#### 4.1 Charge and current

Introduces the ideas of charge and current. Understanding electric current is essential when dealing with electrical circuits. The continuity equation (I = Anev) is developed using these key id.

#### Charge

You will cover:

- electric current as rate of flow of charge; I = ΔQ/Δt t
- the coulomb as the unit of charge
- the elementary charge e equals 1.6 × 10
^{–19}C

an electron has charge –e and a proton a charge +e. - net charge on a particle or an object is quantised and a multiple of e
- current as the movement of electrons in metals and movement of ions in electrolytes
- conventional current and electron flow
- Kirchhoff’s first law; conservation of charge

#### Mean drift velocity

You will cover:

- mean drift velocity of charge carriers
- I = Anev, where n is the number density of charge carriers
- distinction between conductors, semiconductorsand insulators in terms of n

## A Level Maths Home Study Kit

(1 Reviews) £24.99#### 4.2 Energy, power and resistance

Electrical symbols, electromotive force, potential difference, resistivity and power.

Eenvironmental damage from power stations and the impetus to use energy saving devices in the home

#### Circuit symbols, emf and pd

You will cover:

- circuit diagrams using symbols
- potential difference (p.d.); the unit volt
- electromotive force (e.m.f.) of a source such as a cell or a power supply
- Epsilon ε is used as the symbol for e.m.f. to avoid confusion with E which is used for energy and electric field.
- distinction between e.m.f. and p.d. in terms of energy transfer
- energy transfer; W = VQ; W = εQ.
- energy transfer eV = ½mv
^{2}for electrons and other charged particles.

#### Resistance and resistivity

You will cover:

- resistance; R = V/I
- Ohm’s law
- I-V characteristics of resistor, filament lamp, thermistor, diode and light-emitting diode (LED)
- techniques and procedures used to investigate the electrical characteristics for a range of ohmic and non-ohmic components.
- light-dependent resistor (LDR); variation of resistance with light intensity
- resistivity of a material; the equation R = ρL/A
- techniques and procedures used to determine the resistivity of a metal
- the variation of resistivity of metals and semiconductors with temperature
- negative temperature coefficient (NTC) thermistor; variation of resistance with temperature.

#### Power

You will cover:

- the equations P = VI , P = I
^{2}R and P = V^{2}/R - energy transfer; W = V I t
- the kilowatt-hour (kW h) as a unit of energy; calculating the cost of energy

#### 4.3 Electrical Circuits

Internal resistance and potential dividers. LDRs and thermistors – how changes in light intensity and temperature respectively can be monitored using potential dividers.

#### Series and parallel circuits

- Kirchhoff’s second law; the conservation of energy
- Kirchhoff’s first and second laws applied to electrical circuits
- total resistance of two or more resistors in series; R = R1 + R2 + …
- total resistance of two or more resistors in parallel; 1/R = 1/R1 + 1/R2 + …
- analysis of circuits with components, including both series and parallel
- Analysis of circuits with more than one source of e.m.f.

#### Internal resistance

You will cover:

- source of e.m.f.; internal resistance
- terminal p.d.; ‘lost volts’
- the equations E = IR + ri and E = V + Ir
- techniques and procedures used to determine the internal resistance of a chemical cell or other source of e.m.f.

#### Potential dividers

You will cover:

- potential divider circuit with components

potentiometer as a potential divider. - potential divider circuits with variable components e.g. LDR and thermistor
- potential divider equations V
_{out}= R2 /(R1 + R2) × V_{in}

and V1/V2 = R1/R2 - techniques and procedures used to investigate potential divider circuits which may include a sensor such as a thermistor or an LDR.

## A Level Maths Home Study Kit

(1 Reviews) £24.99#### 4.4 Waves

Wave properties, electromagnetic waves, superposition and stationary waves. superposition experiments to determine wavelength of visible light using a laser and a double slit.

