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Generation and Transmission of electricity Cheat Sheet by

VCE unit 3 electricity

magnetic flux

Φ=B⊥A
·B=mag­netic field strength (T)
·A=area perpen­dicular to the magnetic field (m²)
·Φ=mag­netic flux (Wb)

Faraday's Law

ε=-N(∆­Φ/∆t)
ε=EMF(V), N=number of turns in coil
·(∆Φ/∆t) is the derivative of Φ with respect to time.
·ε graph should be negative when Φ-t graph has +ve gradient
·ε graph should be positive when Φ-t graph has -ve gradient

Lenz's Law

An induced current will flow in a direction such that the magnetic field created by the current will oppose the change in flux that induced the current.
Right Hand coil rule:
·thumb: direction of induced magnetic field
·fingers: direction of induced current
 

generators and altern­ators

f=1/T
f=freq­uency (Hz), T=period of revolu­tion(s) - time taken to complete a full cycle
*max ε when coil is parallel to magnetic field, ie. greatest rate of change
*DC current can only be produced in presence of a split ring commutator
Alternator (AC): sinusoidal
DC generator: modulus of AC
·Φ(t)=­aco­s(2πft)
·ε=Φ'(­t)=­-2a­πfs­in(­2πft)

electr­icity recap

V=I·R - V(V), I(A), R(Ω)
Psupp­ly=V·I - also: power rating
Pdiss­ipa­ted­=I­²·R­=V²/R
Power (W) is the rate of change of energy with respect to time
P=∆E/∆t - gradient of E-t graph
series circuit:
·current (I) is the same through the whole circuit
·flow: from positive to negative terminal
·total resistance (RT) is the sum of individual resist­ances: R1+R­2+…
·total voltage supplied to a circuit must be equal to the total voltage used around the circuit (sum of voltage drops): Vsupp­ly­=V­1+­V2+…
 

Transf­ormers, comparing AC and DC

VRMS­=V­pea­k/√2 , IRMS­=I­pea­k/√2
Pavg= VRMS­⋅IRMS = IRMS²⋅R = VRMS²/R - avg power delivered by sinusoidal signal
Transf­ormers:
Pin=­Pout
VIpri­mar­y=­VI­sec­ondary
V1/V­2­=N­1/N2
I1/I­2­=N­2/N1
when V1>V2: Step-down transf­ormer
when V1<V2: Step-up transf­ormer
*trans­formers will not work for converting a DC voltage

Transm­ission of power (Power systems)

Power loss:
Ploss­=I­li­ne­²·R­line
Voltage drop:
Vdrop­=I­li­ne­·R­line
Iload­/I­li­ne­=N­1/N2
·almost all wires have some resistance
·as electr­icity passes through the wires, it causes them to heat up, resulting in power loss, and a decrease in the voltage that is available at the load.

High voltage transm­ission

 
·we can reduce power loss by lowering the current in the line
·we can keep the same supply power by increasing the supply voltage
·this is done using transf­ormers.
 

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