Phasors

Question 1

What is the current-voltage relationship for a resistor?

Answer 1

V = IR

Question 2

What is the current-voltage relationship for an inductor?

Answer 2

V = L × di / dt

Question 3

What is the current-voltage relationship for a capacitor?

Answer 3

i = C × dv / dt

Question 4

What is the impedance equation for an inductor?

Answer 4

X_L = ωL

Question 5

What is the impedance equation for a capacitor?

Answer 5

X_C = 1 / ωC

Question 6

How is the magnitude of V determined for a circuit with complex impedances and resistances?

Answer 6

V = √(V_R² + V_X²)

Question 7

How is the magnitude of Z determined for a circuit with complex impedances and resistances?

Answer 7

Z = √(R² + X²)

Question 8

What is the equation to calculate the magnitude of the phase difference?

Answer 8

ϕ = tan^-1 (X / R)

ϕ = tan^-1 (V_X / V_R)

Question 9

What is the complex impedance of an inductor?

Answer 9

Z = jωL

Question 10

What is the complex impedance of a capacitor?

Answer 10

Z = -j / ωC

Question 11

What is the phase difference for a purely resistive circuit? Does it lag or lead?

Answer 11

I in phase with V

Question 12

What is the phase difference for a purely inductive circuit? Does it lag or lead?

Answer 12

I lags V by 90°

Question 13

What is the phase difference for a purely capacitive circuit? Does it lag or lead?

Answer 13

I leads V by 90°

Question 14

What is the phase difference for an RL circuit? Does it lag or lead?

Answer 14

I lags V by < 90°

Question 15

What is the phase difference for an RC circuit? Does it lag or lead?

Answer 15

I leads V by < 90°

Question 16

What is the equation for instantaneous power?

Answer 16

P(t) = v(t)i(t)

Question 17

What is the equation for average power?

Answer 17

P_avg = 1 / T ∫₀^T(v(t) × i(t))dt

Question 18

How do you calculate RMS? Use X as the example

Answer 18

X_rms = √[1/T × ∫₀^T] (X²)dt ]

Question 19

What is the unit and symbol for active power?

Answer 19

Unit: Watt (W)

Symbol: P

Question 20

What is the unit for reactive power?

Answer 20

Unit: VAR

Symbol: Q

Question 21

What is the unit for apparent power?

Answer 21

Unit: VA

Symbol: S

Question 22

What is the equation for power when there is just a capacitor in the circuit? What type of power is it?

Answer 22

It is purely reactive power.

Q = V² / 2X_C

Question 23

What is the equation for power when there is just an inductor in the circuit? What type of power is it?

Answer 23

It is purely reactive power. Q = V² / 2X_L

Question 24

What is the equation to calculate active power from apparent power?

Answer 24

Active Power = Apparent Power × Power Factor

Question 25

What is the equation to calculate apparent power?

Answer 25

S = P + Qj |S| = √(P² + Q²)

Question 26

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)

Answer 26

[Picture8]

Question 27

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)

Answer 27

Max active = VIcos(ϕ) Max reactive = VIsin(ϕ)

Question 28

What is the equation for the power factor?

Answer 28

PF = P / |S|

Question 29

What is the equation for the power factor in terms of the first harmonic of current?

Answer 29

PF = (I₁ / I)cos(ϕ₁)

Question 30

What is the equation for the displacement power factor?

Answer 30

DPF = cos(ϕ)

Question 31

What is the equation for the power factor?

Answer 31

PF = (I₁ / I)DPF