Physics Topic 4: Electrons

doesn't include core practicals !!

define current

rate of flow of charge

relationship between current, charge and time

I = Q/t

current in metals

rate of flow of electrons

current in electrolytes

rate of flow of ions

unit of charge

coulomb (C)

what is one coulomb

amount of charge transported by a constant current of one ampere in one second.

elementary charge

1.6x10^-19 C

charge of a proton (in terms of e)

+e (1.6×10^-19C)

charge of an electron (in terms of e)

-e (-1.6×10^-19C)

the net charge of any particle is…

a multiple of e (the elementary charge)

net charge formula

Q = ne (where n is an integer)

what is conventional current

flow of positive charge from positive to negative terminal

what is the direction of electron flow

negative terminal to positive terminal

electrons are repelled by the negative terminal, and attracted to the positive terminal

state kirchoff’s first law

the sum of currents entering a junction equals the sum of currents leaving that junction

I_in = I_out

which conservation law supports kirchoff’s first law

the conservation of charge
[charge cannot be created or destroyed. the total charge in a system is constant and conserved]

in series, current is…

equal throughout the circuit, as there are no junctions

in parallel, current is…

shared, as there are junctions

mean drift velocity

average velocity of electrons as they move through a wire

mean drift velocity formula

I = nave
[current = electron number density x area x mean drift velocity x elementary charge]

electron number density

number of free electrons per unit volume

relationship between current and mean drift velocity

proportional

relationship between area and mean drift velocity

inversely proportional

relationship between elementary charge and mean drift velocity

inversely proportional

relationship between electron number density and mean drift velocity

inversely proportional

In “I = nave”, what is “n”?

the number density of charge carriers (electrons)

how is electron number density related to conductivity

conductivity is controlled by how many free electrons/mobile ions there are to carry current.

the more charge carriers (the higher the number density), the more conductive the material is.

explain conductors, semiconductors and insulators in terms of electron number density

conductors have a high electron number density

semiconductors have an intermediate electron number density

insulators have a low electron number density

what’s the difference between a cell and a battery

a cell is a single device, a battery is multiple cells

thermistor symbol

diode symbol

light-dependent resistor symbol

potentiometer symbol

LED symbol

potential difference

energy transferred from electrical energy to other forms per unit charge (work done per unit charge)

what is 1 volt

1 joule of energy transferred per coulomb

electromotive force (e.m.f)

energy transferred from other forms into electrical

(work done on charge carriers)

relationship between emf, work done and charge

V = W/q

how does an electron gun work

1. the cathode (hot filament) is heated by a low potential difference. this causes it to release electrons by thermionic emission

2. a high potential difference between the cathode and anode accelerates the electrons towards the anode. During this, electrical energy is converted to KE

3. The anode has a small gap, so the electrons are fired through the gap to form a narrow beam travelling at constant velocity

how is eV=1/2mv² derived from the electron gun?

1. the work done on an electron by the electrical field id given by “W = qV”. In this case, the charge (q) is the charge of an electron - the elementary charge, e. thus W=qV → W=eV

2. As all electrical energy is converted to kinetic when the electrons are fired, “eV” (the electron volt) is the KE of an electron accelerated across a p.d. of 1V

3. Once the electron reaches the anode, its KE is equal to the work done on the electron by the electrical field. This means KE=W=eV.

4. Thus, KE=1/2mv² → eV = 1/2mv²

resistance

measure of the opposition to the flow of current in a circuit

relationship between resistance, voltage and current

R = V/I

what is 1 ohm

a 1 volt per unit ampere

ohm’s law

for a metallic conductor kept at constant temperature, the current in the component is directly proportional to the p.d across it

[V = IR]

ohmic device

components which follow ohm’s law

non-ohmic device

component which doesn’t follow ohm’s law

relationship between resistance and current in non-ohmic devices

the component’s resistance increases with current:

1. current across component is increased, increasing temperature

2. metal ions are heated, gaining KE and vibrating in the lattice

3. as the ions move more, the frequency of electron-ion collisions increase

4. more work is done on the charge carriers, so resistance is increased

relationship between resistance and current in ohmic devices

the component’s resistance remains constant with current:

1. current across the component is increased

2. metal ions vibrate, but don’t gain KE

3. no matter changes in current, the average frequency of electron-ion collisions per unit time remains constant

4. there is no net change in work done, thus resistance is constant

I-V Characteristic

• graph showing the relationship between current and voltage in a component

• current is on the y axis, voltage is on the x axis

• resistance is 1/gradient

examples of ohmic components

• fixed resistor

• wire

• potentiometer

I-V characteristics of ohmic components

• linear graph - straight gradient

• as current increases, voltage increases

examples of non-ohmic components

• filament lamp

• ntc thermistor

• diode

• LED

I-V characteristic of a filament lamp

• lamp is ohmic at small values of current

• as current increases, heating effect on metal ions causes resistance to increase

I-V characteristics of an ntc thermistor

• as the temperature/current increases, resistance decreases.

relationship between light intensity and resistance in an LDR

as light intensity increases, resistance decreases

resistivity

a property that describes the extent to which a material opposes the flow of electric current through it

resistivity is a constant, and a physical property of the material

resistivity equation

R = ρL/A
[resistance = (resistivity x length)/area]

relationship between resistivity and temperature in metals

as temperature increases, resistivity increases:

1. as temperature increases, metal ions gain KE

2. ions vibrate more, increasing the frequency of electron-ion collisions

3. more collisions = higher resistance. as resistance is proportional to resistivity, resistivity also increases

relationship between temperature and resistivity in semiconductors

as temperature increases, resistivity decreases:

1. as temperature increases, the number density of charge carriers increases. this causes resistance to decrease.

2. as resistance is proportional to resistivity, resistivity also decreases

relationship between temperature and resistance in an ntc thermistor

resistance decreases as temperature increases:

• as temp increases, the number density of charge carriers increases.

• consequently, resistance decreases

relationship between power, voltage and current

P=V/I

relationship between power, voltage and resistance

P=V²/R

relationship between power, current and resistance

P=I²R

electrical power

rate of energy transfer in a component

formula for energy transfer

W = VIt

[energy = voltage x current x time]

kilowatt-hour

energy transferred by a device with a 1kW power rating in 1 hour

kWh is used to calculate the cost of electrical appliances

Kirchoff’s second law

In any circuit, the sum of e.m.f is equal to the sum of p.d around a closed loop

which conservation law supports kirchoff’s second law

conservation of energy:

energy cannot be created or destroyed, only conserved.

resistance in series

R_T= R₁+R₂

resistance in parallel

1/R_T = 1/R₁ + 1/R₂

what does a source of emf have

internal resistance

lost volts

• difference between the p.d. of the power supply and the e.m.f. of the cell

• equal to p.d. across the internal resistor

terminal p.d.

the p.d. across the terminals of a cell

(when there’s no internal resistance, p.d. = emf)

relationship between internal resistance and emf

E = I(R+r)

[emf = current x (resistance + internal resistance)

relationship between internal resistance and terminal p.d.

V = E - Ir

[terminal pd = emf - (current x internal resistance)]

what is a potentiometer

variable resistor with a slider

how do potentiometers work

• sliding contact divides the potentiometer into two parts - one with a higher resistance, and one with a lower resistance. this changes V_out

• if the slider is moved up, the resistance of the lower half increases, increasing the p.d. across it

potential divider equation in terms of R and V_in

V_out = (R₂/R_T) x V_in

potential divider equation in terms of V₁ and R₁

V₁/V₂ = R₁/R₂