AC Circuit Analysis (4)

Question 1

How do we work out the power in a purely reactive load? What is that power called?

Try to give the equation

Answer 1

Note:
* The power is called active power, R.
* This power is found using the normal P = IV. (I and V being r.m.s values)
* This power is energy dissipated (i.e. like electrical to thermal in a resistor).
* You can see how you can go from instantaneous values of current and voltage, to work out instantaneous power and then to average power.
* See how average power is quite simple as both V and I are in phase and thus so is power. It will never drop below 0.

Question 2

How do we work out the power in a purely inductive load? What is that power called?

Try to give the equation

Answer 2

Note:
* The power is called reactive power, Q.
* This power has units VAR, and is really the measure of power being sent back and forth in the circuit. With on average no energy loss.
* Reactive power, QL (L for inductor) = I^2 XL = V^2 / XL.
* You can see how its derived from instantaneous values to average.
* See how the current and voltage is out of phase for a Inductor, so the power phase is different. Also, no the power goes above and below zero. So the average power = 0.
* We say that inductors ‘absorb’ reactive power. That is why QL is positive to show its being ‘used up’.

Question 3

How do we work out the power in a purely capacitive load? What is that power called?

Try to give the equation

Answer 3

Note:
* The power is called reactive power, Q.
* This power has units VAR, and is really the measure of power being sent back and forth in the circuit. With on average no energy loss.
* Reactive power, Qc (C for inductor) = -I^2 XC = -V^2 / XL.
* You can see how its derived from instantaneous values to average.
* See how the current and voltage is out of phase for a Inductor, so the power phase is different. Also, no the power goes above and below zero. So the average power = 0.
* We say that capacitors ‘generate’ reactive power. That is why Qc is negative to show its being ‘created’ instead of used.

Question 4

What is the active and reactive power equations for R,L and C components?

Answer 4

Question 5

What is the Complex power equation? And thus from that the two equations for apparent power, S?

Answer 5

Complex power, S, is the combined complex number of both the active (real) and reactive power (imaginary).

• Apparent power is the magnitude of complex power, shown below. We can also find its equation mathmatically using Voltage complex phasor and the conjugate of current complex phase (see conjugate meaning below if confused).

Question 6

How can we correct power factor, PF, if too high?

Answer 6

• As most loads are inductive, which ‘absorb’ reactive power. We need a ‘generator’ to produce power to reduce the reactive power used.
• This is done by adding a capacitor to the inductive load.
• We can see how the capaictors reactive power cancels out some of the total reactive power in the power triangle.

Question 6

What is power factor, PF, and its equation?

Answer 6

• Power factor is defined as the active power over apparent power. This essentailly refers to the ratio of power that is being dissapated, against power that is being provided in total.
• PF = P/S = cosΦ
• A high power factor is better, for reasons listed below.

Question 7

What does a power triangle look like?

Answer 7

Note:
* S = apparent power
* Q = reactive power
* P = active power