1. Lecture 20. AC Power Analysis
Dr. Holbert
F06-Lect1
Lecture 20. AC Power Analysis
Instantaneous power
Average power
RMS
Examples
EEE 202

2. Instantaneous Power: p(t)
For AC circuits, the voltage and current are
v(t) = VM cos(t+v)
i(t) = IM cos(t+i)
The instantaneous power is simply their product
p(t) = v(t) i(t) = VM IM cos(t+v) cos(t+i)
= ½VM IM [cos(v- i) + cos(2t+v +i)]
Constant
Term
Wave of Twice Original Frequency

3. Average Power (P)
Calculate average power (integrate power over one cycle and divide by period)
Recall that passive sign convention says:
P > 0, power is being absorbed
P < 0, power is being supplied

4. Average Power: Special Cases
Purely resistive circuit: P = ½ VM IM
The power dissipated in a resistor is
Purely reactive circuit: P = 0
Capacitors and inductors are lossless elements and absorb no average power
A purely reactive network operates in a mode in which it stores energy over one part of the period and releases it over another part

5. Average Power Summary
Does the expression for the resistor power look identical to that for DC circuits?

6. Effective or RMS Values
Root-mean-square value (formula reads like the name: rms)
For a sinusoid: Irms = IM/2
For example, AC household outlets are around 120 Volts-rms

7. Why RMS Values?
The effective/rms current allows us to write average power expressions like those used in dc circuits (i.e., P=I²R), and that relation is really the basis for defining the rms value
The average power (P) is

8. Dr. Holbert
F06-Lect19
RMS in Everyday Life
When we buy consumer electronics, the faceplate specifications provide the rms voltage and current values
For example, what is the rms current for a 1200 Watt hairdryer (although there is a small fan in a hairdryer, most of the power goes to a resistive heating element)?
What happens when two hairdryers are turned on at the same time in the bathroom?
How can I determine which uses more electricity---a plasma or an LCD HDTV?
Answer: P = I V, so I = 1200 W / 120 Vrms = 10 Arms
EEE 202

9. Class Examples
Drill Problems P8-10, P8-11, P8-12