Electrical engineering

Measurements and electrical safety

Multimeters, RMS versus peak, transformer ratio, and electrical safety.

Basics

Multimeter

A DMM measures voltage (in parallel), current (in series), and resistance (on a de-energized circuit). Voltage mode is high-Z and barely loads the node; current mode uses a low shunt, so the wrong jack or range can blow a fuse or draw an arc. True-RMS meters track distorted waveforms better. Probe category (CAT) must match expected transients.

RMS versus peak

RMS is the DC-equivalent that would dump the same average power in the same resistor. For a pure sine, V_RMS = V_peak / √2 and V_peak-to-peak = 2 V_peak. Mains “230 V” is RMS. Diode and insulation ratings care about peak; heating and power care about RMS. Cheap average-responding meters lie on non-sinusoids.

Transformer ratio

An ideal transformer obeys V_p / V_s = N_p / N_s = I_s / I_p. Turns ratio steps voltage; power (minus loss) is conserved so current steps the other way. Power transformers give galvanic isolation; an autotransformer shares a winding. Real units have copper and iron loss and leakage inductance, so voltage sags a little under load.

Electrical safety

Shock is current through the body. Even with dry skin, tens of milliamperes can disturb the heart. Earthing, breakers, residual-current devices (RCD/GFCI), and double insulation interrupt or divert the path. Prove the circuit dead before you touch, and keep one-hand, insulated-floor, locked-panel habits. This page is a study sketch, not a worksite code.

Formulas

Sine-wave RMS

V_RMS = V_peak / √2 ≈ 0.707 V_peak

Exact for a pure sine. A square wave has RMS equal to peak.

Symbols

V_peak peak value
V_RMS root-mean-square value

Transformer turns ratio

V_p / V_s = N_p / N_s = I_s / I_p

Ideal transformer. Voltage follows turns; current is inverse.

Symbols

N turns
p, s primary, secondary

Average power in a resistor

P = V_RMS I_RMS = V_RMS² / R

Heating follows RMS. Do not size a wire from peak alone.

Symbols

R resistance

Shock current (sketch)

I = V / R_body

R_body varies wildly with skin and path. Current, not voltage alone, sets harm.

Symbols

R_body body-path resistance

Key table

230 V RMS sine	peak ≈ 325 V, peak-to-peak ≈ 650 V
DMM current jack	break the circuit; never park that jack on a voltage node
RCD/GFCI	trips on a few to tens of mA imbalance (follow local code)