AS level physics unit one section 3

the rate at which electrically charged particles pass through a point in a circuit

coulombs per second or amperes (amps)

1

electrons ,

from the negative terminal of the dc supply towards the positive charge . confusion can arise because current is normally shown as moving from the positive terminal towards the negative terminal . this is referred to as conventional current

the conventional current direction

• I = ΔQ/Δt 
• where :
• I = current in amperes (A)
• Q = charge in coulombs (C)
• t = time in seconds 
• Δ = change in ... (charge or current in this case)

potential difference (p.d.)

the electrical energy transferred or converted per unit of charge passing between the two points

joules per coulomb or volts

1

• V = W/Q 
• were :
• V = p.d. in volts (V) 
• W = work (energy) in joules (J)
• Q = charge in coulombs (C)

passes through a cell

passes through the components in a circuit (e.g. a lamp or resistor) i.e. p.d. exists across the component . thus both a cell and component have a p.d. across them when charge flows in a circuit

flow around a circuit . this is called resistance and it is measured in ohms (Ω)

resistance in the circuit . the bigger the resistance , the more p.d. is required to make a certain current flow

• R = V/I 
• where :
• I = current in amps (A)
• V = p.d. in volts (V)
• R = resistance in ohms (Ω)

• mA
• 1X10^-3 amps 

• A
• 1x10^-6Amps

• K
• 1x10³ ohms 

• M
• 1x10⁶ ohms 

total charge/charge on charge carrier 

• Q = It 
• Q = 4x10^-6 x 1 = 4x10^-6C
• number of charge carriers is equal to the total charge divided by the charge on charge carrier
• number of charge carriers = 4x10^-6/1.6x10^-19
• number of charge carrier = 2.5x10x10¹³

• 
• the component under test is placed in the circuit as shown so that the circuit is complete when the switch is closed (note the diagram should have a switch on it) 
• by varying the resistance using the variable resistor a range of current and p.d. values can be recorded for each change in resistance 
• the battery is reversed and the variable resistor varied over the same range to produce  a second set of readings 
• a graph of current/voltage can be drawn using the results this is the characteristic curve for the component

• when current is plotted against the p.d. a straight line graph is obtained 
• 
• the positive part of the graph shows current flowing from positive to negative and the negative part of the graph shows the current reversed . 
• the current and p.d. are directly proportional to each other (straight line through the origin) when the current flows in either direction . the conductor is said to follows ohms law 

• 
• in the case of the semiconductor diode , the shape of the curve obtained depends on the direction in which the current is flowing . 
• when the diode is forward biased (arrow facing the direction of the conventional current) :
• between 0V and about 0.7V , the diode offers a large resistance to current 
• between about 0.7V and 1V the resistance of the diode falls rapidly and a large current flows - this is shown by the steep rise in the graph 
• when the diode is reversed biased (arrow facing opposite direction to conventional current) :
• the diode offers high resistance , so very little or no current flows 
• at the breakdown voltage typically between 50 and 500 V , a large current flows 
• most diodes cannot recover and are destroyed by the heating effect of the large current

when a filament lamp is connected in a circuit and the voltage is steadily increased the graph becomes less steep . the p.d. and voltage don't increase proportionally because the current heats the filament and so increases the resistance and therefor decreases the rate of increase of current with p.d. . the curve is symmetrical on either side of the origin showing that the lamp behaves in the same way for current flowing through it in either way .

• please note that the filament lamp may be another component . 
• the potential difference is varied across the component under investigation (wire , resistor , lamp , diode) using a potential divider and the current is recorded . the data logger software is then used to display the collected data in a tabular and graphical form

• the current in a conductor is directly proportional to the p.d. across it 
• I is proportional to V 
• provided that the temperature and other physical conditions remain the same 

the resistor/wire is the only ohmic conductor while the semiconductor diode and the filament lamp are non ohmic conductors 

length and cross sectional area 

• proportional 
• doubles

• inversely 
• halves 

pi x (d/2)² 

• reduce 
• a factor of 4 

• resistivity = AR/l
• where : 
• A is the cross sectional area of the conductor in m²
• R is the resistance of the conductor in ohms 
• l is the length in m 
• the resistivity is a constant of the material from which the conductor is made and measured in ohm metres 

