Phasors Flashcards
What is the current-voltage relationship for a resistor?
V = IR
What is the current-voltage relationship for an inductor?
V = L × di / dt
What is the current-voltage relationship for a capacitor?
i = C × dv / dt
What is the impedance equation for an inductor?
XL = ωL
What is the impedance equation for a capacitor?
XC = 1 / ωC
How is the magnitude of V determined for a circuit with complex impedances and resistances?
V = √(VR2 + VX2)
How is the magnitude of Z determined for a circuit with complex impedances and resistances?
Z = √(R2 + X2)
What is the equation to calculate the magnitude of the phase difference?
ϕ = tan-1 (X / R)
ϕ = tan-1 (VX / VR)
What is the complex impedance of an inductor?
Z = jωL
What is the complex impedance of a capacitor?
Z = -j / ωC
What is the phase difference for a purely resistive circuit? Does it lag or lead?
I in phase with V
What is the phase difference for a purely inductive circuit? Does it lag or lead?
I lags V by 90°
What is the phase difference for a purely capacitive circuit? Does it lag or lead?
I leads V by 90°
What is the phase difference for an RL circuit? Does it lag or lead?
I lags V by < 90°
What is the phase difference for an RC circuit? Does it lag or lead?
I leads V by < 90°
What is the equation for instantaneous power?
P(t) = v(t)i(t)
What is the equation for average power?
Pavg = 1 / T ∫0T(v(t) × i(t))dt
How do you calculate RMS? Use X as the example
Xrms = √[1/T × ∫0T] (X2)dt ]
What is the unit and symbol for active power?
Unit: Watt (W)
Symbol: P
What is the unit for reactive power?
Unit: VAR
Symbol: Q
What is the unit for apparent power?
Unit: VA
Symbol: S
What is the equation for power when there is just a capacitor in the circuit? What type of power is it?
It is purely reactive power.
Q = V2 / 2XC
What is the equation for power when there is just an inductor in the circuit? What type of power is it?
It is purely reactive power. Q = V2 / 2XL
What is the equation to calculate active power from apparent power?
Active Power = Apparent Power × Power Factor
What is the equation to calculate apparent power?
S = P + Qj
|S| = √(P2 + Q2)
What is the power equation (where active and reactive power are separated) for the current and voltage waveforms:
v(t) = √2 × Vsin(ωt)
i(t) = √2 × Isin(ωt - ϕ)
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What is the max active and max reactive power for the current and voltage waveforms:
v(t) = √2 × Vsin(ωt)
i(t) = √2 × Isin(ωt - ϕ)
Max active = VIcos(ϕ)
Max reactive = VIsin(ϕ)
What is the equation for the power factor?
PF = P / |S|
What is the equation for the power factor in terms of the first harmonic of current?
PF = (I1 / I)cos(ϕ1)
What is the equation for the displacement power factor?
DPF = cos(ϕ)
What is the equation for the power factor?
PF = (I1 / I)DPF