Fix the power factor and phase angle relation

The power factor and the phase angle was unclearly related.
This problem was fixed by removing the problematic formula,
reformulating surrounding sentences and adding the citation
to support the fact.

problemexpres.tex

@@ -76,16 +76,16 @@ Phasor is a vector that represents a sinusoidally varying quantity, as a current
 
 Considering the figure \ref{f:ph_diff}, the voltage waveform above starts at zero along the horizontal reference axis, but at that same instant of time the current waveform is still negative in value and does not cross this reference axis until 30\textdegree  later. Then there exists a Phase difference between the two waveforms as the current cross the horizontal reference axis reaching its maximum peak and zero values after the voltage waveform.
 
-As the two waveforms are no longer \textit{in-phase}, they must therefore be \textit{out-of-phase} by an amount determined by phi, $\varphi$ and in our example this is 30\textdegree. It can now be said, that the two waveforms are now 30\textdegree  out-of phase. The current waveform can also be said to be \textit{lagging} behind the voltage waveform by the phase angle $\varphi$. This angle represents the phase shift (also called phase difference) between two sinusoids \cite{maxfield2011electrical}.
+As the two waveforms are no longer \textit{in-phase}, they must therefore be \textit{out-of-phase} by an amount determined by phi, $\varphi$. The waveform of the current can also be said to be \textit{lagging} behind the voltage waveform by the phase angle $\varphi$. This angle represents the phase shift (also called phase difference) between two sinusoids \cite{maxfield2011electrical}.
 
 \subsection{Power factor and power factor correction}
 The power factor is just a specific name for a phase shift between the sinusoids of a current and voltage. So the figure \ref{f:ph_diff} in fact shows the power factor. However, it is not expressed in a plane angle, but rather as a dimensionless number between -1 and 1.
 
-The power factor is defined as $\frac{P}{S}$, as a ratio of the real power over the apparent power. If $\varphi$ is the phase angle between the current and voltage, then the power factor is equal to the cosine of the angle, $cos\,\varphi$:
-$$|P| = |S|\,\cdot\,cos\,\varphi$$
-If the power factor is 1, it means that current flows only through purely resistive components. This is the best possible outcome. A positive power factor indicates that the current flow is altered by a reactive components. The lower the factor, the higher the effect. A negative power factor means that the device, considered to be power load is in fact a power source (produces more power than consumes).
+The power factor is defined as $\frac{P}{S}$, as a ratio of the real power over the apparent power\cite{dixit2010electrical}. If $\varphi$ is the phase angle between the current and voltage, then the power factor is equal to the cosine of the angle, $cos\,\varphi$.
 
-Now why is power factor important? Every device with a power factor other than 1 returns some power back to the transmission line. Since the transmission lines does have some resistance, this returned power translates to some wasted power in a form of heat. Energetic companies want to minimise the power wasted in the transmission lines to increase their profit, so numerous laws are coming into effect to correct \cite{singh2008electric} (increase) the power factor.
+If the power factor is 1, it means that all the supplied power is completely consumed by purely resistive load. A positive power factor that is lower than 1 indicates that some power is not consumed by the load and is returned back. The lower the factor, the more power is returned. When power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns to the source on each cycle. A negative power factor means that the device, considered to be power load is in fact a power source (produces more power than consumes).
+
+How can this information be useful? Every load with a power factor other than 1 returns some power back to the transmission line. Since the transmission lines does have some resistance, this returned power translates to some wasted power in a form of heat. Energetic companies want to minimise the power wasted in the transmission lines to increase their profit, so numerous laws are coming into effect to correct \cite{singh2008electric} (increase) the power factor.
 
 
 

tukethesis.bib

@@ -148,4 +148,13 @@
   pages={209}
 }
 
+@book{dixit2010electrical,
+  title={Electrical Power Quality},
+  author={Dixit, J.B. and Yadav, A.},
+  isbn={9789380386744},
+  url={https://books.google.sk/books?id=lxLWYe5sGMsC},
+  year={2010},
+  publisher={Laxmi Publications Pvt Limited},
+  pages={80--81}
+}