Power

Question 1

when defining v = Vm sin(ωt) what is φ when the load is purely resistive, capacitive or inductive

Answer 1

resistive φ = 0
inductive φ = 90
capacitive φ = -90

Question 2

power in a resistive circuit

Answer 2

P = IV = I^2R = V^2 / R

• power is done, no power is returned back into the system
• power period is half that of the voltage and current’s

Question 3

power in a inductive circuit

Answer 3

P_L = VI sin(2ωt)
- φ = 90
- energy absorbed = energy returned
- power period is half that of the voltage and current’s
- net flow of power over one cycle is zero

Question 4

power in a capacitive circuit

Answer 4

P_C = VI sin(2ωt)
- φ = -90
- energy absorbed = energy returned
- power period is half that of the voltage and current’s
- net flow of power over one cycle is zero

Question 5

power factor

Answer 5

F_P = P / S

cosφ = cos(v - I), where φ is the angle between v and i)
- resistor, cos φ = 1
- capacitor, cos φ = 0
- inductor, cos φ = 0

true power (P) / apparent power (s)

for real circuits cos φ is somewhere between 0 and 1

Question 6

average power

Answer 6

also know as active/real power (P), is the power that does work

P = S cos φ
units: watts (W)

Question 7

apparent power

Answer 7

(total power)

S = IV = P / cos φ = sqrt(P^2 + Q^2)
units: volt-amperes (VA)

Question 8

reactive power

Answer 8

Q = IV sin φ = I^2 X_L = sqrt(S^2 - P^2)
units: volt-amperes reactive (VAr)

When Q = Q_L + Q_C = 0, FP = 1
the portion of power that is temporarily stored (the waste), heats the wires and conductors

Question 9

I*

Answer 9

complex conjugate of I
I = 3 + j4
I* = 3 - j4

Question 10

a power factor of 0.6 lagging

Answer 10

The current lags the voltage by an angle, as the load is partially inductive

Question 11

X_L

Answer 11

= V^2 / Q = Q / I^2