di1dt

di1dt refers to the time derivative of a quantity i1 with respect to time t. In many contexts, i1 denotes a current in a particular branch of an electrical circuit, but the symbol can represent any time-dependent quantity labeled i1. The derivative expresses how i1 changes over time and is defined as the limit as Δt approaches zero of (i1(t+Δt) − i1(t)) / Δt. It is commonly written as di1/dt, i1′, or, in dot notation, i̇1.

In physics and engineering, di1/dt appears in a wide range of dynamic equations. For example, in an inductor with inductance L, the voltage across the component is v = L di1/dt, where i1 is the current through the inductor. In other dynamical systems, di1/dt can be a term in differential equations that describe how the system evolves over time, such as control systems or mechanical-electrical models.

Notation and related concepts vary by field. di1/dt is the standard mathematical form; i1′ is a common compact form; and i̇1 uses the dot notation often found in physics to indicate a time derivative. If i1 has units of amperes, then di1/dt has units of amperes per second (A/s).

See also differential calculus, time derivative, i-notation in circuits, and first-order differential equations.