unit 5: electricity and magnetism

electric charge (q)

• current (I) x time (t)

• measured in Coulombs (C)

• 1 Coulomb is the amount of charge carried by 1 Ampere in 1 second (derived unit)

current

• measured in amperes, fundamental unit

potential difference (V)

• work per unit charge, V=W/q

• measured in Volts (V)

• 1 Volt is 1 Joule of work done on or by 1 Coulomb of charge

Coulomb’s law

• The forces on two charges are equal in magnitude and opposite in direction

• F ∝q1q2 → also F∝q1 and F∝q2

• F∝r^-2 → F∝q1q2/r²

• constant → F=k q1q2/r²

• k = 1/4πε0 = permittivity of free space

the elementary charge (e)

• every electron and proton has a charge of the same magnitude → 1.6×10^-19 C

• positive for protons, negative for electrons

drawing electric field lines

• lines don’t cross

• begin on positive charges, end on negative charges

• direction of the field is the direction of the force on a positive charge

• more lines = stronger field

• perpendicular to the surface of conductors

• no field inside a conductor

uniform electric field

• same strength and direction throughout the field

• parallel plates and even distance between field lines

• electric fields = vectors

electric field strength

• the force per unit charge exerted on a stationary positive charge at a point

• E=Fe/q so measured in NC^-1

volts

• work done per unit charge

• JC^-1

show that 1 NC^-1 = 1 Vm^-1

Joule = Nm, so N=J/m

electric field strength measured in N/C

…

behaviour of a charge in a uniform electric field

mathematically same equations for Fg and Fe so charge is also subject to projectile motion following a parabolic path

Finding E ne = mg

electric potential difference (V)

also called voltage

• work is the transfer of energy

• eg when a charge passes through a light bulb electric potential energy becomes thermal and light energy

• in this process the electric potential energy of the electron changes

• this difference divided by the charge (V=W/Q) is the electric potential difference

electromotive force (EMF, ε)

• work done per unit charge by the power supply

• not actually a force

• ε = W/Q

difference between electromotive force and electrical potential difference

whether the charges are doing work (V) or work is being done on the charges (EMF)

energy is transferred from electrical to another form (V)

energy is transferred from another form to electrical (EMF)

Finding electrical power and showing the two meanings of watts

P=W/t

W=VQ

P=VQ/t

I=Q/t

P=VI (so watts are Js^-1 and VA)

[conventional] current (I)

• flow of positive charges, I=Q/t

• measured in amperes (A), fundamental unit

• current is in the direction of positive charges, same direction as the electric field

drift speed

• the average movement of all charge carriers

• current moves in the opposite direction

earth/ground

• where V=0

Ohm’s law

I∝V

R=V/I

ohmic materials

follow Ohm’s law that I∝V

linear graph

non-ohmic materials

do not follow Ohm’s law that I∝V

a lot more non-ohmic materials than ohmic materials in the universe

non-linear graph

resistance

• symbol is capital omega

• measured in Ohms

• R=V/I

how do the flow of positive and negative charges equal each other?

negative charge flowing to the left = positive charge flowing to the right

equation for drift velocity

I=nAvq

• I = current

• n = number density

• A = cross sectional area

• v = drift velocity

• q = charge on each carrier

number density

• number of charge carriers per unit volume

• depends on the material

• units of m^-3

why do electrons start drifting almost instantly after a system is turned on?

an electromagnetic wave propagates through the cable close to the speed of light

what happens to the drift speed if current is doubled?

it will also double (directly proportional)

what happens to the drift speed is the area is halved?

drift speed doubles (inversely proportional)

what happens to the drift speed if number density is halved?

drift speed doubles (inversely proportional)

thermistor IV graph

lightbulb IV graph

diode, current gate IV graph

line is 0 up to a point (resistance is infinite) then current kicks in

series circuit

current can only follow one specific path

parallel circuit

current can follow multiple different paths

resistors in series

• the same current passes through each resistor

• the total potential difference is the sum if the individual potential differences

effect of temperature on drifting electrons

increases resistance

Kirchhoff’s first law

current in = current out

current cannot be created or destroyed

which path will more current in a series circuit take?

the one of least resistance

total resistance in parallel vs series

parallel: 1/R = 1/R1 + 1/R2

series: R = R1 + R2

relationship between Rt and Ri in parallel

Rt < Ri

how does current split in a parallel circuit?

according to the ratio of the resistance

what is constant in a series circuit?

what is used up?

current is constant

potential difference is used up

what is constant in a parallel circuit?

what splits up?

potential difference is constant

current splits up

devices used to measure current and potential difference

potential difference → voltmeter

current → ammeter

for a voltmeter to not affect the current going to the rest of the circuit, it needs to have infinite resistance

connected in parallel

measuring devices should not be part of the experiment

an ammeter should have no resistance because all the current needs to pass through it

connected in series

potential divider

a way to regulate the potential difference supplied to components

knowing the ratio of V total to R total, what is the ratio of V1 to R1 and V2 to R2?

• the ratio for all three situations is the same

• V1 = R1/(R1+R2) V total

	Voltmeter	Ammeter
Ideal resistance
How it is connected

	Voltmeter	Ammeter
Ideal resistance	infinite	zero
How it is connected	in parallel	in series

When is P=I²R and P=V²/R applicable?

if and only if dealing with non-ohmic materials