Difference between revisions of "Ohm's Law"

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* [http://www.youtube.com/watch?v=VPVoY1QROMg&feature=relmfu The Resistor (by MAKE magazine)]
 
* [http://www.youtube.com/watch?v=VPVoY1QROMg&feature=relmfu The Resistor (by MAKE magazine)]
  
=== Reference Material ===
+
===Reference Material===
 +
* Horowitz & Hill, ''The Art of Electronics, 2nd Ed.'', Ch. 1
  
===Reference Material===
 
 
<latex>
 
<latex>
 
\documentclass[11pt]{article}
 
\documentclass[11pt]{article}
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\section*{Ohm's Law}
 
\section*{Ohm's Law}
 +
\begin{equation}
 +
V=IR,
 +
\end{equation}
 +
where $V$ is voltage, measured in Volts ($V$), with typical values ranging from $mV$ (into an oscilloscope) to $kV$ (power lines, severe arcing danger); $I$ is current, measured in Amperes ($A$), typical values ranging from $mA$ (relatively safe for bench-top work) to $A$ (very dangerous); $R$ is resistance, measured in Ohms ($\Omega$), typical values ranging from $\Omega$ (power resistors dissipating a lot of power) to $M\Omega$ (almost a no-connect).
 +
 +
\section*{Resistor}
 +
 +
\begin{figure}
 +
\includegraphics[width=1in]{resistor.jpg}
 +
\caption{A typical (330$\Omega$) resistor}
 +
\end{figure}
 +
 +
A resistor resists the flow of electrons, such that a potential (i.e. voltage) is required to produce a current, as described by Ohm's Law above.  If we imagine electric current flowing as water, a resistor would be a narrow pipe.  The higher the resistance, the narrower the pipe, and the harder you will have to push to get a liter-per-second of water through it.  As per all electronic components, resistors dissipate energy as heat according to the equation:
 +
\begin{equation}
 +
P=IV
 +
\end{equation} 
 +
 +
\subsection*{Resistors in Series}
 +
Resistors in series add because, in the pipe analogy used above, all the water has to go through all of the pipes, and they all contribute drag:
 +
 +
\begin{figure}
 +
\includegraphics[width=1in]{resistor_series.png}
 +
\caption{Resistors in series}
 +
\end{figure}
 +
 +
\begin{equation}
 +
R = R_1 + R_2 + \dots + R_n
 +
\end{equation}
 +
 +
\subsection*{Resistors in Parallel}
 +
Resistors in parallel add reciprocally.  In the pipe analogy, water has a choice of which pipe to flow through, and the bulk of the water will be carried by the widest pipe (or for electrons, the lowest-value resistor).  Having more paths to choose from will always always reduce drag, but a thin straw next to a firehose isn't going to do much:
 +
 +
\begin{figure}
 +
\includegraphics[width=1in]{resistor_parallel.png}
 +
\caption{Resistors in parallel}
 +
\end{figure}
 +
 +
\begin{equation}
 +
R = \frac1{\frac1{R_1} + \frac1{R_2} + \dots + \frac1{R_n}}
 +
\end{equation}
 +
 +
\subsection*{Reading Resistor Values}
 +
 +
\begin{figure}
 +
\includegraphics[width=2in]{resistor_bands.png}
 +
\caption{Color band locations on resistors}
 +
\end{figure}
 +
 +
Resistor values are often encoded on the component using colors.  For determining the value of a resistor in Ohms, place the component with the triplet of color bands on the left side, and then read from left to right.  For the resistor above, we have red-violet-green.
 +
 +
\begin{figure}
 +
\includegraphics[width=6in]{color_chart.png}
 +
\caption{Matching colors to values}
 +
\end{figure}
 +
 +
Match each color with a digit using the chart above (I remember it as "black, brown, ROYGBIV, grey, white", where ROYGBIV is, of course, rainbow ordering).  The first two color bands are a two-digit number (e.g. 27 for red-violet above), and the third number is a power-of-ten multiplier (e.g. $10^5$ for green above).  Hence the resistor red-violet-green resistor above is a $27\times10^5\Omega$ resistor.
  
 
</latex>
 
</latex>

Latest revision as of 10:00, 21 January 2014

Short Topical Videos[edit]

Reference Material[edit]

  • Horowitz & Hill, The Art of Electronics, 2nd Ed., Ch. 1

Ohm’s Law

where is voltage, measured in Volts (), with typical values ranging from (into an oscilloscope) to (power lines, severe arcing danger); is current, measured in Amperes (), typical values ranging from (relatively safe for bench-top work) to (very dangerous); is resistance, measured in Ohms (), typical values ranging from (power resistors dissipating a lot of power) to (almost a no-connect).

Resistor

Resistor.jpg


A typical (330) resistor

A resistor resists the flow of electrons, such that a potential (i.e. voltage) is required to produce a current, as described by Ohm’s Law above. If we imagine electric current flowing as water, a resistor would be a narrow pipe. The higher the resistance, the narrower the pipe, and the harder you will have to push to get a liter-per-second of water through it. As per all electronic components, resistors dissipate energy as heat according to the equation:

Resistors in Series

Resistors in series add because, in the pipe analogy used above, all the water has to go through all of the pipes, and they all contribute drag:

Resistor series.png


Resistors in series

Resistors in Parallel

Resistors in parallel add reciprocally. In the pipe analogy, water has a choice of which pipe to flow through, and the bulk of the water will be carried by the widest pipe (or for electrons, the lowest-value resistor). Having more paths to choose from will always always reduce drag, but a thin straw next to a firehose isn’t going to do much:

Resistor parallel.png


Resistors in parallel

Reading Resistor Values

Resistor bands.png


Color band locations on resistors

Resistor values are often encoded on the component using colors. For determining the value of a resistor in Ohms, place the component with the triplet of color bands on the left side, and then read from left to right. For the resistor above, we have red-violet-green.

Color chart.png


Matching colors to values

Match each color with a digit using the chart above (I remember it as "black, brown, ROYGBIV, grey, white", where ROYGBIV is, of course, rainbow ordering). The first two color bands are a two-digit number (e.g. 27 for red-violet above), and the third number is a power-of-ten multiplier (e.g. for green above). Hence the resistor red-violet-green resistor above is a resistor.