Intro to Electrical Engineering
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Volt
Work per unit charge  (difference in potential energy)
V = 1J/C = (1 kg·m^{2}/s^{2})/C
V = IR

Coulomb
Measure of charge
1C = 1 A*s

Joule
Work to move 1 Newton 1 meter.
1J = 1 kg·m2/s2

Resistance
Measure opposition to the passage of current.
R=l/σA

Power (P)
 P = VI
 = I^{2}R
 = V^{2}/R

Charge for Electron
q_{e} = 1.602*10^{19} C

Charge for Proton
qe = 1.602*10^{19} C

Electric Current
i = Δq/ΔT
units: 1C/s

Kirchoff's Current Law
charge is conserved
i = i_{0} + i_{1 }+ i_{n}

Ohm's Law
V = IR
Conductance
I=GV G: element

Equivalent series resistance
Resistors appear as a single equivalent resistance of value R_{eq}.
R_{eq} = R_{1} + R_{2} + R_{3}

Voltage Divider
When source voltage is divided among the resistors.
V_{n} = (R_{n}/(R_{1} + R_{2} + R_{n})) x v_{s}

In Series
Circuit elements are in series when identical current flows through each element.

In Parallel
Circuit elements are in parallel when identical voltage flows through each element.

Max current
i_{s} = V_{s}/r_{s}
r_{s }: resistance


Short Circuit
Circuit element with resistance approaching zero.
R = 0

Open Circuit
Circuit element with resistance approaching infiinty.
R = infinity

Loop
any closed connection of branches.

Mesh
A loop that does not contain other loops.

Node Voltage Method
i = (v_{a}v_{b})/R

Principle of Superposition
i = (v_{B1} + v_{B2})/R

Thevenin Equivalent Circuit
Represented by voltage source v_{T} in series with R_{T} (equibalent resistance).

Norton Equivalent Circuits
Represented by voltage current source i_{N} in parrallel with R_{N}.

Method for solving Thevenin & Norton Req.
 1. Remove load
 2. Zero all independent voltage and current sources
 3. Compute total resistance with load removed
R
_{T} = R
_{N}

Method to compute Thevenin voltage
 1. Remove the load
 2. Define v_{OC} across the open load termnials
 3. Apply any circuit analysis to solve v_{OC}
 4. The Thevenin voltage is vT = v_{OC}
Thevenin voltage is v_{T} = v_{OC}

Method to solve Norton Current
 1. Replace the load with a shortcircuit
 2. Define the shortcircuit current i_{SC} = i_{N}
 3. Apply any method to solve i_{SC}
 4. Therefore i_{N} = i_{SC}
Norton current = shortcircuit current

Ideal Capacitors
Q = CV
units : Farad > C/V

Capacitors in parallel
C_{eq} = C_{1} + C_{2} + C_{3}

Capacitors in series
1/(1/C_{1} + 1/C_{2} + 1/C_{3})

Periodic Signal Waveform
x(t) = x(t + nT) , n = 1,2,3

Sinusoidal Waveforms
x(t) = Acos(ωt) & Acos(ωt + Φ)


phase shift
Asin(ωt) = Acos(ωt  π/2)


Impedance of a resistor
ZR(jω) = VS(jω) / I(jω) = R

Impedance of an inductor
ZL(jω) = VS(jω) / I(jω)= ωL∠π/2 = jωL

Impedance of a capacitor
 ZC(jω) = VS(jω) / I(jω)= 1ωC∠−π/2=−j / ωC
 = 1 / jωC

the impedance of a circuitelement
Z(jω) = R(jω) + jX(jω)

Circuit law for a capacitor.
i(t) = C*(dv(t) / dt)

Energy stored in a capacitor (J)
W_{C}(t) = 1/2*Cv^{2}_{C}(t)

Voltage in an inductor.
v_{L}(t) = L*(di_{L} / dt) units : 1 H = 1 Vs/A
Inductors in series add. Inductors in parallel combine according to thesame rules used for resistors connected in parallel.

Energy stored in an inductor (J)
W_{L}(t) = 1/2*(Li^{2}_{L}(t))


Ae^{jθ} =
Acos θ + jAsin θ = A∠θ

Energy stored in steady state Capacitor
Energy stored in steady state Inductor
(1/2)*C*V^{2}
(1/2)*L*V^{2}
^{ }