Electricity is a flow of charge or charges like electrons. They carry energy from a source of energy to a component. By the way, you're going to see me mix up cells and batteries in this video because they're just the same thing really and they do the same job. Leave an angry comment below if you're really that mad about it. The battery has a store of chemical potential energy.
When connected in a complete circuit, this energy is transferred to the electrons, which moves through the wires. This movement of charge is called a current. And we say it always goes from the positive terminal of the battery to the negative.
Don't think about it too much. As the electrons pass through the bulb, their energy is converted into light. But the electrons don't just disappear once they transfer all the energy to the bulb.
As this is one big loop, these electrons are pushed back round to the battery by the ones behind them, where they're refilled with energy ready for another trip around the circuit. This constant flow of electrons transferring energy is what keeps the light bulb on. Because electrons are so small and there are so darn many of them, we don't deal with individual electrons, but instead deal in coulombs of electrons or coulombs of charge. Potential difference, PD for short, also known as voltage, tells us how much energy is transferred per coulomb of electrons. So if a cell or battery says it's one volt, that means that one joule of energy is given to every coulomb of electrons that pass through it.
If a battery is six volts, that means six joules is supplied per coulomb instead. We measure PD with a voltmeter. They're always connected in parallel to the components you want to measure the voltage of. In the real world, that means the leads or cables from the voltmeter always piggyback into other leads.
If we put the voltmeter across the battery, it should measure six volts, right? Because six volts is supplied to the electrons in the circuit, and that's just six joules per coulomb. But put it across the bulb and it should still say six volts.
Why? Because the electrons have to lose all of that six volts worth of energy as they pass through. Here's the equation for PD. PD in volts is equal to energy in joules divided by charge in coulombs.
In simple form, V is equal to E over or divided by Q. Q is the symbol for charge, but it's measured in C in coulombs. You'll see the rearranged version E equals QV on your formula sheet.
Current, on the other hand, tells us what the rate of flow of charge is. Like any equation, for a rate, as per usual, it's something divided by time. So here, it's current in amps, equals charge in coulombs divided by time in seconds, or I equals Q divided by T. Yes, we use capital I as the symbol for current, not C. Blame the French for that, as they called current intensité de courant.
It does mean, though, that we don't get confused between current and coulombs, so we stick with it. You're going to see the rearranged version of this equation on your formula sheet. Q equals IT.
That's I times T. We measure current with an ammeter. Note that it's not ampmeter.
Unlike a voltmeter, it must go in series, that means in line with the component we want to measure the current for. Components in a circuit have resistance, that is, they resist the flow of charge or current through them. But that's not a bad thing, this has to happen in order for them to work. A bulb has resistance, which causes energy to be transferred and light to be emitted. A resistor of course has resistance too, but it just produces heat when current flows through it.
If we make a circuit with a resistor and change the PD available to it, we can get a very good result. What we find is that an increasing PD results in a greater current flowing. In fact, doubling one doubles the other, so we can say that PD and current, or V and I, are directly proportional. Drawing a graph of these two makes a straight line, and if we turn the battery round, we can get negative values for both too, but still a straight line through the origin. This straight line, a constant gradient, shows that a resistor has constant resistance.
We say it's ohmic. The steeper the gradient of this line, the lower the resistance of the resistor, as more current is flowing per volt. The equation for resistance is Ohm's law, V equals IR.
We can get the resistance of a component from an IV graph like this by just picking a point on the line and rearranging Ohm's law, so R is equal to V over I. For a resistor, you'll end up with the same answer no matter what point you pick. If you repeat the same experiment for a bulb in place of the resistor, however, you'll end up with a curved graph like this. This shows that the resistance is changing, the resistance of the metal filament in the bulb. In fact, you'll find that any metal has a changing resistance if you increase the PD and current.
They're non-ohmic. At higher PDs, the current increases less and less, so that means they can't be proportional. This shows that the resistance of the metal is increasing with a higher PD and higher current. The change in gradient shows us that this is true, but we still just take a point on the line and use Ohm's law if we want to find the resistance.
It's just that it does matter where you pick that point in this case. So why does resistance change for a metal? Well, it's because metals consist of a lattice or grid of ions surrounded by a C.
of delocalised electrons. That just means they're free and free to move, or rather they're fairly free to move because they do collide with the ions as they flow. That's why the metal heats up when you pass a current through it.
