5.1.1 Temperature

Temperature is a pretty nice topic (which is pretty nice for a change)...

Firstly, we need to know a bit about thermal equilibrium. When two objects are in thermal equilibrium there is no net flow of thermal energy between them. This means they are they same temperature. If one object was hotter than the other, there would be a net flow of thermal energy from the hotter object to the colder one - this means they are not in thermal equilibrium. However, the temperature of the colder one would increase and the temperature of the hotter one would decrease until they are in thermal equilibrium.

The zeroth law of thermodynamics states: if two objects are in thermal equilibrium with a third, then all three are in thermal equilibrium.

In order to measure temperature a scale is needed with two fixed defined points. We often use the Celsius scale with the freezing (0°) and boiling (100°) points of water as the fixed points. However, this cannot always be used as the boiling point of water changes depending on the surrounding atmospheric pressure (e.g up a mountain water boils at a lower temperature). This means that the boiling point of water is technically not really a fixed point.

Instead, we can use the absolute/thermodynamic temperature scale and use the triple point of water and absolute zero. The SI unit of this scale is kelvin (K). Thankfully, the increments on the absolute scale and Celcius scale are the same. There are 273.16 increments between absolute zero and the triple point of water meaning we can use the following relationship to switch between the two scales:

T(K) ≈ θ(°C) + 273

NOTE: The triple point of a substance is a specific temperature and pressure at which the substance can exist in all three states of matter, solid, liquid, and gas. For water is it 0.01° and 0.61kPa.

NOTE: The symbol 'K' for Kelvin is capital, this is because Kelvin was a person.

4.4.2 Electromagnetic waves

The electromagnetic spectrum
Electromagnetic waves are able to travel in a vacuum - they do not need a medium. It is a transverse wave that can be thought of as alternating electric and magnetic fields oscillating at right angles to eachother. the electromagnetic spectrum is a spectrtum of all the types of electromagnetic wave - they are classified according to the wavelength of each wave. We need to learn the frequencies and wavelengths of each wave class. However, we know that v = f λ and v for amm electromagnetic waves is 3x10⁸ m^s. This means that if we learn just the frequencies then we can work out the wavelengths (and vice versa), meaning we only hae to learn one (frequencies or wavelegths). That being said, here are the wavelengths (commit these to memory even if s the last thing you do - it is a must!! tbh I'm just willing myself on here as I havetn learnt them yet):

• Radiowaves; 10⁶ - 10^-1
• Microwaves: 10^-1 - 10^-3
• Infrared radiation: 10^-3 - 7^-7
• Visible light: 7^-7 - 4^-7
• Red: 7^-7
• Blue: 4^-7
• Ultraviolet: 4^-7 - 10^-8
• X-rays: 10^-8 - 10^-13
• Gamma rays: 10^-10 - 10^-16

NOTE: The  wavelength range of X-rays and gamma rays overlap so these waves are classified by their origin (X-rays are emitted by fast moving electrons and gamma rays are emitted from unstable atomic nuclei).

All electromagnetic waves can be reflected, refracted, diffracted, and polarised. I have covered polarisation of electromagnetic waves (microwaves) in post 4.4.1.


The refractive index and the refraction of light
The angle at which light is bent depends on the relative speeds of light through the two materials. Each material has a refractive index which can be calculated using the following equation:

n = c / v

The law of refraction: The product of the refractive index and sinθ (sin of angle between the normal and the incident ray) is constant. In other words:

n₁sinθ₁ = n₂sinθ₂

Investigating total internal reflection
Total internal reflection occurs at the boundary between two different media provided the angle at which the light strikes the boundary is above the critical angle (depends on the refractive index) and the light is travelling through a medium with a higher refractive index as it strikes a boundary with a lower refractive index. The relationship between C (the critical angle) and n (the refractive index) is as follows:

sin C = 1/n

You can determine the refractive index and the critical angle and also investigate total internal reflection all at the same time by measuring the critical angle of a semi-circular block. By directing a ray of light towards the center of the semi-circular block and moving it until TIR occurs is a good way to accurately measure the critical angle.

Optical fibers totally internally reflect very well and such have many uses including the fast transmission of data and keyhole surgery! A simple optic fibre has a fine glass core surrounded by a glass cladding which has a lower refractive index. This ensures that light travelling in the fine glass core reflects at the cladding boundary and stays in the core.

4.3.3 Potential dividers

Potential divider circuits can vary the p.d. across an output (e.g a lamp) when connected to a fixed point. These are useful in circumstances such as having a 10V battery but only needing 6V for the task you are about to perform.

Basically, there are two resistors in a series circuit. All you have to do is connect a circuit across one of these resistors. The p.d. into this circuit (which is Vout of the potential divider circuit) can be varied from zero to maximum depending on the resistances of R1 and R2.

This  means that the p.d. across each resistor in a potential divider depends on the resistances of the individual resistors...

V1/V2 = R1/R2

We can determine Vout by the potential divider equation:

Vout = (R2/(R1+R2)) x Vin

You can also 'load' a potential divider circuit. This refers to adding an additional resistor/component to the Vout part in parallel which overall decreases the total resistance of this part which lowers Vout. A small additional resistance in parallel significantly reduces Vout.

The potentiometer
To vary Vout we can replace one of the fixed resistors with a variable resistor. A potentiometer is a type of variable resistor that has 3 terminals and a sliding contact. If you adjust the contact the p.d. between two of the terminals will vary. Potentiometers are very compact which is useful so they can be used for portable electronic devices etc.

