= Load impedance
{title2=$Z_L$}
The \b[load impedance] $Z_L$ is the terminal <electrical impedance> of the receiving <electrical load>, at a stated <frequency> and operating condition. With <electric current> defined as entering the load's positive-voltage terminal, sinusoidal steady-state <phasors> obey
$$
Z_L=\frac{V_L}{I_L}.
$$
The <complex number> records both the amplitude ratio and the phase difference. It belongs to the selected terminals and model; an arbitrary nonlinear device need not have a single amplitude-independent impedance.
A <resistor> gives $Z_L=R$. A series <resistor> and <capacitor> give
$$
Z_L=R+\frac1{\mathrm i\omega C}=R-\frac{\mathrm i}{\omega C}.
$$
For $R=1\,\mathrm{k\Omega}$, $C=1\,\mathrm{\mu F}$ and $f=1\,\mathrm{kHz}$, this is about $(1000-159.15\mathrm i)\,\Omega$, with magnitude $1012.59\,\Omega$ and phase $-9.04^{\circ}$. Load <electric current> leads its terminal <electric potential difference> in this example. The component laws and <phasor> interpretation follow the sinusoidal circuit model.<University Physics Volume 2 by Samuel J. Ling and others>[Section 15.3, RLC series circuits and impedance]{ref}
The load changes the source's operating point. A source with open-circuit <phasor> $V_s$ and series impedance $Z_s$ supplies
$$
I_L=\frac{V_s}{Z_s+Z_L},\qquad V_L=\frac{Z_LV_s}{Z_s+Z_L}.
$$
For RMS <phasors>, the <complex power (electrical engineering)> entering the load is $S_L=V_LI_L^*$. Its <real part> is the mean delivered <power>,
$$
P_L=|I_L|^2\operatorname{Re}Z_L.
$$
Using peak rather than RMS amplitudes would introduce a factor $1/2$ in that power expression.
An original resistive example has $V_s=1\,\mathrm V$ RMS and $R_s=1\,\mathrm{k\Omega}$. A $9\,\mathrm{k\Omega}$ load draws $0.100\,\mathrm{mA}$, receives $0.900\,\mathrm V$ and dissipates $0.090\,\mathrm{mW}$. A $1\,\mathrm{k\Omega}$ load instead receives $0.500\,\mathrm V$ and dissipates $0.250\,\mathrm{mW}$. More delivered power need not mean a smaller voltage error.
The <input impedance> of an instrument is a load when the instrument is connected to a source. High-input-impedance buffering reduces this interaction in voltage measurements.<Instrumentation amplifier (IA) topologies: three-amp by Tamara Alani>[Presentation slides 3–5, source loading and input buffering]{ref} <Impedance bridging> prioritizes preserving the source signal; <impedance matching> addresses other objectives such as maximum power transfer under its assumptions.
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