How the double-slit experiment demonstrated the wave-like behaviour of light

#### Wave Motion

You will cover:

- progressive waves; longitudinal and transverse waves
- displacement, amplitude, wavelength, period, phase difference, frequency and speed of a wave
- techniques and procedures used to use an oscilloscope to determine frequency
- the equation f = 1/T
- the wave equation v = f λ
- graphical representations of transverse and longitudinal waves
- reflection, refraction, polarisation and diffraction of all waves
- know that diffraction effects become significant when the wavelength is comparable to the gap width.
- techniques and procedures used to demonstrate wave effects using a ripple tank
- techniques and procedures used to observe polarising effects using microwaves and light
- intensity of a progressive wave; I = P/A

intensity ∝ (amplitude)^{2}

#### Electromagnetic waves

You will cover:

- electromagnetic waves
- orders of magnitude of wavelengths of the principal radiations from radio waves to gamma rays
- plane polarised waves; polarisation of electromagnetic waves
- know about polarising filters for light and metal grilles for microwaves in demonstrating polarisation.
- refraction of light; refractive index; n = C/v

n sin θ = constant at a boundary where θ is the angle to the normal - techniques and procedures used to investigate refraction and total internal reflection of light using ray boxes, including transparent rectangular and semi-circular blocks
- critical angle; sin C = 1/n

Total internal reflection for light

#### Superposition

You will cover:

- the principle of superposition of waves
- techniques and procedures used for superposition experiments using sound, light and microwaves
- graphical methods to illustrate the principle of superposition
- interference, coherence, path difference and phase difference
- constructive interference and destructive interference in terms of path difference and phase difference
- two-source interference with sound and microwaves
- Young double-slit experiment using visible light confirmed the wave-nature of light
- λ = ax/D for all waves where a << D
- techniques and procedures used to determine the wavelength of light using a double-slit, and a diffraction grating.

#### Stationary waves

You will cover:

- stationary (standing) waves using microwaves,stretched strings and air columns
- graphical representations of a stationary wave
- similarities and the differences between stationary and progressive waves
- nodes and antinodes
- stationary wave patterns for a stretched string and air columns in closed and open tubes
- techniques and procedures used to determine the speed of sound in air by formation of stationary waves in a resonance tube
- the idea that the separation between adjacent nodes (or antinodes) is equal to λ/2, where λ is the wavelength of the progressive wave
- fundamental mode of vibration (1st harmonic); harmonics.

#### 4.5 Quantum physics

Photons, the photoelectric effect, de Broglie waves and wave-particle duality.

In the photoelectric effect experiment, electromagnetic waves are used to eject surface electrons from metals.

The electrons are ejected instantaneously and their energy is independent of the intensity of the radiation.

The wave model is unable to explain the interaction of these waves with matter. This single experiment led to the development of the photon model and was the cornerstone of quantum physics.

#### Photons

You will cover:

- the particulate nature (photon model) of electromagnetic radiation
- photon as a quantum of energy of electromagnetic radiation
- energy of a photon; E = hf and E hc/ λ
- the electronvolt (eV) as a unit of energy
- using LEDs and the equation eV – hc/λ to estimate the value of Planck constant h

No knowledge of semiconductor theory is required.

#### The photoelectric effect

You will cover:

- photoelectric effect, including a simple experiment to demonstrate this effect
- photoelectric effect provides evidence for particulate nature of electromagnetic radiation.
- demonstration of the photoelectric effect using, e.g. gold-leaf electroscope and zinc plate
- a one-to-one interaction between a photon and a surface electron
- Einstein’s photoelectric equation hf = Φ + KE
_{max}work function; threshold frequency - the idea that the maximum kinetic energy of the photoelectrons is independent of the intensity of the incident radiation
- the idea that rate of emission of photoelectrons above the threshold frequency is directly proportional to the intensity of the incident radiation.

#### Wave-particle duality

You will cover:

- electron diffraction provides evidence for wave-like behaviour of particles.
- diffraction of electrons travelling through a thin slice of polycrystalline graphite by the atoms of graphite and the spacing between the atoms
- the de Broglie equation λ = h/p

## A Level Maths Home Study Kit

(1 Reviews) £24.99- All of the major A Level Maths topics covered
- Practice questions and answers on every topic

- Revision for the NEW A Level Maths Course
- All exam boards e.g. AQA, OCR, Edexcel, WJEC.