In this paper, a model for the a.c./transient behaviour of an Si resistor at liquid-He temperatures is established, taking account of the dominant carrier-dopant interactions, i.e. shallow-level impact ionisation and carrier capture. As will be shown, the corresponding set of coupled differential equations can be linearized in the small-signal approximation, enabling an analytical solution. The resulting small-signal impedance is a damped oscillatory circuit, whereby the impact ionisation/capture events are represented by an R-L series equivalent. The corresponding R-L time constant is characteristic for the (quasi-) exponential variation of the injected space-charge and consequently for the transient behaviour of Si devices at 4.2 K. Finally, the occurrence of spontaneous, or forced oscillatory behaviour, which is occasionally observed in the low-frequency noise spectrum of e.g. a metal-oxide semiconductor transistor, is discussed.