Circuits and waves are two subjects built on the same handful of proportional relationships. Ohm's law (V = IR) fixes how voltage, current and resistance relate in a steady circuit, and electrical power (P = VI) turns that into the watts printed on an appliance label. Waves obey v = fλ — speed equals frequency times wavelength — which is as true for sound in air as it is for light in a vacuum.
Calculate current and power from voltage and resistance with Ohm's law (V = IR, P = V²/R).
I = V / R, P = V² / RCalculate wavelength from wave speed and frequency (λ = v/f) — for light, radio, WiFi and sound.
λ = v / fCalculate image distance and magnification with the thin lens equation.
1/f = 1/dₒ + 1/dᵢCalculate pressure from force and area (P = F/A).
P = F / AConvert watts to amps: calculate the current a device draws from its power and supply voltage (I = P / V).
I = P / VBecause light is itself an electromagnetic wave, the optical tools belong here too: the thin-lens equation (1/f = 1/do + 1/di) predicts where a lens forms an image and how big it is. Use these to size a cable or fuse, convert an appliance's watts into the amps it will draw, find the wavelength of a given frequency, or place a lens. Circuit results assume direct current and a constant resistance; wave results assume a single uniform medium.