10⁶

• please note that the wire under test is taped to a metre rule . 
• start by measuring the 100cm of the wire under test . tape the wire on to a metre rule , to avoid any kinks or twists . connect the wire to the circuit using crocodile clips . 
• record , in a table , the p.d. displayed on the voltmeter and the current displayed on the ammeter for this length of wire . 
• move the voltmeter connection along the wire in the range 100cm to 30cm and record the p.d. and current for each length 
• calculate the resistance of wire for each recorded length using R = V/I 
• measure the diameter of the wire several times over its length , using a micrometer , to determine a mean value for the diameter 
• use the mean diameter to calculate the cross sectional area using A=pix(d/2)²
• plot resistance (y axis) against length (x axis) 
• since R = resitivity x l /A 
• the graph is a straight line through the origin and resistivity can be found from the gradient . the gradient = R/l = resistivity/area so to find resistivity we have to find the gradient go the graph and times it by the cross sectional area 
• essential notes // avoid large currents which will heat the wire and increase the resistance
• essential notes // a multimeter set on the ohms range could be used to measure the resistance directly , instead of using a battery , ammeter and voltmeter . however the ohms range usually has an uncertainty of + or - 1 ohms 

the temperature increases 

free electrons that move when a p.d. is applied , causing a current to flow . the metal also has vibrating positive ions . electrons collide with these ions . causing the wire to have resistance to current 

the positive ions and electrons asorb heat energy , causing the ions to vibrate with greater amplitude and the electrons to move faster . both of these effects result in a greater number of collisions between electrons and ions i.e. the resistance of the conductor increases . However the gradient of the graph isn't very steep showing that resistance doesn't change greatly with temperature 

temperature measurement and control

temperature increases 

• the thermistor is made from semiconductor material and therefor has few electrons to produce a current . as the temperature of the thermistor increases , the thermal energy is enough to release further electrons from the ions to make the material conductive , this means resistance decreases .
• essential notes// at higher temperatures the ions of the semiconductor vibrate more . This would normally cause the resistance to rise . However the release of conduction electrons is the dominant effect . this also explains the shape of the graph .

currents produce heat and this decreases the resistance of the thermistor , allowing more currents to flow . this further heats the thermistor producing further resistance changes and the process can continue until the component overheats and burns out or melts

it disappears completely . The material is said to have become a superconductor . Its resitivity has dropped to zero and an electric current can pass through without transferring any energy to the conductor . the temperature at which the material becomes superconducting is known as the critical temperature T_C 

close to absolute zero , 1 to 4k . ceramic superconductors now exist that have critical temperatures as high as 125K (-148⁰C)

carrying electrical power without losses and constructing very strong electromagnets

that acquire zero resistance when they are cooled below a critical temperature 

• potential difference is shared between various components . so the voltages round a series circuit always add up to the equal the source voltage 
• current is the same everywhere 
• the total resistance is the sum of all the resistances 
• cell voltages add up

• p.d. is the same across all components 
• current is shared between branches
• the total resistance of any number of resistors is given by 1/R_T = 1/R₁ + 1/R₂ + 1/R₃

p.d. must exist 

amount of electrical energy that must be transferred to the charge and is measured in joules per coulomb , or volts 

passes through components in the circuit (e.g. lamp , motor , resistor etc) . all the potential energy lost by the charge is ultimately changed into heat 

joules 

• energy change (work done) W = VIt 
• where :
• W = energy change in joules (J)
• V = p.d. in volts (V)
• I = current in amperes (A)
• t = time in seconds (s)

rate of change of change of energy and is measured in joules per second (Js^-1) or watts (W) 

• P = IV 
• where :
• P = power in watts (W) or (Js^-1)

• P=I²R

P=V²/R

it shows the heating effect is proportional to the square of the current . Therefor doubling the current will produce four times the rating of heating

original power is given by P=I²R but I₁ = (I/2)²  R₁= 2R . Now power is given by P=I²/4X2R = I²XR/2 = 1/2 P

electric charge i.e. all charge which arrives at a point must leave it 

• the total current flowing away from the point . or the algebraic sum of currents at a junction is zero . this is known as Kirchhoff's first law .
• 

potential differences and measured in volts .

• filament lamps are more likely to blow (the filament breaks) when you first switch them on . 
• when you first switch a bulb on , the filament has a lower resistance because its cold . This means that the initial current flowing through the filament will be larger than the normal current , so the filament is more likely to burn out at this time . 
• the filament also heats up very quickly from cold to its operating temperature when it's switched on . the rapid temperature change could cause the filament wire to break to