Voltmeter loading
= Voltmeter loading
<Voltmeter loading> is the change in an <electric potential difference> caused by the <electric current> drawn by the measuring <voltmeter>.
For a <loaded voltage divider> in steady <direct current>, a <voltmeter> connected across the lower <resistor> places its finite input <electrical resistance> $R_m$ in parallel with the lower arm's <electrical resistance> $R_2$ and any intended <electrical load> of <electrical resistance> $R_L$. With positive, fixed <electrical resistances>, an upper <resistor> of <electrical resistance> $R_1$, and an ideal <voltage source> supplying <electric potential difference> $V_{\mathrm{in}}$, <Kirchhoff's current law> and <Ohm's law> give
$$
\frac{V_{\mathrm{in}}-V_m}{R_1}=\frac{V_m}{R_2}+\frac{V_m}{R_L}+\frac{V_m}{R_m},\qquad
R_p=\left(\frac1{R_2}+\frac1{R_L}+\frac1{R_m}\right)^{-1},\qquad
V_m=V_{\mathrm{in}}\frac{R_p}{R_1+R_p}.
$$
Here $V_m$ is the connected circuit's <electric potential difference> across the <voltmeter>; omit $1/R_L$ if there is no intended <electrical load>. The parallel connection and need for large input <electrical resistance> are standard <voltmeter> operating principles.<University Physics Volume 2 by Samuel J. Ling and others/10.4 Electrical Measuring Instruments>[§10.4, Measuring Voltage with a Voltmeter: parallel connection and large input resistance]{ref}
<Voltmeter loading> is a bias relative to the target <electrical circuit> with the <voltmeter> absent and any intended <electrical load> still present. <Voltage divider loading error> instead compares the attached-load output with the wholly unloaded output. An accurate readout of $V_m$, supported by <measurement calibration>, can still differ from either target: calibration accuracy concerns the indication of the connected <electric potential difference>, whereas <voltmeter loading> changes that <electric potential difference> itself.