measurement procedure

problemexpres.tex

@@ -14,7 +14,7 @@ $$I = \frac U R $$
 where I is the current expressed in Amperes [A], V is the voltage, bearing the Volt units [V] and R is the electrical resistance in ohms [$\Omega$].
 
 The Ohms's law can be further expanded, to get these three quantities in relationship with \textbf{power}, such as
-$$P = IV = I^2R = \frac{V^2}R$$
+$$P = I \cdot V = I^2 \cdot R = \frac{V^2}R$$
 
 \subsection{Direct current (DC) circuits}
 Generally, Ohm's law is used on direct current (DC) circuits. A DC voltage or current has a fixed magnitude (amplitude) and a definite direction associated with it. Both DC currents and voltages are produced by power supplies, batteries, dynamos and solar cells to name a few.
@@ -23,7 +23,7 @@ We also know that DC power supplies do not change their value with regards to ti
 
 \subsection{Waveforms and alternating current (AC) circuits}
 An alternating function or AC waveform on the other hand is defined as one that varies in both magnitude and direction in more or less an even manner with respect to time making it a “bi-directional” waveform \cite{whitaker2006ac}. An AC function can represent either a power source or a signal source with the shape of an AC waveform generally following that of a mathematical sinusoid as defined by
-$$A(t) = A_{max}\,sin(2 \pi f t)$$
+$$A(t) = A_{max} \cdot sin(2 \pi f t)$$
 
 \begin{figure}[ht!]
 \centering
@@ -44,7 +44,7 @@ Alternating voltages and currents can not be stored in batteries or cells like d
 \end{itemize}
 
 
-\subsection{Power in AC circuits}
+\subsection{Power in AC circuits} \label{ss:ac_power}
 When a reactance (either inductive or capacitive) is present in an AC circuit, the Ohm's law formula does not apply and different approach must be taken to express and calculate power.
 
 \textbf{Real power} (or true power) is the power that is used to do the work on the load:
@@ -101,9 +101,12 @@ The appliances under test work on mains voltage. In Europe, the nominal voltage
 
 If not handled with care, operating or manipulating with voltage can cause permanent damage to appliance or health, or can cause fire or even death. Thus, respect, increased care and knowledge is necessary in all further practical steps involved.
 
-%\subsubsection{Measurement procedure}
-
+\subsubsection{Measurement procedure}
+With the formula for the electrical power being
+$P = I \cdot V$
+the conclusion can be made, that the procedure for measuring the electrical power produced or consumed by circuit consists of measuring the current flowing at the given voltage at the time instant and then multiplying them together. Repeating this sufficiently enough times, the power can be plotted with respect to time.
 
+However, as seen in a subsection \ref{ss:ac_power}, this procedure would measure the \textit{apparent} power, which includes the power stored in reactive elements and later returned to the circuit. To have a useful result of a measurement, the \textit{real} power is desired. Thu keeping track of the \textit{phase angle} is needed.
 
 
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