# Ohm's Law

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### Reference Material

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

## Ohm’s Law

${\displaystyle V=IR,\,\!}$

where ${\displaystyle V}$ is voltage, measured in Volts (${\displaystyle V}$), with typical values ranging from ${\displaystyle mV}$ (into an oscilloscope) to ${\displaystyle kV}$ (power lines, severe arcing danger); ${\displaystyle I}$ is current, measured in Amperes (${\displaystyle A}$), typical values ranging from ${\displaystyle mA}$ (relatively safe for bench-top work) to ${\displaystyle A}$ (very dangerous); ${\displaystyle R}$ is resistance, measured in Ohms (${\displaystyle \Omega }$), typical values ranging from ${\displaystyle \Omega }$ (power resistors dissipating a lot of power) to ${\displaystyle M\Omega }$ (almost a no-connect).

## Resistor

A typical (330${\displaystyle \Omega }$) 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:

${\displaystyle P=IV\,\!}$

### 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:

Resistors in series

${\displaystyle R=R_{1}+R_{2}+\dots +R_{n}\,\!}$

### 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:

Resistors in parallel

${\displaystyle R={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\dots +{\frac {1}{R_{n}}}}}\,\!}$

### Reading Resistor Values

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.

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. ${\displaystyle 10^{5}}$ for green above). Hence the resistor red-violet-green resistor above is a ${\displaystyle 27\times 10^{5}\Omega }$ resistor.
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