Electricity & Magnetism 2 Flashcards
Current
Rate of change of charge
Electric circuit
Charges follow conductive path that forms a closed loop
Electric potential energy transferred from a source to a device in which that energy is stored or converted
Electrons do not escape from metal as
They are attracted to its positive ions
With steady electric field E in the conductor, electric force F=qE imposes
A small drift in the direction of the force
Microscopic view of Ohm’s law
Electrons speed up nd colllide with stationary ions which vibrate around equilibrium position
Much electrical energy wasted as heat instead of moving electrons
Each collision randomly changes direction of motion
Net effect: in addition to radndom motion, there is a very slow net motion, drift velocity CONSTANT
Drift velocity
F=ma and F=qe gives a=qe/m
V=u+at but with mean free time
Drift velocity for E=0
Typical electron has V0 at random direction so average velocity over many electrons is zero
Drift velocity for E not =0
Electric field causes acceleration a=qE/m of every electron
Why is switching on a light almost instantaneous
Electric field in metal travels close to c so electrons everywhere start moving with drift velocity
Electron concentration
Conductor with n atoms per unit volume
n=Nap/A
=avogadro. Density/ atomic mass
Direction of drift
Constant velocity in direction opposite to E
Total charge through cross section A of conductor in time dt
dQ=nqAvddt
no= free charge per volume
Avddt= volume
Current is
I=dQ/dt=nqAvd =JA where J is current density
Current density
J=I/A
Conductivity (sigma)
Scalar depending on conductor material
Resistivity
1/conductivity ( unit ohm m)
Ohm’s law
J=signage=E/p
Does J change
Vector
Can vary around a circuit as A changes
Conductivity and thermal conductivity
Good electrical conductors are also good thermal conductors
Perfect conductor
Zero resistivity
Perfect insulator
Infinite resistivity
Greater resistivity,
Greater field needed to cause given current density
Non ohmic materials
Resistance has non linear response
Resistivity
Material property that is temperature dependent , increases with T for metal conductors
For a conductor to have steady state current
Must be part of path that forms a closed loop/complete circuit
Four components of electric circuit
Source of electrical power
Conductors (wire with low R)
A load
A means of control (etc)
In an electric circuit, charge moves
From higher to lower electric potential (similar to water in fountain due to gravity)
Source of emf causes charges to move against electrostatic force
Ideal source of emf
Maintains constant potential difference between conductors
Real sources of emf
Have different potential difference than E
Ring due to charge moving through material of the emf source
Voltaic cell
Voltage generated by connecting different metals in circuit due to different electronegativities
Daniel cell uses copper and zinc electrodes in electrolytes
Idealised voltmeter
Infinite,y large resistance so no current flow
Idealised ammeter
Zero resistance so no voltage drop associated with it
Closed circuit condition
R —>0
I—> E/Rint
Short circuit condition
R=0
Vab =0
I —> infinity for small Rint
Open circuit condition
Vab=E
I—>0
Power
dUdt
What does E.I represent
It is rate of work done by forces in source
Represents rate of conservation of non electrical energy to electrical energy within the source
I^2.Rint
Rate of dissipation of energy
Junction
Point where three or more conductors meet
Loop
Any closed conducting path
Junction rule
Algebraic sun of currents into any junction is zero
In +, out -
Loop rule
Algebraic sum of potential differences in any loop must equal zero
Sign conventions for junction rule
In +
Out -
Loop rule - sign conventions for emfs
+E travel direction from - to +
-E travel direction from + to -
Loop rule - sign conventions for resistors
+IR travel opposite to current direction
-IR travel in current direction
Easier way to set up junction rule
Flows in = flows out
Where to start when using Kirchoff’s rules
Highest potential in the loop
Thevenin’s theorem
Any combination of batteries and resistors with two terminals can be replaced by a single voltage source e and a single series resistor r
Thenevin voltage e
The open circuit voltage between terminals A and B
Thenevin resistance r
resistance seen between terminals A and B when voltage sources are replaced with short circuits
take load out and calculate Vab
Thenevin steps
Short all voltage sources
Find the equivalent resistance
Charge conservation
In junction rule
Energy conservation
In loop rule
Open loop systems
No way of checking if results have been achieved
Eg central heating without a thermostat
Closed loop systems
A KE to correct themselves in order to meet target results
Feedback
Sensor used to look at the output and adjust the process accordingly
Op amp main purpose
To amplify signals
How we treat op amp
Like a black box
Analysing only it’s external behaviour
Three fundamental properties of op amps
- Gain A (multiplier between differential input and output represented by diamond shape)
- Input impedance (Rin) resistance at the input of the circuit, very high
Output impedance (Rout) resistance seen from output of the circuit, very low
Closed loop system response
Distinguish between negative and positive feedback depending on the phase relationship
Negative feedback
Portion of the output is combined out of phase with the input
Promotes stability and setting to equilibrium
How does negative feedback loop reduce perturbations
Fluctuation in input cause flux. in out which fed back to in compensating original fluc so minimising out fluc
Examples of negative feedback loop
Thermo regulation (sweating)predator and prey population (more mice = more food for cats, more cats = more mice eaten, less mice = less cats
Closed loop positive feedback
Portion of output is combined in phase with the input
Minus sign in equation
What does positive feedback promote
Instability and chaos through exponential growth
Example of positive feedback
Panic buying toilet roll
Motivation and success
Condition A0B=1 results in
Gain becoming infinite
Non inverting op amp
Produces bigger version of original graph
Inverting op amp
Bigger and flipped version of original
Graph of Vin against Vout
Horizontal- saturation region
Slope = gain A0 through linear region
Horizontal + saturation region
Ideal op amp
Slope is infinite (vertical line) A0= infinity
Linear region only occurs at Vin=0 (virtual short circuit)
2 golden rules for circuit analysis with op amps
- Both input terminals are at the same voltage
- No current flows in or out of either input
Transfer function
Independent of gain A
Non inverting
Non inverting op amp
Vout/Vin=R2+R1/R1
Inverting op amp
Vout/Vin = =Rf/Rin
Summing op amp
If Rf=R1=R2 then Vout=-[v1+v2]
Subtracting op amp
Vout=-[V1-V2]
Rules for adding binary numbers
As expected except 1+1=0 carry 1
Logic gate
Idealised or physical device implementing a Boolean function
Made of transistors or diodes acting as electronic switches
AND gate
Read as A,B,AandB
0,0,0
0,1,0
1,0,0
1,1,1
A AND B need to be 1 for A and B to be 1
OR gate
If A or B is high then output high
XOR gate
Same as or except if both inputs are 1, output 0
NAND gate
0,0,1
0,1,1
1,0,1
1,1,0
NOR gate
Inverse
So
0,0,1
0,1,0
1,0,0
1,1,0
Half adder
Performs binary addition on two input numbers
Flip flop
Basic data storage
Stores a single bit of data
SR latch
Made from two cross coupled NAND gates
