you'll be using that far more.
V equals IR. All of electricity boils down to that equation, really. Okay, so let's have a look at IV characteristics.
We know for a resistor, it's gonna be a straight line, positive and negative. And that's because it's ohmic, means it has a constant resistance. If we change the PD, double the PD, the current through it doubles too. For a filament like a lamp, that's a piece of metal, we have this curve at the ends. That's because it's non-ohmic, it doesn't have a constant resistance and you need to know word for word why this is the case.
So when current is increased the frequency of collisions of electrons with the ions in the metallic lattice in the filament increases. They bat into the ions more. This makes the ions vibrate more. They're always vibrating, but we say they're now vibrating more.
This then, as it were, blocks the electrons even more, so it increases the frequency of the collisions even more, therefore increasing the resistance of the filament. That's why it curves at the end. The current can't get through as well. Okay, we have an LDR, light-dependent resistor, and we have a thermistor, or NTC thermistor, which stands for negative temperature coefficient.
That just means that the hotter it gets, the lower the resistance. And it's the case for an LDR but in terms of light. We can draw straight lines for both of these.
We have a higher resistance when it's dark for the LDR or cold for the thermistor and we get a lower resistance when it's light for the LDR and hotter for the thermistor. Notice that we've got straight lines for both but a different straight line depending on the conditions. So we can say they are ohmic provided that the temperature or the light intensity stays the same for the respective component. So why do we get a lower resistance?
Well it's because the energy that goes in shakes electrons loose as it were, so that means that there are more electrons available to conduct. Proper explanation, it's going to be technical, it's because the electrons are moved into the conduction band. And if you need a nice easy way to remember it both these things do the opposite to a piece of metal as it were.
So we have a diode and we know that diodes only let current through in one direction so this is what the graph looks like the resistance breaks down in the positive direction at about 0.5 to 1 volt something like that but the proper explanation is that it has a very high resistance in one direction and a very low resistance in the other okay so let's move on to looking at circuits here we have a simple series circuit one loop with two resistors in and a battery and because they're in one loop we know the total voltage is going to be shared between the two but they're going to have the same current If they're in parallel, well they have branches, they're going to have the same PD and that's the same as the battery but the current is going to be shared between them. Two resistors in series can also be called a potential divider. Here's how you might see a diagram of this.
We don't have a full circuit but the power supply is implied with that plus 12 volts at the top. We have the two resistors. I'm going to make one of them a thermistor.
The thermistor has a resistance of 20 ohms and the fixed resistor has 10 ohms. So that means the 12 volts is going to be split between them as 8 volts and 4 volts respectively. That's because the bigger resistor will have the bigger share of the total voltage available.
And that's because the ratio of the resistances is equal to the ratio of the voltages. And that goes for the individual resistors, but that also goes for one of the resistors and the total resistors as well. So we can say V1 over V2 equals R1 over R2 or V1 over V total.
equals R1 over R total. Excuse my mistakes, don't worry. It's gonna be fixed for the mind map.
And something I'll add to the PDF as well. These kind of circuits are used for sensing. When it gets colder, the resistance of the thermistor goes up, so that means that its share of the voltage also goes up, so you'd want your heater wired up in parallel with that. Okay, in reality, it's probably just gonna be a sensor that's attached to it, so the increase in voltage is detected, and then that will switch on a heater instead. And you can use an LDR in a similar situation.
to make a circuit that detects when it gets dark and so it turns on a street lamp for example. This is a bit that a lot of people hate internal resistance this is just for A-level batteries aren't perfect conductors far from it they have a resistance of their own so we can model a battery as a perfect battery with a little resistor inside little r so this is the circuit the volt meter it doesn't matter where it goes it can go across the battery or across the whole circuit or across just the load resistance. it's the same thing it's going to give you the same value every time.
Terminal PD is the voltage available to the circuit or the load resistance after some of the voltage or energy has been lost in the battery due to the internal resistance. So just remember it is not the emf of the battery unless there's no circuit in that case it is. So here's our graph what we do is that we increase current by decreasing the load resistance and we see that the terminal PD goes down.
I seem to have forgotten to write that on the Y axis. But the Y intercept is the EMF of the battery and the gradient gives you the magnitude of the internal resistance. Here's the equation, epsilon equals I big R plus I little r. All this equation is really is voltage equals voltage plus voltage, but specifically epsilon is the EMF, that's the total voltage supplied by the battery. I big R is the terminal PD. and I little r is the voltage lost inside the battery.
And we can change it as well. We can say epsilon equals V plus IR, and we can factorize it as well to give epsilon equals I times R plus R. Okay, very quickly, power, electrical power is equal to IV. And if you replace V with IR from Ohm's law, we end up with P equals I squared R. Do the same with current, and we get P equals V squared over R.
Resistivity, the symbol is rho. It's a constant that is just dependent on the type of material. The technical definition is it's the resistance of a cube of unit length sides. So that means a one meter times one meter times one meter cube.
It's not a one meter cube volume. It has to be a cube specifically. That's because of the way it's calculated.
It's not ohms per meter, it's ohm meters. So the equation is R equals rho L over A. Here's a circuit that we can use to...
get the resistance for a varying length of wire. This goes for GCSE as well. And we can see that we have that flying lead on the wire and that's changing the length. The PD is just across the whole circuit. Hopefully we'll get the same or similar PD.
A is the cross-sectional area. Like we said, the unit is ohm meters. Here's our graph if we do that experiment. Resistance on y-axis, L on the x-axis. The gradient gives you R over L.
Rearranging the resistivity equation gives us rho equals RA over L. So that means that resistivity is equal to the gradient of this graph times A, the cross-sectional area. Because if we double the diameter of the wire, then the area goes up by a factor of 4. So that means that the resistance goes down by a factor of 4. And that's because the area being greater, there's more electrons able to flow. A thinner wire has a greater resistance. Kirchhoff or Kirchhoff's laws.
First law is that charge is conserved at a junction. So that means that whatever current goes in. into a junction it must equal the total current coming out of a junction as well e.g.
I1 equals I2 plus I3 if we draw a little junction like this. Second law is that the sum of EMFs must equal the sum of PD drops in any closed loop in a circuit and that links into what we were talking about right at the start the fact that that six volts from the battery has to get used up by the whole of the circuit so we have a six volt EMF and a six volt PD drop. Don't forget that EMFs can be minus as well if we have three batteries like this, all three volts, but one of them is facing in the wrong direction then two of them cancel each other out as it were so therefore the total EMF of this setup is only three volts.
And one thing that I probably should have put in earlier, if we want to find the resistance of resistors in parallel we do one over R total equals one over R1 plus one over R2 and then we can do that as many times for as many resistors that we have in parallel. And don't forget that if they are the same resistance, then the shortcut is that the total resistance is half one of them. So I hope that's helpful. If it is, then please leave a like. If you wanna test your knowledge on this, then click on the card and it'll take you to my flashcard questions.
See you there.