Charge, Current and Voltage
CURRENT is the rate of flow of charge, or the number of electrons per unit time
ΔQ = IΔt charge is measured in coloumbs - the amount of charge that passes in 1s when the current is 1A
DRIFT VELOCITY is the average velocity of the electrons
I = nAQv I = Current | n = number of charge carriers | A = cross sectional area | Q = charge carried by each charge carrier (for electrons Q= 1.6x10^-19 C) | v = drift velocity
Different materials have different numbers of charge carriers: in conductors - there are loads of charge carriers, so n is large, meaning v has to be only very small even for a high I. In semiconductors, there are fewer charge carriers, so v will need to be higher if you're going to maintain the same current. A perfect insulator would have no charge carriers, so n=0, so you'd get no current.
Charge carriers in Liguids and Gases are Ions.
POTENTIAL DIFFERENCE (voltage) is energy per unit charge
V = W/Q Voltage is measured in Volts - the potential difference across a component is 1V when you convert 1J of energy moving through 1C of charge through the component
Resistance and Resistivity
RESISTANCE is the obstruction of the flow of electrons
R = V/I measured in Ohms - a component has a resistance of 1Ω if a voltage of 1V makes a current of 1A flow through it
Resistance is determined by 3 things:
- LENGTH - the longer the wire, the harder for current to flow through it
- AREA - the wider the wire, the easier it is for the current to flow
- RESISTIVITY - depends of the material's structure, as well as environmental factors such as temperature and light intenisty
R = ρl/A
OHM'S LAW: Provided the temperature is constant, the current through an ohmic conductor is directly proportional to the potential differences across it.
I/V Graphs for Metallic Conductors
- I/V graphs show how the current changes as the potential difference changes
- The shallower the gradient, the greater the resistance
- A curve shows changing resistance
Metallic conductors show current to be directly proportional to voltage. These conductors are ohmic - the resistance is constant providing the temperature doesn't change.
When the temperature does change, i.e in a filament lamp, the resistance is not constant. Despite the filament being an ohmic conductor, because it gets hot - the resistance increases (shown by the curve getting shallower). This is because the charge carriers vibrate more when heated, so they collide more often, so more energy is dissipated.
I/V Graph for Thermistor
Semiconductors are not as good as conductors at conducting (obviuosly), due to their mlimited number of charge carriers. However, when energy is supplied to them more carriers are released. there are 3 semi-conductor components you need to know about: thermistors, LDRs and Diodes.
NTC THERMISTORS - negative termperature coefficient thermistors decrease their resistance when the temparture in them increases. Warming the electrons give them more energy to escape their atoms - when an atom escapes it leaves behind a positive hole, allwoing more electrons to escape to fill the vacant 'holes'. An exponential effect is produced:
I/V Graph for LDR
LDRs - light dependant resistors change their resisiance depending on the intensity of the light shining on them. The greater the intensity, the lower the resistance.
The I/V characteristic has the same shape as the I/V characteristic for Thermistors.
I/V Graph for Diodes
Diodes only let current flow in one direction:
- Forward bias is the direction the current
- Most need a threshold voltage of about 0.6V in the forward direction before they'll conduct
- In reverse bias, the resistance is really high, so the current that flows is very small.
Electrical Energy and Power
POWER, as we know from Unit 1, is the rate of tranfer of energy, or P = W/t
In Electrical circuits, we can find power using this equation:
This is derived from P=W/t:
- Voltage is energy tranferred per coloumb
- Current is the number of coloumbs tranferred per second
- so voltage x current = energy tranferred per second i.e. power
We also know that V=IR, so we can combine the 2 equations to get different ways of calcualting power:
Using power, we multiply by time to calculate ENERGY:
W = VIt.. .(or...W = (V^2/R)t...or...W = I^2Rt )
E.m.f and internal resistance
Batteries have INTERNAL RESISTANCE
Chemical energy in batteries is what makes electrons move. They collide with atoms in the battery, losing energy - by definition, this means the battery has resistance - called internal resistance. This is what makes cells heat up when used.
ELECTROMOTIVE FORCE (e.m.f.):
- The amount of electrical energy produced by the battery for each coloumb of charge is the e.m.f, also known as the maximum amount of voltage between two elctrodes in the cell. This value of voltage will never be the same as the terminal p.d., as some of it will always be used to overcome internal resiatance.
- The energy wasted per coloumb overcomng internal resistance is called the lost volts - conservation of energy says: energy per coloumb supplied by source = energy per coloumb used in load resistance + energy per coloumb wasted in internal resistance
- Remember: It is NOT A FORCE, but voltage - measured in volts.
E = I(R + r)......E = V + Ir......E = V + v. E = e.m.f. | I = Current | R = load resistance | r = internal resistance | V = terminal p.d. | v = lost volts
Kirchoff's Laws and Combining Resisitors
KIRCHOFF'S FIRST LAW: the total current entering a junction = the total current leaving it
KIRCHOFF'S SECOND LAW: the total e.m.f around a series circuit = the sum of the p.d.s across each component or the sum of potential rises and falls around a closed circuit is sero
Combining resistors in SERIES - where resistors are added to a circuit one after the other
Simply add them together: Rtotal = R1 + R2 + R3
Rules: Voltage is shared between the components, the current is the same everywhere
Combining resistors in PARALELL - where the resistors are joined in branches, providing slternative paths for the electricity and reducing thr overall resistance of the circuit:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 remember to take an inverse calcualte at the end to find Rtotal
Rules: Voltage is the same everywhere, the current is shared between the branches
The Potential Divider
A potential divider is a circuit with a voltage source and some resistors in series, used if an electrical supply voltage is too high to be useful.
In the circuit, R1 has R1/(R1+R2) of total resistance.
You can use LDRs and thermistors as any one of the resistors in a potential divider, for an output voltage that varies with light/temperature. Add a transistor for a switch e.g.for a heating system.
Potentiomenters use a variable resistor to replace R1 and R2. You move a slider to change the relative sizes of R1 and R2, so you can vary Vout from ) 0V up to the imput voltage. This good for e.g. volume controls