4.2.3: I-V characteristics

I-V characteristics show the relationship between the electric current in a component and the potential difference across it. This information is commonly collected using a potentiometer/variable resistor. One main point to look at is whether the component behaves the same way if the current is reversed (goes through it in the opposite direction). We need to know the shape of I-V graphs for a few components...

Resistors

• Fixed resistors are designed to keep constant resistance regardless of temperature fluctuations
• The potential difference across a resistance is proportional to current so the resistor can be said to obey Ohm's law.
• This means it is an ohmic conductor (just a conductor that obeys Ohm's law)
• The resistors behave in the same way regardless of polarity
• The shallower the gradient the greater the resistance

Filament lamps

• The potential difference across a filament lamp is not proportional to the current through the resistor so a filament lamp does not obey Ohm's law (it is a non-ohmic conductor)
• The resistance of a filament lamp is not constant, it increases as the p.d. increases (remember: shallower gradient = greater resistance). The increase in resistance is caused by the wire getting hot as it glows (this point here).
• The filament lamp behaves the same way regardless of polarity

Light emitting diodes

• Diodes only allow current in one direction - its behaviour depends on the polarity. With a negative p.d there is no current - resistance is infinite and the diode will not conduct. As p.d. increases resistance gradually starts to drop. This is known as the threshold p.d.. Above threshold p.d., an increase in p.d. leads to a larger decrease in resistance and the diode begins to have very little resistance. The value for threshold p.d. varies depending on the colour (wavelength) of light they emit.
• The potential difference across a diode is not directly proportional to the current through it therefore it does not obey Ohm's law (it is a non-ohmic component)
• Resistance is not constant (seen by a fluctuating gradient)

Thermistor

Thermistors are temperature sensing components with a negative temperature coefficient. This means that their resistance DROPS when temperature increases (this is the opposite of a metal wire). This effect can be explained in terms of number density. In certain semiconductors (the ones with negative temperature coefficients) the number density of the charge carriers increases as the temperature increases. Often the resistance drop is large meaning a small change in temperature can be detected by monitoring the resistance of the thermistor. Thermistors are used in thermostats (controlling heating/air-conditioning units), to measure the temperature of engines and electrical devices to ensure they do not overheat, and in simple thermometers.

Like LEDs and filament lamps, thermometers are non-ohmic. With a thermistor, as the current increases temperature also increases (like a filament lamp) but this leads to a DROP in resistance because the number density of the charge carriers increases. The graph is pretty similar to a filament lamp (don't get them confused!) but the gradient increases for a thermistor (= decreased resistance) and the gradient decreases for a filament lamp (= increased resistance)...

We need to know how to investigate the relationship between resistance and temperature. This can be done using an ohmmeter and a water bath, or also an ammeter and voltmeter at different temperatures then use V=IR to calculate resistance. Results for this experiment will vary slightly with different thermistors. This can ensure that the best thermistor is selected for the right application.

LDR

Light dependant resistors are little electrical components which change their resistance depending on the light intensity. Some uses are in sports/street lamps/brightness metres in phones and laptops. An LDR is made from a semiconductor in which the number density of charge carriers changes depending on the incident light intensity. Dark conditions = low number density = high resistance, light conditions = high number density = low resistance.

We need to know about the relationship between the resistance and light intensity or an LDR and how to experiment it...

Image credit: Kerboodle OCR A Physics textbook p160

Vary the distance from the LDR to the constant light source (the lamp). This will change the intensity of light recieved by the LDR. Putting a small black cardboard tube around the LRD will redice background light interfering. The results will give a calibration curve that you can use to read unknown readings off...

Image credit: Kerboodle OCR A Physics textbook p160

Image sources: Kerboodle OCR A Physics textbook p.149-159

4.2.3: Resistance

All components in a circuit have their own resistance. Resistance is the ratio between the pd across a component and the current in a component. The unit of resistance is the ohm. The ohm is the resistance of a component when a pd of 1 V is produced per ampere of current. In other words, 1 Ω is 1VA⁻¹.

