Charge and current
- Electric current is a basic quantity defined in terms of the force between two long, parallel, current-carrying conductors.
- Current is the rate of flow. Q=I/t. Current is measured using an ammeter connected in series.
- 1 coulomb is the quantity of charge which passes when a current of 1 ampere passes for a time of 1 second.
- The elementary charge is e=1.60x10^-19. This is the size of the negative charge of an electron and the positive charge of a proton.
- In a metal charge is carried by movement of free electrons; in an electrolyte, charge is carried by positive and negative ions.
- The conventional current is the direction in which positive charges would move. The electron current is in the opposite direcction.
- Conductors, semiconductors and insulators have different numbers (n) of charge carriers per unit volume.
- In a metal wire of cross-sectional area (A) with electrons moving with drift velocity (V), the current is I=nAve.
Potential difference and e.m.f.
- The potential difference between two points is defined as the work done in moving unit charge between those points. V=W/Q.
- The p.d. or voltage across a component is measured using a voltmeter (of very high resistance) connected across it, i.e. in parallel with it.
- There is a p.d. of 1 volt between two points if 1 joule of work is done when 1 coulomb of charge moves between the points. 1V= 1JC^-1.
- The electromotive force (e.m.f.) of a sourse is defined as the work done in moving unit charge round a circuit.
· The functions of a resistor in a circuit are to control the current, and to dissipate energy in heating.
· The resistance (R) = p.d across the conductor (V)/ current though it (I). R=V/I.
· A conductor has a resistance of 1 ohm ( Ω) if the current though it is 1 ampere when the p.d. across it is 1 volt.
· Ohm's law: for a metallic conductor at constant temperature, the current through it is proportional to the p.d. across it.
· The I–V characteristic (graph) for a fixed resistor at constant temperature is a straight line through the origin.
· The I–V characteristic for a filament lamp curves away from the current axis, because the resistance of the lamp increases with temperature.
· The I–V characteristic for a diode shows zero current for negative p.d.s, and for positive p.d.s up to about 0.5 V. The current then rises steeply, showing that the diode has low resistance in the forward direction.
· The resistivity of a conductor of length L, cross-sectional area A and resistance R is ρ = RA/L. Thus R = ρL/A.
· The unit of resistivity is Ωm. The resistivity of a metallic alloy used to make resistance wires is, typically, ρ = 4.9 × 10−7 Ωm.
· The resistance of a metal increases with temperature, because the increased vibration of atoms impedes the movement of electrons.
- The resistance of an (NTC) thermistor decreases with temperature because the greater energy releases more charge carriers.
Power in electrical circuits
· Power P developed in a circuit is P = VI = I2R = V2/R.
· Energy transferred = power × time W = Pt = ItV.
· Fuse wire is made of tinned copper, which has a low melting point. If the current rises too high, the fuse melts and protects the device.
· The kilowatt-hour is the energy transferred by a device of power 1 kW in a time of 1 hour. Electricity companies use the kWh for costing. 1 kWh = 1 kilowatt × 1 hour = 1000 J s−1 × 3600 s = 3.6 MJ.
Series and Parallel Ciruits
· Kirchhoff’s first law: at any circuit junction, total current in = total current out. This is a consequence of the conservation of charge. It follows that the current is constant round any series circuit.
· Kirchhoff’s second law: round any circuit loop, the sum of the e.m.f.s is equal to the sum of the p.d.s. Σ(e.m.f.) = Σ(IR). This is a consequence of the conservation of energy.
· Resistors or circuit components connected in parallel have the same potential difference across them.
Resistors in circuits
· For three resistors in series: Rs = R1 + R2 + R3
· For three resistors in parallel: 1/Rp = 1/R1 + 1/R2 + 1/R3
· A cell has internal resistance due to the resistance of its chemicals. Some energy is dissipated in the internal resistance, and the terminal p.d. of a cell or battery which delivers a current is less than the e.m.f.
· For a cell of e.m.f. E and internal resistance r passing a current I through an external resistor R, E = I(R + r)
The terminal p.d. is therefore V = IR = E − Ir
· A p.d. V is applied across two resistors R1 and R2 in series. The p.d.s across the resistors are V1 = VR1/(R1 + R2) and V2 = VR2/(R1 + R2)
· The resistance of a light-dependent resistor (LDR) decreases as the intensity of light falling on it increases.
· The resistance of an NTC thermistor decreases with increasing temperature.
LDRs and thermistors are used as sensors in potential-divider circuits to give p.d.s which change with light or temperature.
· A progressive wave transfers energy from one place to another, but the medium only vibrates or oscillates.
· All wave motions, including water waves, sound, light and microwaves can show reflection, refraction, diffraction and interference.
