el. power as phys. quantity in ac circuits

problemexpres.tex

@@ -70,7 +70,7 @@ OpenWrt is an \gls{os} (in particular, an embedded \gls{os}) based on the \Gls{l
 
 OpenWrt is configured using a command-line \gls{interface} (ash \gls{shell}), or a web \gls{interface} (LuCI). There are about 3500 optional \gls{sw} packages available for installation via the opkg package management \gls{system}.
 
-\subsubsection{Components of the OpenWRT}
+\subsection{Components of the OpenWRT}
 The main components are the \Gls{linux} \gls{kernel}, \texttt{util-linux-ng}, \texttt{uClibc} and \texttt{BusyBox}. The \Gls{linux} \gls{kernel} was already mentioned. \texttt{util-linux-ng} is self explanatory - it is a set of \gls{linux} utilities.
 
 \texttt{BusyBox} is a software that provides several stripped-down \Gls{unix} tools in a single executable file. It runs in a variety of \gls{posix} environments such as \Gls{linux}, \Gls{android}, \gls{bsd} family and others, such as proprietary \glspl{kernel}, although many of the tools it provides are designed to work with \glspl{interface} provided by the \Gls{linux} \gls{kernel}.
@@ -200,13 +200,34 @@ $$P = \frac Et$$
 where P is the electric power in watt (W), E is the energy consumption in joule (J) and 
 t is the time in seconds (s).
 \subsubsection{In resistive circuits}
-In the case of resistive (Ohmic, or linear) loads, Joule's law can be combined with Ohm's law (V = I·R) to produce alternative expressions for the amount of power that is dissipated:
+In the case of purely resistive (Ohmic, or linear) loads, Joule's law can be combined with Ohm's law (V = I·R) to produce alternative expressions for the amount of power that is dissipated:
 $$P = IV = I^2R = \frac{V^2}R$$
-where R is the electrical resistance.
+where R is the electrical resistance in ohms ($\Omega$).
 
 \subsubsection{In alternating current (AC) circuits}
+When a reactance (either inductive or capacitive) is present in an AC circuit, the previous formula does not apply. The product of voltage and current is, instead, expressed in volt-amperes (VA). This product is known as
+the \textit{apparent power}.
 
+\textbf{Real power} (or true power) is the power that is used to do the work on the load:
+$$P = V_{rms}I_{rms}\,cos\,\varphi$$
+where P is the real power in watts (W), $V_{rms}$ is the RMS voltage, defined as $V_{peak}/\sqrt{2}$ in Volts (V), $I_{rms}$ is the RMS current, defined as $I_{peak}/\sqrt{2}$ in Amperes (A) and $\varphi$ is the impedance phase angle - phase difference between voltage and current.
 
+\textbf{Reactive power} on the other hand, is the power that is wasted and not used to do work on the load. Curiously, it is defined as 
+$$Q = V_{rms}I_{rms}\,sin\,\varphi$$
+with $Q$ being the reactive power in volt-ampere-reactive (VAR).
+
+\textbf{Apparent power} is the power that is supplied to the circuit. Definition:
+$$S = V_{rms}I_{rms}$$
+where the unit of apparent power $S$ is volt-ampere (VA). It can be seen that it is not phase-angle dependent.
+
+The relation all these three quantities are in is defined as 
+$$ P^2 + Q^2 = S^2 $$
+however, again, nothing in the real world is perfect, and this relation only applies for a perfectly sinusoidal waveforms.
+
+
+
+
+\subsection{Power factor}
 
 
 \subsection{Measuring electric power with a microcontroller}

tukethesis.bib

@@ -59,4 +59,13 @@
   publisher={O'Reilly Media}
 }
 
+@book{whitaker2006ac,
+  title={AC Power Systems Handbook, Third Edition},
+  author={Whitaker, J.C.},
+  isbn={9781420005813},
+  series={Electronics Handbook Series},
+  url={https://books.google.sk/books?id=a988UyrJttYC},
+  year={2006},
+  publisher={CRC Press}
+}