Colomb’s Law
The force is dependant on:
 Size of each charge
 Square of the distance between them
where ε is the “permittivity of free space.”
Where: k = “coulomb constant”
= 9 x 109 Nm2C2
q1 + q2 are charges measured in coulomb’s.
Electric Fields:
 We often draw field lines to visualize forces.
 You draw a field by pretending to put a small positive point charge in a situation and draw an arrow pointing where it would go.
 The length of the arrow shows the strength of the force.
 If the arrows are close together there are stronger forces, further apart, weaker forces
large positive charge

The strength of the field defined as the force felt per charge
 E = F / q
 E = electric field

so therefore, E = kq / r2
Electric Currents
 imagine a metal wire

delocalized electrons randomly move around the wire

they move at speeds approx. 106 m/s!!
 they collide and bounce a lot.
If there is an electric field:

the electrons still move randomly, almost but the net movement is now lightly to the right.
 The nett flow is called the current

The speed of the net flow is ‘drift velocity’ – approx. 104 m/s
 With the extra motion comes extra friction which causes heat. This is why wires get hot.
 This is how light bulbs (incandescent), toasters, electric kettles, etc work.

Electric current is defined as the rate at which charge flows past a given cross section of a wire.
 I = Δq / Δt
 Measured in amps, but we usually deal in milli and micro.
CONVENTIONAL CURRENT
 The rules of how electricity work…

By convention, current is defined as a flow of positive charge.
 Flow is drawn as positive to negative always
 But the actual movement of the electrons is the other way
 Current flows from positive to negative, or from “high electric potential” to “low electric potential”.
Electric Potential Difference
 This is usually similar to gravitational potential.

ΔV = W / q
 where V is the electric potential difference
 where W is the work done, the change in energy, the JOULES
 and q is the charge.
 A volt is also a measure of J/C.
 Joules per coulomb
 Voltage measures energy, current measures flow
Coulomb of Charge – what is it?
 Electrons are very small.

The charge on one is 1.6 x 1019 C.

So 1C is the amount of charge you get from 1/ 1.6 x 1019.

IC is the charge on 6.25 x 1018
 Sometimes we don’t use joules either, we use the electronvolt
 1eV is the energy an electron gets when made to move by a 1V potential.

1eV = 1.6 x 1019 J
 i.e. an electron that accelerates through 1.5V will lose 1.5eV of potential energy but gain 1.5eV of kinetic energy.
Precise Definition:
The electric potential at a point in an electric field is the amount of work that would be done in bringing a positive test charge from infinity to that point.

The F here is Felec = kq1q2 / r2
 Where ‘r’ is the distance between the two charges.
CIRCUITS
 Key concept:
 Current = rate of flow of charge
 Voltage = energy of charge
 q = ΔI Δt
 for a circuit to work we need:
 a path for the charge to travel along
 a field to get the charge to move
i.e. wire and battery
 the 2 common circuit elements that we use are resistors and light bulbs.
 Resistors convert electrical potential energy into heat
 Light bulbs convert electrical potential into light and heat
 ALL circuit elements convert some energy to heat
 Because a current flows through them – friction = heat
Resistance
 Obviously if you have current you can increase or decrease the potential difference (voltage)
 This will change the current running through the circuit
 The amount of increase current you can get by increasing voltage depends on the resistance of the circuit.
 R = V / I
 ohm categorized circuit elements by their VI characteristic curves
 by definition, an ohmic device is one in which you can get a straight line graph when plotting V vs I.
 nonohmic is everything else

ohmic devices have constant resistance for all ranges of voltage.
 Common resistors are ohmic. Nonohmic devices include diodes, lightbulbs, etc.
Circuits

There are two ways to connect electronic devices
 Series:
Kirchoff’s current and voltage laws
going in = 7 + 2
going out = 4 + 6
therefore 9 = 10 + ?
? =  1
there 1 A in.
 This is often called “current conservation” or “charge conservation”

ξ often represents E.M.F
 electro motive force
 a very old fashioned term for input voltage
 voltage supplied
 E, Vin, Vsupply, Vs
 This is just energy conservation

In a series circuit, ξ = V1 + V2 + V3 + …

There is only one path so I1 = I2 = I3
 You can calculate the total resistance (sometimes called the effective resistance)

RT = VT / IT = (V1 + V2 + V3 + …) / I
 i.e. the sum of the individual resistors
 in a parallel circuit, each charge only goes through a single branch
 the current splits up but the amount in each branch is the same

1/ RT = 1/ R1 + 1/ R2 + 1 / R3 + …
 adding resistors in series INCREASES total resistance and DECREASES total current
 adding resistors in parallel DECREASES total resistance and INCREASES total current
Circuits can be simplified. E.g 3 resistors side by side can be added and made the one circuit.
AMMETERS & VOLTMETERS

Ammeter measures current

connect in series so that the current flows through the ammeter
 ammeters have VERY low resistances so that they do not influence the circuit

Voltmeters measures voltage (measure of energy)

Connect in parallel so that it has the same voltage as what you connect it to.

Voltmeters have very large resistances so that they don’t “steal” any of the current
 Easy to kill ammeter, hard to kill voltmeter
POWER
 POWER = ENERGY / TIME
 Measure in watts
 Electrical energy = qV
 q = It
 therefore P = ItV / t = IV
 P = IV
 E = VIt
The KiloWatt – hour
 Electricity companies don’t use joules to measure energy use.
 1kWh = 1000 x 60 x 60
 = 3, 600, 000
 = 3.6MJ
VOLTAGE dividers
 voltage dividers are used in LOTs of places. From dimmer switches to sensor systems.
Recall from our knowledge of parallel circuits
The bigger one resistor is than the other, the closer the total resistance is to the lowest resistor.
A voltage divider uses this property. To examine the circuit we just ignore the “something useful” part of the circuit → ignore the bigger voltage.
SENSORS
 streetlights are a good example of the use of a voltage divider & sensor
 a change in environment is what drives the sensor
 e.g. colder = makes a heater more conductive
Power shortcut
P = VI
V = IR
P = IRI = I2R
P = I2R
P = VV / R
P = V2 / R