Resistance can be calculated using the equation V=IR.

Ohms law states that or a metallic conductor kept at constant temperature, the current in the wire is directly proportional to the p.d. across its ends.

It is important to remember that temperature affects resistance (which is why Ohms law states at a constant temperature). In the example graph below, the p.d of the wire remains constant (1.5V) but the current deceases with time. This is because resistance increases with time (by looking at V=IR we can see that if V is constant then I is inversely proportional to R). Over time, the temperature of the wire increases and as the wire gets hotter its resistance increases. This is because the positive ions inside the wire have more internal energy therefore they vibrate with greater amplitude about their mean positions. The frequency of collisions between charge carriers and positive ions increases and this means that charge carriers do more work (transfer more energy as they travel throughout the wire).

Photo credit: kerboodle OCR A physics textbook p.147

As well as temperature, the material of the wire, the length of the wire, and the cross-sectional area of the wire all affect resistance.

4.2.2: E.m.f and p.d (electromotive force and potential difference)

Okay so EMF and PD can get a little confusing as they’re very similar so i’ll try my best here:

Basically;

Potential difference is defined as the energy transferred from electrical energy to other forms per unit charge. The term is used when charged particles lose energy in a component (when work is being done by the electrons/charge carriers). It is measured in volts. One volt is the potential difference across a component when 1 joule of energy is transferred per unit charge: 1V = 1JC^-1. To determine p.d., use the equation: W=VQ. You can measure p.d. using a voltmeter. They are placed in a parallel formation in a circuit and should have a very very high resistance so no current passes through it when it is placed in the circuit.

Electromotive force is defined as the energy transferred from chemical energy (or another form) into electrical energy per unit charge. The term is used when charged particles gain energy (when work is being done on the electrons/charge carriers). It also is measured in volts. You also use a voltmeter to measure it. You also use W=VQ to measure it (but in this instance, it is W=EQ, where E is emf). See what I mean….they’re pretty similar:/

Nonetheless we can learn it ahaha. The energy transferred to or from the charges can be calculated using W=VQ=EQ. The amount of energy transferred depends on the size of the charge passing through the component and also the size of the p.d or emf.

Okay so there’s this bit about eV=0.5mv^2 in the spec that best fits in here if I explain the electron gun, so that’s what i’ll do…

Basically in an electron gun (a device that produces a narrow beam of electrons) a metal filament is heated by an electric current and the electrons gain kinetic energy (well, first they gain thermal energy then it turns into kinetic energy). Some gain enough kinetic energy to escape from the metal (thermionic emission). The anode has a small hole in it. The escaped electrons accelerate towards the anode (gaining more kinetic energy as they do). The electrons in line with the hole pass through, creating a beam of electrons with a specific kinetic energy.

The work done on an electron travelling in this beam (p.d.) is equal to e x V (eV, but do not get this mixed up with electron volts! that is a different thing, in this instance eV means elementary charge x the accelerating p.d.). The work done on the electron equates to its gain in kinetic energy. Therefore...

...provided the electrons have negligible kinetic energy at the cathode.

This means that the greater the p.d (eV), the greater the kinetic energy of the electrons.

4.2.1: Circuit symbols

tbh, just learn these...

Image source: https://en.wikibooks.org/wiki/A-level_Physics/Electrons,_Waves_and_Photons/D.C._circuits

4.1.2: Mean drift velocity

Number density is the number of free charge carriers per unit volume. The higher the number density the better the electrical conductor. This is because the material has more free charge carriers per unit volume. 

Materials can be classified into insulators, semiconductors, and conductors depending on their number density.