The higher the current, the more frequent these collisions are, and this makes the ions vibrate more and more, which in turn makes it harder for the electrons to flow. The resistance has increased. Now there is another component called a diode.
It will give you this graph. The circus symbol might give you a clue as to why this is. A diode only lets current flow through in one direction. We say that in one direction the resistance is very high and it's very low in the other, which is why the current increases suddenly at around one volt.
An LED is a light emitting diode, similar symbol just with a couple of extra bits. These are what most lights in electronics are these days rather than filament lamps. They act in the same way as a diode so they give you the same graph but they just happen to emit light as well.
A superconductor is a material that has a resistance of zero, not nearly zero, zero. Generally, these materials need to be cooled before they reach that point. So you might see a graph like this, the temperature is going down, so the resistance goes down until, boom, we hit what we call the critical temperature.
At the critical temperature and below, resistance falls to zero. Every material has a different resistivity, or resistivity some people say. The definition is this, it's the resistance of a... cube of unit length sides of that material.
So in SI units that's the resistance in ohms of a one meter cube. Note that that is not resistance per meter cubed. The definition must involve an actual cube. The unit we use is ohm meters. Again be careful that's not ohms per meter.
To find resistivity we measure the diameter of a wire with a micrometer and calculate area from that using pi d squared over four. We then measure V and I to calculate R for varying lengths L of the wire measured with a metre rule. Plotting R against L gives a proportional relationship. The equation for resistivity therefore is this, R equals rho L over A, where rho is resistivity in ohm metres. Rearranging this, we have rho equals RA over L.
The gradient of the graph is R over L, so multiplying by the area gives us the resistivity. Series and parallel circuits. This is where things get a bit tricky.
Remembering what happens to current PD and resistance when we have components in series or in parallel. Here's the simplest series circuit we can make really, just two resistors in line with the battery. What you need to remember is that for components in series, total PD is shared between them, current is the same for all of them, and the total resistance is just the sum of all resistances.
That just means add it up. Let's deal with that first point. If these resistors are the same, let's say 10 ohms each.
then that 6V total PD from the battery must be shared between them. So if we put a voltmeter across each of these, they'd both read 3V. It wouldn't matter what resistance these resistors are. They could be a million ohms each. If they're the same, then that total PD is shared equally.
By the time the electrons leave the second resistor, they have to have lost all 6V worth of energy, ready to go back to the battery to be refilled. This idea is actually just Kirchhoff's second law. The sum of EMFs must...
equal the sum of PD drops in a closed loop. Just remember that if batteries are pointing in opposite directions, one of them must be a minus. By the way, we can also call this setup a potential divider circuit, as the total potential total PD is being shared. If the resistors don't have the same resistance, then we can use the second point to help us, that is the current is the same for both. Let's say the first resistor is 20 ohms, using 4 volts of the total 6 volts available, we know two things out of V, I and R.
So let's use Ohm's law to find out the third for it. Current in this case, I. Rearranging Ohm's law, we get I is equal to V over R.
So that's four divided by 20, 0.2 amps. Same for the second resistor too. Is there also a second thing we know about the other resistor?
Why, yes, there is. Remembering the first rule up here, we know that if the first resistor is using four volts of the total six volts available, well, then the other resistor must be using up two volts. We could then use Ohm's law again to find its resistance, 10 ohms. The rule of thumb is this, the greater the resistance, the greater the share of the total PD it gets.
We can also use Ohm's law for a whole circuit, we just need to make sure that we're dealing with the total PD, total current and total resistance. The rules for parallel circuits are the opposite. The PD is the same for every branch. Again, this is true because of Kirchhoff's second law, the battery is actually involved in two loops, so therefore the PD drops in both loops must be the same. Current is shared between each branch, and the more resistors you add in parallel, the lower the total resistance.
This, by the way, is because you're giving the current more roots to move through the circuit, which means more current can flow. So if these two resistors are connected to the 6V battery in parallel, you know straight away that the PD for both has to be 6V. Voltage isn't shared in parallel circuits. If, however, we say 0.5A total current is flowing through the battery, and 0.2A of that is flowing through the top resistor, that must mean that there's 0.3 amps flowing through the bottom resistor. This is actually Kirchhoff's first law.
