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 Nm2C-2
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
-
de-localized 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. 10-4 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 10-19 C.
-
So 1C is the amount of charge you get from 1/ 1.6 x 10-19.
-
IC is the charge on 6.25 x 1018
- Sometimes we don’t use joules either, we use the electron-volt
- 1eV is the energy an electron gets when made to move by a 1V potential.
-
1eV = 1.6 x 10-19 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 V-I characteristic curves
- by definition, an ohmic device is one in which you can get a straight line graph when plotting V vs I.
- non-ohmic is everything else
-
ohmic devices have constant resistance for all ranges of voltage.
- Common resistors are ohmic. Non-ohmic 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.
- 1kW-h = 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