· In transverse waves the vibration of the medium is perpendicular to the wave direction. Examples: waves on water, all electromagnetic waves.
In longitudinal waves the vibration of the medium is along the wave direction. Examples: waves in a slinky spring, sound.
· The amplitude A of a wave motion is the maximum displacement of the vibrating medium, or the maximum value of an oscillating signal.
· The wavelength λ of a wave motion is the distance between successive points in phase.
· The frequency f of a wave motion is the number of oscillations passing a point per unit time. Frequency is measured in hertz (Hz). The period T is the time duration for one complete oscillation. T = 1/f
For all wave motions: speed = frequency × wavelength v = fλ
· All electromagnetic waves travel at the same speed c in a vacuum or free space. c = 3.00 × 108 m s−1
· All e-m waves are transverse waves and can be polarised.
· The wavelengths of visible light range approximately from 400 nm for violet to 700 nm for red.
· Typical wavelengths for other e-m radiations are:
gamma X-rays ultraviolet infrared microwaves radio
10−12 m 10−10 m 10−8 m 10−5 m 10−2 m
· In unpolarised waves the vibration of the medium is in all possible directions in the plane perpendicular to the direction of wave travel.
· In plane-polarised waves the vibration of the medium is only in one plane which is parallel to the direction of wave travel.
· Polarisation occurs with transverse waves but not longitudinal waves. Light reflected from a non-metallic surface is partially polarised.
Malus’ law: I = Io cos2 θ where I = transmitted intensity, Io = incident intensity, θ = angle between planes of incident radiation and medium.
Superposition of waves, diffration
· The Principle of Superposition: if two wave motions are superposed, the resulting displacement at any point is the vector sum of the individual displacements.
· At any point: intensity ∝ (amplitude of wave motion)2
· Diffraction is the spreading out of waves when they pass through an aperture or round an obstacle.
· If light of wavelength λ is incident on a diffraction grating of spacing d, then a pattern of order n is seen at angle θ where nλ = d sin θ
· Two coherent sources have the same frequency and a constant phase difference between them.
· Constructive interference occurs when two wave trains arrive at a point in phase and reinforce. Path difference from the sources = nλ
· Destructive interference occurs when two wave trains arrive at a point with phase difference 180° and cancel. Path difference = (n + ½)λ
For light of wavelength λ incident on double slits of spacing a, the fringe separation on a screen at distance D is x = λD/a
· Stationary (standing) waves are formed when two identical waves travelling in opposite directions are superposed.
· Nodes are formed where the amplitude of oscillation is zero. Antinodes are formed where the amplitude of oscillation is maximum.
· The separation of adjacent nodes = λ/2
The fundamental mode of oscillation is the lowest frequency f0, when there is one antinode, and length = λ/2. Frequencies which are integral multiples of f0 give harmonics, with more loops in the pattern.
· A photon is one quantum of energy of electromagnetic radiation.
· The energy of a photon of radiation of frequency f is E = hf = hc/λ where h is the Planck constant: h = 6.63 × 10−34 J s
· When an electron is accelerated from rest through a p.d. V, the kinetic energy is ½mv2 = eV
The Planck constant h may be estimated using the voltage required to excite an LED: hc/λ = eV
The photoelectric effect
· A negatively charged and freshly cleaned zinc plate will lose electrons if ultraviolet radiation is incident on it.
· Photoelectric effect shows that e-m radiation has particle properties.
· The work function Φ of a metal is the minimum energy to release an electron from its surface. The threshold frequency is the minimum frequency of radiation to release electrons from the metal’s surface.
One photon of frequency f may release one electron. The maximum KE of the electron released is ½mvmax2 = hf − Φ
Wave–particle duality, spectra
· The diffraction of electrons by graphite shows that they have wave properties. Diffraction of electrons can show the size of a nucleus.
· De Broglie equation: The wavelength of the wave motion associated with a moving particle of momentum mv is λ = h/mv
· The line spectrum from a gaseous-discharge lamp provides evidence of discrete energy levels for the electrons in an atom.
If an electron falls from energy level E1 to energy level E2, then a photon of frequency f is emitted, where hf = E1 − E2
Glossery A -C
- absorption spectrum - A spectrum of dark lines across the pattern of spectral colours produced when light passes through a gas and the gas absorbs certain frequencies depending on the elements in the gas.
- ammeter - A device used to measure electric current, connected in series with the components.
- amount of substance - SI quantity, measured in moles (mol).
- ampere - SI unit for electric current, e.g. 4 A.
- amplitude (xo) - The maximum displacement of a wave from its mean (or rest) position, measured in metres (m).
- antinode - A point of maximum amplitude along a stationary wave caused by constructive interference.
- area (A) - A physical quantity representing the size of part of a surface, measured in metres squared (m2).
- coherence - Two waves with a constant phase relationship.
