Electronics Examples

Short worked examples for the ideas in Electronics Equations and definitions.

1. Single resistor

A $12\mathrm{V}$ supply is connected across a $6\Omega$ resistor.

$I=\frac{V}{R}=\frac{12}{6}=2\mathrm{A}$

Power dissipated:

$P=IV=2\times 12=24\mathrm{W}$

Sanity check: $24\mathrm{W}$ is a lot for a small resistor, so the physical part must be rated for it.

2. Series resistors

Two resistors, $4\Omega$ and $8\Omega$, are in series on a $12\mathrm{V}$ battery.

$R_{eq}=4+8=12\Omega ,I=\frac{12}{12}=1\mathrm{A}$

Voltage drops: $4\mathrm{V}$ across the $4\Omega$ resistor and $8\mathrm{V}$ across the $8\Omega$ resistor. Drops add back to the supply voltage.

3. Parallel resistors

A $6\Omega$ and $3\Omega$ resistor are in parallel across $6\mathrm{V}$.

$\frac{1}{R_{eq}}=\frac{1}{6}+\frac{1}{3}=\frac{1}{2}\Rightarrow R_{eq}=2\Omega$

Total current is $I=6/2=3\mathrm{A}$. Branch currents are $1\mathrm{A}$ and $2\mathrm{A}$, which add to the total.

4. Sign check

If a guessed loop current gives $I=-0.5\mathrm{A}$, keep the magnitude and reverse the direction. The negative sign is information.

5. Voltage divider

Two resistors in series split the supply voltage in proportion to resistance. With $R_1=1\mathrm{k}\Omega$, $R_2=2\mathrm{k}\Omega$, and $V_{in}=9\mathrm{V}$, the output across $R_2$ is

$V_{out}=9\frac{2}{1+2}=6\mathrm{V}$

This is a common way to make a reference voltage when the load current is small.

Related: Voltage, Current, Resistance, Electronics Common pitfalls.