# Complex Power: $S = V \cdot I^*$ OR $S = \frac{V \cdot I^*}{2}$. Which formula is correct?

Different examples and videos have shown that: $$P_{complex} = V \cdot I^*$$

However, my textbook shows: $$S = \frac{V \cdot I^*}{2}$$

My professor has even using $$\S = V \cdot I^*\$$ himself during an example problem, yet other problems were solved using the other formula. Which formula is correct or, if both are correct, what circumstances do you use either formula?

• Use MathJax to express formulas. Like this $S=V\cdot I$ Which is the correct answer. Apr 20, 2020 at 20:58

Both answers are correct, it's simply a matter of what $$\V\$$ and $$\I\$$ are supposed to represent. If they are the RMS value of voltages and current, then complex power is $$\|S|=V\times I\$$. If they instead represent a voltage amplitude (i.e. $$\v(t)=V\cos(...)\$$ and $$\i(t)=I\cos(...)\$$), then you must first take the RMS value by dividing amplitude by square root of 2. This leaves you with $$\|S|=\frac{V}{\sqrt{2}}\times\frac{I}{\sqrt{2}}=\frac{V\times I}{2}\$$.

Well according to Fundamentals of Electric Circuits 5th ed Alexander/Sadiku, they define complex power as S=Vrms x Irms. However when they use peak values of V and I then the complex power is S=(V x I*)/2 using the fact that Vrms=V/sqrt(2) and Irms=I/sqrt(2). Perhaps your professor is using rms values and the book uses peak values.

S = Vrms * Irms

OR

S= Vp * Ip / 2

Where Vrms and Irms stands for root mean square values of voltage and current

And Vp and Ip stands for peak values of voltage and current.