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Work per unit charge - (difference in potential energy)
V = 1J/C = (1 kg·m2/s2)/C
V = IR
Measure of charge
1C = 1 A*s
Work to move 1 Newton 1 meter.
1J = 1 kg·m2/s2
Measure opposition to the passage of current.
Charge for Electron
qe = -1.602*10-19 C
Charge for Proton
qe = 1.602*10-19 C
i = Δq/ΔT
Kirchoff's Current Law
charge is conserved
i = i0 + i1 + in
V = IR
I=GV G: element
Equivalent series resistance
Resistors appear as a single equivalent resistance of value Req.
Req = R1 + R2 + R3
When source voltage is divided among the resistors.
Vn = (Rn/(R1 + R2 + Rn)) x vs
Circuit elements are in series when identical current flows through each element.
Circuit elements are in parallel when identical voltage flows through each element.
is = Vs/rs
rs : resistance
Circuit element with resistance approaching zero.
R = 0
Circuit element with resistance approaching infiinty.
R = infinity
any closed connection of branches.
A loop that does not contain other loops.
Node Voltage Method
i = (va-vb)/R
Principle of Superposition
i = (vB1 + vB2)/R
Thevenin Equivalent Circuit
Represented by voltage source vT in series with RT (equibalent resistance).
Norton Equivalent Circuits
Represented by voltage current source iN in parrallel with RN.
Method for solving Thevenin & Norton Req.
- 1. Remove load
- 2. Zero all independent voltage and current sources
- 3. Compute total resistance with load removed
Method to compute Thevenin voltage
Thevenin voltage is vT = vOC
- 1. Remove the load
- 2. Define vOC across the open load termnials
- 3. Apply any circuit analysis to solve vOC
- 4. The Thevenin voltage is vT = vOC
Method to solve Norton Current
Norton current = short-circuit current
- 1. Replace the load with a short-circuit
- 2. Define the short-circuit current iSC = iN
- 3. Apply any method to solve iSC
- 4. Therefore iN = iSC
Q = CV
units : Farad -> C/V
Capacitors in parallel
Ceq = C1 + C2 + C3
Capacitors in series
1/(1/C1 + 1/C2 + 1/C3)
Periodic Signal Waveform
x(t) = x(t + nT) , n = 1,2,3
x(t) = Acos(ωt) & Acos(ωt + Φ)
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)
WC(t) = 1/2*Cv2C(t)
Voltage in an inductor.
vL(t) = L*(diL / dt) units : 1 H = 1 V-s/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)
WL(t) = 1/2*(Li2L(t))
Acos θ + jAsin θ = A∠θ
Energy stored in steady state Capacitor
Energy stored in steady state Inductor