Current, and therefore charge, must be conserved at any junction. If you're not in a rush, why not pause the video and see if you can calculate these two resistances. By the way, if you want a little bit more help on this, then have a look at my video, How to Answer Any Electricity Question. It's not only metals that can change resistance. We can have a thermistor.
and you have a circuit that responds to changes in temperature. A thermistor's resistance decreases if the temperature increases. So in essence, it does the opposite to a metal. By the way, you might see a thermistor called an NTC, negative temperature coefficient.
That just means that higher temperature, lower resistance. In this case, if the temperature increased, the resistance of the thermistor would go down, as does its share of the total PD. That means the PD measured by this voltmeter will increase.
This could be the basis of a temperature sensor for your central heating, for example. An LDR is a light-dependent resistor, very similar to a thermistor, but resistance goes down with increased light intensity, not temperature. So this circuit could be on the top of a street lamp.
Light intensity goes down, resistance of the LDR goes up, as does its share of the voltage. This could then be connected in some way to the light bulb, so it turns on as it gets dark. Power is the rate of energy transferred, so energy divided by time. However, when it comes to electricity, we can also calculate it with this equation too. P equals VI, power equals voltage, PD times current.
A battery or cell produces DC, direct current. The PD and therefore current also only point in one direction. Electronics need DC to work. However, AC, alternating current, is needed to transmit electricity over long distances, say through the national grid. This is because transformers are needed to step up the voltage, reducing the current before it enters the grid.
More on transformers in magnetic fields. The neutral wire in mains stays at a potential of 0V, while the live wire varies between plus 325V and minus 325V. So we say the peak voltage is 325V, and we might say that the peak-to-peak voltage is double that, 650. However, to do any measurements with AC, we must convert it to a DC equivalent by using root-mean-square values. To convert from peak voltage to RMS voltage, or VRMS, the conversion factor is root two. 325 divided by root two gives us 230 volts, which you know is what UK mains voltage is known to be.
It's the RMS value that we're given. And it also works going from peak current to RMS current too. To go from peak power to mean or average power, it's a little bit different.
We don't call it RMS power, by the way. It's not quite the same. As peak power equals peak voltage times peak current, we divide by V and I by root two to get both.
RMS values. Doing that twice is the same as dividing by two, so that means that the average power is half the peak power delivered. It turns out batteries or cells have a resistance of their own, so if you attach a bulb to a 6V battery, the bulb will get less than that.
A voltmeter across it might measure 5.5V say. This would also be the same if we attached a voltmeter across the battery terminals instead, so we can call this the terminal PD. Be careful, that means the voltage available to the rest of the circuit.
That means 0.5 volts is being lost inside the battery due to its internal resistance, little r. The EMF, electromotive force, epsilon is the symbol we use, is the total PD provided. That's the 6 volts here.
So the equation is this. EMF equals terminal PD, V, plus I, little r, where little r is internal resistance. So I times little r is the voltage lost due to internal resistance. If we increase the load resistance, that's the resistance of the circuit, the current flowing through the battery decreases of course.
But this results in less PD being lost in the battery, so the terminal PD increases. Drawing a graph of terminal PD against current gives us a straight line. The magnitude of this gradient is equal to the internal resistance. If we extrapolate the line back to the y-axis, the y-intercept is equal to the EMF, which makes sense as if there's no current flowing then in theory the circuit should get the whole of the EMF.
There's no volts lost in the battery. You can of course also get the EMF by just attaching a voltmeter across the battery by itself with nothing else connected. This works as voltmeters generally have very high resistance. The reason that thermistors and LDRs work is because they're made out of semiconducting material.
Such materials have electrons that are only free to move when they are provided with enough energy to first move from what we call the valence band to the conduction band, passing straight through the forbidden band. Semiconductors sit between insulators and conductors, you might have guessed, but it's a spectrum, naturally. We can tell how well a material conducts electricity by comparing their number densities.
That is, how many charge carriers, not necessarily electrons, there are per metre cubed. For conductors like metals, the number density is around 10 to the 28. Semiconductors around 10 to the 17, give or take. Moving more electrons into the conduction band changes this number, of course. Insulators have very low number densities.
Drift velocity is what we call the literal speed of an electron as it flows through the wire in metres per second. I don't see the point in knowing this, but there we go. The equation is this.
Current is equal to cross-sectional area. times the number density, times charge of an electron, times drift velocity. We can then rearrange this for v if needed. Leave a like if you found this helpful. I've also put together these into videos that cover whole papers to help you revise for your exams more effectively.
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