Wheatstone Bridge Calculator

At a glance:The Wheatstone bridge (Wheatstone bridge): four resistors R₁, R₂, R₃, R_x form a diamond; the supply V_in is across one diagonal and a galvanometer (or voltmeter) across the other. At balance V_out=0, giving the balance condition R_x/R₃=R₂/R₁, i.e. R_x=R₂·R₃/R₁. Off balance, V_out=V_in·(R_x/(R_x+R₃) − R₂/(R₁+R₂)). Invented by Samuel Hunter Christie (1833) and improved/popularised by Charles Wheatstone (1843) to measure unknown resistances precisely (accuracy to 10⁻⁴ Ω). Classic example: R₁=100 Ω, R₂=200 Ω, R₃=100 Ω, R_x=200 Ω → balanced (R_x=R₂·R₃/R₁=200×100/100=200 Ω), V_out=0. Off-balance example: with R_x=250 Ω, V_out>0 (R_x above balance), current flows from R₃ toward R₁. Applications: (1) precise resistance measurement — set three known resistors, adjust R_x until the galvanometer reads zero, then back-calculate R_x; (2) strain gauges — R_x is a gauge whose resistance changes slightly under deformation (ΔR/R≈10⁻⁶), so V_out reveals strain; (3) temperature sensing (platinum Pt100/Pt1000) — R_x is a platinum resistor whose value tracks temperature, V_out infers the temperature; (4) pressure sensing and load cells — four gauges form a bridge measuring force and weight (core of electronic scales); (5) AC bridges compare capacitance/inductance. History: Christie first built it in 1833; Wheatstone demonstrated it to the Royal Society in 1843, and it became named after him. Galvanometer sensitivity sets the bridge accuracy; modern designs use op-amps. Notes: (1) larger V_in raises sensitivity but increases power; (2) R₁–R₄ typically 100 Ω–10 kΩ — too low wastes power, too high is noise-sensitive.