- components - Parts of electric circuits, including bulbs, LDRs, thermistors, etc.
- compressive force - Two or more forces that have the effect of reducing the volume of the object on which they are acting.
- conductor - A material with a high number density of conduction electrons and therefore a low resistance.
- conservation of charge - Physical law stating charge is conserved in all interactions; it cannot be created nor destroyed.
- conservation of energy - Physical law stating energy cannot be created or destroyed, just transformed from one form into another or transferred from one place to another.
- conventional current - A model used to describe the movement of charge in a circuit. Conventional current travels from + to –.
- de Broglie equation - An equation expressing the wavelength of a particle as a ratio of Planck’s constant and the particle’s momentum, mn.
- diffraction - When a wave spreads out after passing around an obstacle or through a gap.
- drift velocity - The average velocity of an electron as it travels through a wire due to a p.d.
- dynamo - A device that converts kinetic energy into electrical energy.
- efficiency - The ratio of useful output energy to total input energy.
- electric charge (Q or q) - Physical property, measured in coulombs (C); a scalar quantity.
- electric current (I) - A flow of charge. An SI quantity, measure in Amperes (A); a vector quantity.
- electrolyte - A fluid that contains ions that are free to move and hence conduct electricity.
- electromagnetic wave - A self-propagating transverse wave that does not require a medium to travel through.
- electromotive force, e.m.f. - The electrical energy transferred per unit charge when one form of energy is converted into electrical energy, measured in volts (V).
- electron - Negatively charged sub-atomic particle. Conduction electrons travel around circuits creating an electric current.
- electron diffraction - The process of diffracting an electron through a gap (usually between atoms in a crystal structure, for example graphite). An example of wave–particle duality.
- electron flow - The movement of electrons (usually around a circuit), from – to +.
- electronvolt - One electronvolt is the energy change of an electron when it moves through a potential difference of one volt. Its value is 1.60 × 10–19 J.
- emission spectrum - A pattern of colours of light, each colour having a specific wavelength.
- energy (E) - The stored ability to do work, measured in joules (J); a scalar quantity.
- energy levels - One of the specific energies an electron can have when in an atom.
- equilibrium - When there is zero resultant force and zero torque acting on an object.
- force constant (k) - The constant of proportionality in Hooke’s law, measured in newtons per metre (N m–1).
- frequency (f) - The number of oscillations per unit time, measured in hertz (Hz), e.g. 50 Hz.
- fundamental frequency - The lowest frequency in a harmonic series where a stationary wave forms.
- fuse - An electrical component designed to heat up, melt and break the circuit (hence stop the current) when a specified amount of electric current passes through it. Used as a safety device.
- gamma rays - A form of electromagnetic wave with wavelengths between 10–16 m and 10–9 m. Used in cancer treatment.
- gradient of a graph - The change in y-axis over the change in the x-axis (rise over step).
- harmonics - Whole-number multiples of the fundamental frequency of a stationary wave.
- Hooke’s law - The extension of an elastic body is proportional to the force that causes it.
- infrared - A form of electromagnetic wave with wavelengths between 7.4 ´ 10–7 and 10–3 m. Used in remote controls.
- insulator - A material with a small number density of conduction electrons and therefore a very high resistance.
- intensity - The energy incident per square metre of a surface per second, measured in watts per metre squared (W m–2).
- interference - The addition of two or more waves (superposition) that results in a new wave pattern.
- internal resistance (r) - The resistance of a battery or cell, measured in ohms (Ω).
- I–V characteristic - A graph to show how the electric current through a component varies with the potential difference across it.
- joule - Unit of energy (J), e.g. 1200 J. 1 J is the work done when a force of 1 N moves its point of application 1 m in the direction of the force.
- kilowatt - Unit of power (kW), e.g. 3.5 kW. 1k W = 1000 W.
- kilowatt-hour - Unit of energy (kWh), e.g. 3 kWh. Used by electricity companies when charging for electricity. 1 kWh = 3.6 MJ.
- kinetic energy - The work an object can do by virtue of its speed, measured in joules (J); a scalar quantity.
- Kirchhoff’s first law - The sum of the currents entering any junction is always equal to the sum of the currents leaving the junction (a form of conservation of charge).
- Kirchhoff’s second law - The sum of the e.m.f.s is equal to the sum of the p.d.s in a closed loop (a form of conservation of energy).
- light dependent resistor, LDR - A component that changes its resistance with changes in the light intensity (dark = high resistance, light = low resistance).
- light emitting diode, LED - A component that only allows electric current to pass through it in one direction and that emits light when a p.d. is applied across it.
- line spectrum - A spectrum produced by a material that contains only certain frequencies due to electron transitions between energy levels.
