Power in RLC Circuits

Question 1

What is the equation for resistive power of an AC circuit?

Answer 1

P = iv
P = Vsin(ωt)Isin(ωt)
P = (V^2/R)((1-cos(2ωt))/2)

Question 2

How does voltage and current vary in an AC circuit with just resistive components?

Answer 2

They vary sinusoidally in phase

Question 3

What is the equation for reactive power of an AC circuit for a capacitor?

Answer 3

P = iv
P = Vsin(ωt)Icos(ωt)
P = (IV/2)sin(2ωt)
P = (V^2/2Xc)sin(2ωt)

Question 4

Prove I = V/Xc

Answer 4

I = V/Z
Z = 1/jωC
I = V/(1/jωC)
I = V/(-j/ωC)
I = V/-jXc
I = V/Xc

Question 5

What is the equation for the peak reactive power of a capacitor?

Answer 5

Q = V^2/2Xc

Question 6

For an AC circuit with a capacitor, who leads who?

Answer 6

Current leads voltage

Question 7

What is the equation for reactive power of an inductor?

Answer 7

P = iv
P = Vsin(ωt)(-Icos(ωt))
P = (IV/2)(-sin(2ωt))
P = -(V^2/2Xl)sin(2ωt)

Question 8

Prove I = V/Xl

Answer 8

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Question 9

What is the equation for the peak reactive power of an inductor?

Answer 9

Q = V^2/2Xl

Question 10

For an AC circuit with a capacitor, who leads who?

Answer 10

Current leads Voltage

Question 11

What is the equation for calculating power in an RC circuit?

Answer 11

P = iv
P = Vsin(ωt)Isin(ωt + ϕ)
P = (IV/2)[cos(ϕ) - cos(2ωt + ϕ)]

Question 12

How is the phase angle calculated for an RC circuit?

Answer 12

ϕ = tan^-1(Xc/R)

Question 13

What is the equation for calculating power in an RL circuit?

Answer 13

P = iv
P = Vsin(ωt)Isin(ωt + ϕ)
P = (IV/2)[cos(ϕ) - cos(2ωt + ϕ)]

Question 14

How is the phase angle calculated for an RL circuit?

Answer 14

ϕ = - tan^-1(Xl/R)

[REMEMBER THE NEGATIVE SIGN]

Question 15

What is active power? What are its other names, its symbol, and units?

Answer 15

This is the power that the circuit dissipates.
Symbol: P
Unit: Watts, W

Question 16

What are the 2 equation to calculate active power?

Answer 16

P = IV
P = Apparent power × Power factor

Question 17

What is reactive power? What is its symbol and units?

Answer 17

This is the power that is not dissipated by the circuit but is transferred between components.
Symbol: Q
Unit: var (VAreactive)

Question 18

What is apparent power?

Answer 18

This is the combination of active and reactive power.

It is complex because of both the active and reactive component.

Question 19

What is the symbol and unit for apparent power?

Answer 19

Symbol: S
Unit: VA (VoltAmpere)

Question 20

What are the equations to calculate apparent power?

Answer 20

S = P + jQ
S = V × I*

Question 21

What is the equation for power factor?

Answer 21

Power factor = Real power/Apparent power