Temperature sensing circuits
To vary Vout we can replace one of the fixed resistors with a variable resistor.

Replacing the variable resistor with a fixed resistor allows Vout to vary depending on the temperature of the surroundings (as temperature increases resistance of the thermistor decreases as thermistors have a negative temperature coefficient).

Light sensing circuits
A similar principle to temperature sensing circuits only replace the variable resistor with an LDR. As light intensity increases, resistance falls.

4.3.2 Internal resistance

It is important to understand that different power sources have different internal resistances. E.g if a large current is needed, a power supply with a small internal resistance is used. If a small current is needed, a power supply with a large internal resistance is used.

So, what is internal resistance? Basically, when there is a current in a power source work has to be done by the charges to move through the power source. The p.d. measured at the terminals of the power source (the terminal p.d.) is always less than the actual emf (provided there is a current in the circuit) - the difference is the lost volts.

From K2 we can determine this equation:

electromotive force (emf) = p.d. + lost volts

It is important to realise that changing the current will change the lost volts and consequently the terminal p.d.. An increase in the current means that more charges travel through the cell each second meaning overall more work is done by the charges. This increases the lost volts which subsequently reduces the terminal p.d.

We can apply V=IR to lost volts too (lost volts = Ir, where r is the internal resistance). This means that total emf is equal to IR + Ir...

emf = I(R+r)

We also need to be able to determine the internal resistance of a cell/source of emf:

• Create a series circuit with a variable resistor
• Introduce a voltmeter across a power supply
• Have an ammeter in the circuit (it doesn't matter where as it is a series circuit)
• Change the resistance of the circuit - this will draw different currents from the power source.
• Rearrange E= V+Ir to give V = -Ir + E
• Plot a graph of V against I
• The gradient will be -r, the y intercept will be the emf

4.3.1 series and parallel circuits

Kirchoff's Laws
Kirchoff's first law states that the sum of currents into a point always equals the sum of currents out of a point. This is conservation of charge.
Kirchoff's second law states that the sum of the emfs is equal to the sum of the pds around a closed loop. This is conservation of energy.

During GCSE you will have come across series and parallel circuits (I hope!). Here is a reminder...

A series circuit has only one path for current. From K1 we can deduce that, since charge is not used up, the rate of flow of charge is the same at all points in the circuit. Since current is the rate of flow of charge this means current is the same at all points in the circuit. From K2 we know that the emf is shared between each component as there is only one closed loop. Adding additional components in series reduces the emf that is shared between the original components. We know that V=IR and I is constant (in series circuits). The total V = V1+V2... this means that the total resistance (R)= R1+R2...

A parallel circuit has more than one possible path for current. The resistance of each path determines how much current will flow down it. The greater the resistance, the lower the current that passes down it (V=IR and V is constant). Each branch of a parallel circuit forms it's own loop. from K2 we can deduce that the pd around each individual loop is equal to the emf from the power supply. In parallel circuits, V is constant. This means that I/V=I1/V+I2/V..... I/V = 1/R. This means that 1/R = 1/R1+1/R2...

These rules can be used to create a circuit with a required resistance.


When using more than one emf source, we must look at which polarity the emfs are in. We need to think about the internal resistance when combining emf sources in series and parallel.

In series: the emf will change but resistance will be constant

In parallel: the emf will be constant but resistance will change

Image source: Kerboodle OCR A Physics textbook p183

4.2.5 Power

Electric circuits are used to transfer energy from one place to another. Whenever there is a current in a circuit energy is transferred from the power source to the component. Opening a switch/turning off the power source will result in no current as no energy is transferred.

Power is the rate of energy transfer between each electrical component. It is measured in watts and can be calculated using the equation:

P=IV

Using V=IR we can get two more equations for power...

P= I²R and P=V²/R

The derivation:

P=W/t

W=VQ

P=(VQ)/t

I=Q/t

P=IV

If we substitute P=W/t (--> W=Pt) into P=IV we get W=VIt. This is an equation for energy transferred.

Last bit in this section (yayy). We just need to know about the kilowatt hour and how to calculate the cost of energy...

The energy transferred to a device depends on how long the device is used for and the power of the device.

One joule is a very minuscule amount so instead electricity bill people use the kilowatt hour (kWh). This is the energy transferred by a device with a power of 1kW operating for a time of 1 hour. It is equal to 3.6MJ.

4.2.4 Resistivity

Four different things affect the overall resistance of a wire: the material, the length, the cross-sectional area, and the temperature. resistance is directly proportional to length and inversely proportional to cross sectional area.

Resistivity can be used to describe the electrical property of a material (resistance only describes the electrical property of a single component). E.g copper wires may have a different resistance (e.g if they are different lengths) but overall copper has a unique resistivity. We can use the above facts (that resistance is directly proportional to length and inversely proportional to cross sectional area) to make an equation with resistivity as the constant:

R = (ρL)/A

Resistivity has the symbol pho (ρ) and the unit ohm meter (Ωm). Resistivity is defined as the product of the resistance of a component made of the material and it's cross sectional area, divided by it's length. 

A bit of a mouthful if you ask me.

Like resistance, resistivity also varies with temperature.

How would we determine the resistivity of a material?...
Investigate how the resistance of a wire varies with length. Measure values of potential difference across varying lengths of wire. Use V=IR to determine R. A graph of R against L will give a gradient of ρ/A. Multiply the gradient by A and you have ρ, the resistivity.

Good conductors have a very small resistivity whilst insulators have a very large resistivity.

In this section we also need to know about NTCs and the variance of resistance with temperature of a thermistor. I have put this information in this section.