- longitudinal wave - A wave where the oscillations are parallel to the direction of wave propagation, e.g. sound.
- Malus’ law - A physical law describing the change in intensity of a transverse wave passing through a Polaroid analyser.
- microwaves - A form of electromagnetic wave with wavelengths between 10–4 and 10–1 m. Used in mobile phones.
- monochromatic light - Light waves with a single frequency (or wavelength).
- node - A point that always has zero amplitude along a stationary wave caused by destructive interference.
- ohm - Unit of resistance (Ω), e.g. 24 Ω. 1 Ω = 1 V A–1.
- Ohm’s law - The electric current through a conductor is proportional to the potential difference across it, provided physical conditions, such as temperature, remain constant.
- parallel circuit - A type of circuit where the components are connected in two or more branches and therefore provide more than one path for the electric current.
- phase difference (f) - The difference by which one wave leads or lags behind another. For example, in-phase waves are in step with each other. In waves that are completely out phase one wave is half a wavelength in front of the other. Measured in radians (rad).
- photocell - A component that reduces its resistance when light shines on it due to photoelectric emission of electrons.
- photoelectric effect - The emission of electrons from the surface of material when electromagnetic radiation is incident on the surface.
- photon - A quantum of light, often described as a particle of light.
- Planck constant (h) - Constant used in quantum physics; 6.63 × 10–34 J s.
- plane polarised wave - A transverse wave oscillating in only one plane.
- polarisation - The process of turning an unpolarised wave into a plane polarised wave (for example, light passing through a Polaroid filter).
- potential difference, p.d. - The electrical energy per unit charge when electrical energy is converted into some other form of energy.
- potential divider - A type of circuit containing two components designed to divide up the p.d. in proportion to the resistances of the components.
- power (P) - The rate of doing work, measured in watts (W); a scalar quantity.
- progressive wave - A wave that travels from one place to another.
- quantum - A discrete, indivisible quantity.
- radian (rad) - Unit of angle or phase difference, e.g. 3p rad. One radian is the angle subtended at the centre of a circle by an arc of circumference that is equal in length to the radius of the circle. 2p = 360°.
- radio waves - A form of electromagnetic wave with wavelengths between 10–1 and 104 m. Used in telecommunications.
- reflection - When waves rebound from a barrier, changing direction but remaining in the same medium.
- refraction - When waves change direction when they travel from one medium to another due to a difference in the wave speed in each medium.
- resistance (R) - A property of a component that regulates the electric current through it. Measured in ohms (Ω), e.g. 24 Ω.
- resistivity (r) - The ratio of the product of resistance and cross-sectional area of a component and its length (best defined by using the equation r = RA/l).
- semiconductor - A material with a lower number density of conduction electrons than a conductor and therefore a higher resistance.
- series circuit - A type of circuit where the components are connected end to end and therefore provide only one path for the electric current.
- spectral line - A line relating to a specific frequency either missing from an absorption spectrum or present in an emission spectrum.
- standing wave - An alternative name for a stationary wave.
- stationary wave - A wave formed by the interference of two waves travelling in opposite directions.
- superposition - The principle that states that when two or more waves of the same type exist at the same place the resultant wave will be found by adding the displacements of each individual wave.
- temperature (T or θ) - SI quantity, measured in kelvin (K), e.g. 273 K. Also measured in degrees Celsius (°C).
- thermistor - A component that changes its resistance depending on its temperature. An NTC thermistor’s resistance reduces as the temperature increases.
- time interval (t) - SI quantity, measured in seconds (s), e.g. 60 s; a scalar quantity.
- transverse wave - A wave where the oscillations are perpendicular to the direction of wave propagation, e.g. water waves, electromagnetic waves, etc.
- ultraviolet - A form of electromagnetic wave with wavelengths between 10–9 and 3.7 × 10–7 m. Causes sun tanning.
- volt - Unit of potential difference and e.m.f (V), e.g. 230 V. 1 V = 1 J C–1.
- voltmeter - Device used to measure the p.d. across a component. It is connected in parallel across a component.
- watt - Unit of power (W), e.g. 60 W. 1 W = 1 J s–1.
- wavelength (l) - The smallest distance between one point on a wave and the identical point on the next wave (e.g. the distance from one peak to the next peak), measured in metres (m).
- wave–particle duality - The theory that states all objects can exhibit both wave and particle properties.
- work (W) - The product of force and the distance moved in the direction of the force, it can also be considered as the energy converted from one form into another, measured in joules (J); a scalar quantity.
- work function energy (ϕ) - The minimum energy required to release an electron from a material, measured in joules (J).
- X-rays - A form of electromagnetic wave with wavelengths between 10–12 and 10–7 m. Used in X-ray photography.
- Young’s double slit - An experiment to demonstrate the wave nature of light via superposition and interference.