Electrical Power, in a circuit is the amount of energy that is absorbed or produced within the circuit. A source of energy such as a voltage will produce or deliver power while the connected load absorbs it. Light bulbs and heaters for example, absorb electrical power and convert it into heat or light. The higher their value or rating in watts the more power they will consume.
\subsection{Ohm's law}
Ohm's Law deals with the relationship between voltage and current in an ideal conductor. This relationship states that: The potential difference (voltage) across an ideal conductor is proportional to the current through it. The constant of proportionality is called the \textit{resistance}.
Ohm's Law deals with the relationship between voltage and current in an ideal conductor. This relationship states that: The potential difference (voltage) across an ideal conductor is proportional to the current through it\cite{henry2008ohm}. The constant of proportionality is called the \textit{resistance}.
$$I =\frac U R $$
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 power, such as
The Ohms's law can be further expanded, to get these three quantities in relationship with \textbf{power}, such as
$$P = IV = I^2R =\frac{V^2}R$$
\subsection{Direct current (DC) circuits}
@ -21,8 +21,31 @@ Generally, Ohm's law is used on direct current (DC) circuits. A DC voltage or cu
We also know that DC power supplies do not change their value with regards to time, they are a constant value flowing in a continuous steady state direction. In other words, DC maintains the same value for all times and a constant uni-directional DC supply never changes or becomes negative unless its connections are physically reversed.
\subsection{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 \gls{voltage} and \gls{current} is, instead, expressed in volt-amperes (VA). This product is known as the \textit{apparent power}.
\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
\caption{The common types of waveforms visualised as a function of amplitude}\label{f:waveforms}
\end{figure}
The term AC or to give it its full description of Alternating Current, generally refers to a time-varying waveform with the most common of all being called a \textbf{Sinusoid} better known as a \textbf{Sinusoidal Waveform}. Sinusoidal waveforms are more generally called by their short description as \textbf{Sine Waves}. Sine waves are by far one of the most important types of AC waveform used in electrical engineering.
This means then that the AC waveform is a “time-dependent signal” with the most common type of time-dependant signal being that of the Periodic Waveform. The periodic or AC waveform is the resulting product of a rotating electrical generator. Generally, the shape of any periodic waveform can be generated using a fundamental frequency and superimposing it with harmonic signals of varying frequencies and amplitudes but that is out of the waveform fundamentals theory
Alternating voltages and currents can not be stored in batteries or cells like direct current (DC) can, it is much easier and cheaper to generate these quantities using alternators or waveform generators when they are needed. The type and shape of an AC waveform depends upon the generator or device producing them, but all AC waveforms consist of a zero voltage line that divides the waveform into two symmetrical halves. The main characteristics of an AC waveform are defined as:
\begin{itemize}
\item the \textbf{period (T)} is the length of time in seconds that the waveform takes to repeat itself from start to finish. This can also be called the Periodic Time of the waveform for sine waves, or the Pulse Width for square waves
\item the \textbf{frequency} is the number of times the waveform repeats itself within a one second time period. Frequency is the reciprocal of the time period, defined as $f =\frac1 T$, with the unit of frequency being the Hertz [Hz]
\item the \textbf{amplitude} is the magnitude or intensity of the signal waveform
\end{itemize}
\subsection{Power in AC circuits}
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:
$$P = V_{RMS}I_{RMS}\,cos\,\varphi$$
@ -38,9 +61,9 @@ where the unit of apparent power $S$ is volt-ampere (VA). It can be seen that it
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.
however, again, nothing in the real world is perfect, and this relation only applies for a perfectly \textbf{sinusoidal waveforms}!
\subsubsection{Phasor}
\subsection{Phasor}
A phasor is a constant complex number representing the complex amplitude (magnitude and phase) of a sinusoidal function of time. It is usually expressed in exponential form. Phasors are used in engineering to simplify computations involving sinusoids, where they can often reduce a differential equation problem to an algebraic one. The origin of the word phasor comes from phase + vector.
Phasor is a vector that represents a sinusoidally varying quantity, as a current or voltage, by means of a line rotating about a point in a plane, the magnitude of the quantity being proportional to the length of the line and the phase of the quantity being equal to the angle between the line and a reference line.
@ -53,10 +76,10 @@ Phasor is a vector that represents a sinusoidally varying quantity, as a current
\subsection{Measuring the electric power}
Measuring the electric power makes most sense on the customer appliances. The first reason is, that they generally consume power that is purchased on contract. The energetic company measures all the power used up by the end customer, but customer has no easy way to see how much and how \textit{effectively} is power used by the appliances. The second important reason is that the appliances has a standardised connector (plug) that is guaranteed to fit in all the area using it, which is not a case for example on battery powered devices (batteries has different sizes, connectors and general properties.
When it comes to measuring the electrical power, the first and the most important thing to discuss is safety. Only after all the safety precautions had been made clear, the theory can be clarified and subsequently, the practice can be applied. The chapter focuses solely on the first two topics.
When it comes to measuring the electrical power, the first and the most important thing to discuss is safety. Only after all the safety precautions had been made clear, the theory can be clarified and subsequently, the practice can be applied.
\subsection{Voltage ranges and safety disclaimer}
\subsubsection{Voltage ranges and safety disclaimer}
The \gls{iec} international standard \textbf{IEC 60038:1983} defines a set of standard \glspl{voltage} for use in AC electricity supply systems.
\begin{table}[ht!]
@ -78,6 +101,9 @@ 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.
Peter Babič
9 years ago