= Null measurement method
A \b[null measurement method] adjusts a reference or a system setting until a difference signal is brought to zero. A <null detector> tests the residual mismatch; the final <measured quantity value> follows from the reference and the balance condition. The VIM lists null measurement among <measurement methods>.<International vocabulary of metrology by JCGM>[VIM3entry2.5, note, null measurement method]{ref}
A <Wheatstone bridge> provides a concrete electrical apparatus. The PHYWE manual connects a source across two resistor dividers and a current detector between their middle junctions; balance occurs when those junction potentials agree and detector current vanishes.<Wheatstone bridge by PHYWE (P2410200)>[p4, Theory (1/3)–(2/3), Figure2 and equations1–4]{ref} A sliding-wire implementation adjusts the divider ratio continuously.
For an original notation, let the left branch contain upper resistance $R_a$ and lower $R_b$, while the right contains upper unknown $R_x$ and lower reference $R_s$. With source <electric potential difference> $V_s$ and negligible loading at balance, the middle-junction potentials above the lower supply terminal are
$$
V_L=V_s\frac{R_b}{R_a+R_b},\qquad
V_R=V_s\frac{R_s}{R_x+R_s}.
$$
Setting $V_L-V_R=0$ yields
$$
R_x=\frac{R_a}{R_b}R_s.
$$
For $R_a=2000\,\Omega$, $R_b=1000\,\Omega$ and $R_s=500\,\Omega$, the balance identifies $R_x=1000\,\Omega$ independently of the nonzero source magnitude in this ideal model.
Zero on a display has finite meaning. With $V_s=3\,\mathrm V$, the derivative of residual $V_L-V_R$ with respect to $R_x$ at this balance is $1/1500\,\mathrm{V\,\Omega^{-1}}$. A residual magnitude below $10\,\mathrm{\mu V}$ therefore corresponds locally to about $0.015\,\Omega$ of unresolved mismatch. A detector zero offset can also shift the apparent balance. The <null measurement method> reduces reliance on calibrated detector gain at exact balance, but reference uncertainties, lead effects, detector sensitivity and <instrumental drift> remain relevant to the complete <measurement result>.
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