# Ohm's Law

### Reference Material

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

## Ohm’s Law

$V=IR,\,\!$ 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).

## Resistor

A typical (330$\Omega$ ) 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:

$P=IV\,\!$ ### 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

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

$R={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\dots +{\frac {1}{R_{n}}}}}\,\!$ 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 $27\times 10^{5}\Omega$ resistor.