Physics OCR A-Level A Chapter 8 Charge and current

Electric Current

The rate of flow of charge, and can be the flow of any charge carrier.

Equation for Current (when given time)

Current = Charge/Time
I = ΔQ/ Δt

1A is the same as...

one coulomb of charge passing a given point per second (1Cs^-1)

Electric charge

Is a physical property and is a measure of how charged an object is. Measured in coulombs.

A neutral object

an object with no charge.

Like charges

repel

Opposite charges

attract

The coulomb

the electric charge flowing past a point in one second when there is an electric current of one ampere.

ΔQ = I x Δt

one coulomb (1C) is equivalent to one ampere second (1As)

Charge Carrier

any particle which carries electric charge.

proton

1.60x10^-19

electron

-1.60x10^-19

Copper 2+ ion

3.20x10^-19

Sodium + ion

1.60x10^-19

Chloride- ion

-1.60x10^-19

Net Charge

Net charge is generally the total charge of an object due to the loss or gain of electrons

Q = (+/-) ne

Q- the charge in coulombs
n- number of electrons
e- elementary charge

Elementary Charge

1.60x10^-19

Quantised

Being limited to strict values, in this case multiples of e, not a continuous set of values.

Millikan's experiment

Determined the charge of an electron. Done by dropping charged oil droplets between two oppositely charged plates. The droplets experienced gravitational force, air resistance and upthrust. Some were held stationary some drifted slowly through the electric field. From this he calculated charge on electrons and that charge on the droplets was quantised.

Charge carriers in metals

electrons

Charge carriers in liquids

tend to be ions

The electric current in the nerve cells in your brain involves..

potassium and sodium ions

structure of metal

a regular crystal structure or lattice of positive ions, surrounded by a number of free electrons. The metal ions are fixed in place and vibrate about a fixed point more vigorously at higher temps. Electrons are free to move and flow when the metal is given a positive and negative end.

A larger current may be due to...

A greater number of electrons moving past a given point each second
The same number of electrons moving faster through the metal.

The greater the rate of charge flow..

the greater the electric current in the wire.

Conventional Current

From the positive terminal to the negative.

Flow of electrons

From the negative terminal to the positive.

Electrolytes

liquids that conduct electricity due to the presence of ions within the liquid which are charge carriers.

All electrolytes are either...

molten ionic compounds or ionic solutions.

Pure water is...

an excellent insulator

Tap water...

is an ionic solution.

Salt dissolved in water

is an ionic solution, the salt separates into positive sodium ions (cations) and negatively charged chlorine ions (anions).

Ionic Solutions and electrodes

If a positive electrode (anode) and a negative electrode (cathode) are places in the solution ions are attracted to the electrodes. The cations move towards the cathode and anions towards the anode this flow of ions induced an electric current as it is a flow of charge. When cations reach the cathode, they accept an electron and when anions reach the anode they donate an electron so electrons can flow through the metal part of the circuit.

Cations

Positively charged ions.

Anions

Negatively charged ions.

Ammeters

are used to measure the electric current at any part of the circuit, so is placed directly in series in the circuit at the point you want to measure the current.

An ideal ammeter will...

have the lowest possible resistance to reduce the effect they have on the current a high resistance would reduce the current it should be measuring. The ideal ammeter has zero resistance and so has no effect on the current.

Conservation of charge

electric charge can neither be created nor destroyed. The total amount of electrical charge in the universe is constant.

Kirchhoff's First Law

that for any point in an electric circuit the sum of currents into that point is equal to the sum of currents out of that point.
∑I(in) = ∑I(out)

Kirchhoff's First Law is based upon...

conservation of charge, where the charge (coulombs) is the product of the current (amperes)and the time (seconds). Charge cannot be created nor destroyed so the charge carriers entering s point in a given time must equal the total number of charge carries leaving the same point during that time.

Number density

the number of free electrons per cubic metre of material.

Conductors have...

a number density of approximately 10^28

Semiconductors have...

a number density of approximately 10^18

Insulators have...

the lowest number density

Copper (conductor)

8.5x10^28

Zinc (conductor)

6.6x10^28

Germanium (semiconductor)

2.0x10^18

Silicon (semiconductor)

8.7x10^15

Semiconductors have...

a much lower number density than metals so in order to carry the same current the electrons in the semiconductors need to move faster.

Faster moving electrons in semiconductors...

increases the temperature of the semiconductor.

Most charge carriers like electrons...

move slowly, free electrons repeatedly collide with the positive metal ions as they drift through the wire towards the positive terminal.

Mean Drift Velocity

distance travelled per unit time along the length of the wire

Equation for Current (given number density)

I = Anev
I - current
A- cross sectional area in M^2
n- number density
e- elementary charge
v- mean drift velocity

derivation of I=Anev

I = ΔQ/ Δt
Number of electrons in a given volume of the conductor is nv where n is number density, the total charge of the electrons in this volume of conductor is nev where e is the elementary charge. Giving
I = neV/ Δt
When there is an electric current in the conductor a certain volume of charge carriers pass, a given point each second. This volume depends on the CSA of the conductor and the mean drift velocity of the charge carriers.
V/ Δt = Av
Substituting this into our previous equation for electric current gives
I= neV/ Δt = neAv
Or I = Anev

If cross sectional area of a wire changes...

so must the drift velocity, the narrower the wire the greater the drift velocity must be in order for the current to be the same. If the radius halves the CSA will decrease by a factor of 4.
This is because v is proportional to 1/A