The carrier dynamics in InGaN/GaN light-emitting diodes (LEDs) are directly tied to their efficiency and maximum modulation speed, which are important metrics for solid-state lighting, displays, and optical communication. In this work, we measure the carrier dynamics of InGaN/GaN light-emitting diodes using small-signal electroluminescence (SSEL) methods. We specifically study the carrier dynamics of commercial-grade c-plane LEDs with various indium compositions, various deep-level defect densities, and various quantum well thicknesses.  A rate equation approach and associated small-signal circuit are used to model carrier injection, recombination in the active region, recombination in the cladding regions, and carrier escape. The model is fit to the measured optical frequency response (S21) and input impedance (S11) of the LEDs to extract the various carrier lifetimes, the carrier density, and the recombination rates. The results offer insight into the underlying causes of efficiency droop and the green gap and may inform application-specific device design strategies.