dVdI

dVdI is commonly written as dV/dI and denotes the differential of voltage with respect to current along an I–V characteristic. In electronics the quantity is also called the differential resistance and is the reciprocal of the differential conductance (Gd = dI/dV). While some informal texts may render it as dVdI, the standard notation uses the division to indicate a derivative.

Mathematically, if a device has a voltage V that depends on current I, V = V(I), then dV/dI evaluated at a given operating point is the slope of the V–I curve there. Its units are ohms, and it describes the small-signal, incremental change in voltage for a small change in current around that point. For a linear resistor with constant resistance R, dV/dI equals R. For nonlinear components, dV/dI varies with bias and may differ significantly from any static DC resistance.

Measurement and use in circuit analysis rely on small-signal or incremental modeling. By applying a tiny perturbation around a bias point and observing the resulting voltage change, engineers determine Rd, which informs impedance, stability, and dynamic response in circuits containing diodes, transistors, superconducting junctions, memristors, and other nonlinear elements.

Examples of relevance include diode forward bias, where Rd = nVt/I decreases as current increases, and superconducting Josephson junctions, where Rd varies with current and voltage steps. Overall, dV/dI captures how an electronic element resists changes in current at a given operating point and is essential for small-signal analysis.