Electricity

current

• the rate of the flow of charge

conventional current vs actual current

conventional current: positive to negative

actual current: negative to positive

resistance and temperature

• temperature increases - amplitude of vibrations increases - more frequent collision of electrons with metal ions - resistance increases

• current increases - more conduction electrons collide with the metal lattice ions - transfer of the electron kinetic energy to the positive ions - component / wire heats up due to increase in amplitude of vibrations of positive metal ions / increase in rate of vibration - greater number of collisions per second - increased resistance

• the resistance of a filament lamp will be lowest when it is first switched on, hence the initial current will be at its largest value, causing a sudden rapid change in temperature - this is why it is more likely to fail when it is first switched on.

potential difference

the work done per unit charge between two points when charges when charge moves between them

insulator, conductor and semiconductor

• insulator - electrons are not free to move - don’t flow when a potential difference is applied

• metals - conductor - some delocalised electrons - will flow when a potential difference is applied

• semiconductor - number of charge carriers increases with temperature or light intensity as electrons are liberated - reducing resistance

number of electrons

(current x time) / e = number of electrons

potential difference in series vs in parallel

series: Vs = V1 + V2 + …

parallel: Vs = V1 = V2 =…

electromotive force: emf

• the amount of chemical energy transferred to electrical energy per unit charge through power source / work done in moving 1C of charge whole way around circuit

• similar to voltage but takes into account internal resistance of the power supply, making it greater than the voltage

$$emf=IR+Ir$$

R is circuit resistance and r is internal resistance

Internal resistance

• the resistance inside a source of electrical energy

• courses a loss of pd per unit charge when current passes through it

Terminal potential difference

• the pd across the terminals of a power supply

power

work done per unit time

power = current x potential difference

resistance and ohms law

• a measure of how difficult it is for current to flow through a component in a circuit - ratio of voltage across component to current through component

• R = V/I

• the pd across a metallic conductor is proportional to the current it, provided the physical physical conditions. (temperature) do not change

measuring resistance

• set up a series circuit

• ammeter placed in series used to measure current flowing through it

• ammeter should have zero resistance to avoid altering the reading due to internal resistance

• voltmeter placed in parallel and used to measure pd across it

• voltmeter should have infinite resistance to stop current flowing though it

• each time variable resistor is adjusted, a reading is taken from the ammeter and the voltmeter

• voltage current graph plotted - gradient is the resistance of the resistor for an ohmic component only

• for non ohmic components, instantaneous resistance must be found using instantaneous values of current and pd.

factors affecting resistance

• resistance is directly proportional to length

• inversely proportional to cross sectional area

• the constant of proportionality is the resistivity

• current takes the path of least resistance

resistivity

the resistance per unit length x the cross sectional area of a material

superconductors and the critical temperature

• wire or device made of a material that has 0 resistivity at and below a critical temperature

• electrical resistivity drops to 0 as soon as cooled to critical temperature - superconducting

• when a current flows through it, no resistance so no pd - current has no heating effect

applications of superconductors

• superconducting power cables - high temperature superconductors - lossless transmission of electrical power - no electrical energy dissipated in overcoming resistance

• superconducting electromagnet - uses coils of superconducting wire - cooled to low temperatures during operation. can produce stronger magnetic fields than ordinary iron core electromagnets and can be cheaper to operate - used in mri scanners

ohmic and non ohmic components

• ohmic components have a constant value of resistance as the current through it varies- current directly proportional to potential difference provided physical conditions do not change

• non ohmic component have resistance varying with current

positive and negative temperature coefficient

ptc - resistance increases with increasing temperature

ntc - resistance decreases with increasing temperature

filament lamp

• When switched on, temp is low - resistance is low

• current increases rapidly and becomes very high

• temperature of filament also increases rapidly and becomes very high

• maximum heating at start as current peaks - energy supplied more rapidly than lost - filament could melt and fail

• resistance also increases with temperature

• increase in resistance decreases current

• curren steady when constant temperature - energy supplied = energy dissipated from filament

Measuring resistivity of wire

• measure diameter at 3 different points along wire and take an average

• calculate cross sectional area

• switch on and take readings of current from ammeter and potential difference from voltmeter

• change length of wire and measure new I and V

• measure length of wire

• vary resistance on variable resistor to take multiple I V readings for each length of wire ( and find a average)

• calculate R using V/I for each length

• plot R against L (graph is straight line)

• R = rho*L / A

• gradient = rho/A

• A x gradient to find resistivity

maximum power delivered to load

• when load resistance = internal resistance of the source

conservation of energy and charge in a circuit

• 1C of the charge gains $\char"0190$ J on passing through cell

• 1C transfers Ir J in cell

• then transfers energy to components IR J

measurement of internal resistance

• circuit with cell, ammeter, variable resistor in circuit

• voltmeter in parallel across cell

• take readings of the pd and current using ammeter and voltmeter while resistance is varied

• as current increases, terminal pd decreases because energy transferred by internal resistance Ir increases

• emf is displayed on a voltmeter as terminal pd only when no current flows

rearrange emf equation $V=-Ir+\char"0190$

circuit with cells in series

• if in same direction, emfs add

• if in different directions, find difference

identical cells in parallel

• each time an electron passes through the power supply, it can only pass through one of the cells, therefore all the cells combined act as a single source of emf

• $$$$

potential divider

• two or more resistors in series connected to a source of pd

• the ratio of the potential differences across each resistor is equal to the resistance ratio of the two resistors

potential divider with variable pd

• when sliding contact at B, resistance of branch parallel to bub has no resistance - resistance of branch with bulb has greater resistance -all current arriving from positive terminal to the junction will flow through first loop - no current through bulb. Also no potential difference across bulb as it is connected in parallel to a wire with no potential drop across it - does not turn on

• as sliding contact moves towards A, the resistance of branch connected in parallel to bulb increases - not as small compared to resistance in branch with bulb - proportion of current through bulb increases (current through branch with resistor decreases) - the pd across bulb also increases as the potential drop it is connected in parallel to becomes greater - gets brighter as power transferred electrically to bulb increases

• At A, the supply pd is across branch connected in parallel to bulb and so across the bulb - bulb also receives maximum possible current

Kirchhoff’s 1st Law:

at any junction in a circuit, the total current entering the junction is equal to the total current leaving the junction.

Kirchhoff’s 2nd Law:

for any closed loop in a circuit, the sum of the emf’s round the loop is equal to the sum of the potential drops around the loop.

potentiometer circuit vs variable resistor circuit

• Fig 4 (potentiometer) voltage range 0 -12V

• Fig 2 voltage range 0.75 - 12V

• Potentiometer has wider voltage range

• At any particular voltage across lamp, more power dissipated in potentiometer circuit (12V across variable resistor always)

• whereas for Fig 2, variable resistor only receives a portion of 12V across it

• for any current in lamp, there is always more current in figure 4 circuit, producing more heating

purpose of a fixed resistor in a variable resistor circuit

• to limit the current, preventing a short circuit and overheating of battery

• to divide the terminal potential between two resistors

operating current

• required to turn on / normal brightness