How to use a multimeter .

Useful formulas

DC (Direct current) circuits

$V = I \times R \;\; \mathrm{(Ohm's} \; \mathrm{Law)}$

$P = I V = I^2 R = \frac{V^2}{R} \,\!$

$V = \sqrt{PR}$

where V = voltage difference (SI unit: volt), I = electric current (SI unit: ampere), R = resistance (SI unit: ohm), P = power (SI unit: watt).

AC (Alternating current) circuits

$V = \frac{P}{I\;\cos\phi}$

$V = \frac{\sqrt{P\;Z}}{\sqrt{\cos\phi}} \!\$

$V = \frac{I\;R}{\cos\phi}$

Where V=voltage, I=current, R=resistance, P=true power, Z=impedance, φ=phase difference between I and V.

AC conversions

$V_{avg} = 0.637\,V_{pk} = \frac{2}{\pi} V_{pk} = \frac{\omega}{\pi}\int_0^{\pi/\omega} V_{pk} \sin(\omega t - k x) {\rm{d}}x \!\$

$V_{rms} = 0.707\,V_{pk} = \frac{1}{\sqrt{2}} V_{pk} = V_{pk} \sqrt{\langle \sin^2(\omega t - k x) \rangle} \!\$

$V_{pk} = 0.5\,V_{ppk} \!\$

$V_{avg} = 0.319\,V_{ppk}\!\$

$V_{rms} = 0.354\,V_{ppk} = \frac{1}{2 \sqrt{2}} V_{ppk}\!\$

$V_{avg} = 0.900\,V_{rms} = \frac{2 \sqrt{2}}{\pi} V_{rms}\!\$

Where V_pk=peak voltage, V_ppk=peak-to-peak voltage, V_avg=average voltage over a half-cycle, V_rms=effective (root mean square) voltage, and we assumed a sinusoidal wave of the form $V pk sin(ω t - kx)$ , with a period $T = 2π / ω$ , and where the angle brackets (in the root-mean-square equation) denote a time average over an entire period.