Conductors have a number density of about 10^28 m^-3

Semiconductors have a number density of about 10^17 m^-3

Insulators have a number density of below around 10^17 m^-3

Semiconductors can carry the same current than conductors but the electrons need to move much faster. Computer semiconductors are made of silicon because electrons moving faster means the temperature increases

Mean drift velocity:

Mean drift velocity is the average velocity of electrons/charged particles in a  wire/medium. It can be calculated using the equation I = Anev

I = current

A = cross-sectional area

n = number density

e =elementary charge (1.6x10^-19 C)

v = mean drift velocity

From the above equation we can see that increasing the cross sectional area decreases the mean drift velocity. They are inversely proportional.

4.1.1: Kirchoff's first law

Charge must always be conserved. It cannot be created or destroyed and the amount of charge after an interaction must always equal the amount of charge before an interaction.

Kirchoff’s first law states that for any point in an electrical circuit the sum of currents into hat point always equals the sum of currents out of that point. 

Charge is the product of current and time. This law means that charge cannot be created or destroyed therefore the amount of charge carriers entering a point always equates to the amount of charge carriers leaving that point.

4.1.1: Charge and current

Electric current is the rate of flow of charge. It is measured in amperes (amps) and is the amount of charge passing through a given point per unit of time (e.g one coulomb (unit of charge) is 1 amp second (As)).

You can use the equation Q = It for questions involving charge, current, and time.

To measure electric current we use an ammeter. They are placed in series so must have a very low resistance as a high resistance will greatly affect the value of current measured.

Electric charge is a physical property, a measure of how charged something (e. a particle) is - a charge carrier is simply a particle that has electric charge. They can be electrons (usually in metals) or ions (usually in electrolytes), for example. Charge can either be positive or negative, opposite charges attract (negative and positive) and the same charges repel each other (e.g positive and positive, or negative and negative). A charge of -1, or +3 that you may see on the periodic table, for example, is known as a relative charge. It means that element has a charge of -1e or +3e. e is a constant charge (it is the elementary charge, 1.6x10^-19C).

As mentioned above, charge is measured in coulombs.

A coulomb is the amount of electrical charge flowing past a point in one second when there is a current of one amp.

Electrons are negatively charged. It therefore follows that if an object gains electrons, it becomes more negatively charged and if an object loses electrons it becomes more positively charged (as removing negative charge is like misusing a minus, you plus it). You can determine the net charge on an object using the equation Q=ne (n= number of electrons). From this equation we can see that charge is quantised as it can only take values of e (the elementary charge). You cannot get an object with a charge of 0.5e as that would result in it having gained/lost 0.5 electrons and this is not possible as electrons are fundamental particles.

So, how do charged particles move through the medium they are in?

Well, in metals most electrons remain fixed to their atoms. However, there are a number of free/delocalised electrons. The positive ions do not move but the free electrons are free to move around the metal. When a negative charge is applied at one end/positive charge at the other, these free electrons will flow from the more negative pole to the more positive pole. This is because the are negatively charged and so repel the negative end. This induces a current as it is a flow of charged particles. To increase the current we must increase the rate of flow of charge. This can be done by increasing the amount of electrons tat cross a given point per second (e.g greater cross-sectional area), or by making the same number of electrons move faster (introduce a bigger negative pole).

Just a tiny bit more in this section…

Long ago before we knew about electrons and stuff, we thought things flowed in the positive to negative direction. Well, now we know that electrons flow from negative to positive. If something is referring to conventional current/flow, it means positive to negative. If something refers to electron flow, it means negative to positive.

Also, electrolytes are just liquids that can carry an electrical current (therefore, they must have charged particles inside them somewhere). Electrolytes are either ionic solutions or molten ionic compounds. In electrolytes current is a flow of IONS (there are no free electrons in electrolytes). A good example is NaCl (tale salt, sodium chloride) as it contains the cations (positive ions) Na⁺ and anions (negatively charged ions), Cl^2-. The anions (negative ions) are attracted to the positive electrode (the anode) and the cations (positive ions) are attracted to the negative electrode (the cathode). This movement of ions is a flow of charge meaning there is a current.