An expression is derived for the perturbative response of a lumped resonance circuit to a sudden change in the circuit parameters. This expression is shown to describe also the photo-induced conductivity of a semiconductor mounted in a single-mode microwave cavity. The power dissipated in the cavity is measured in the two dimensions corresponding to time (after photo-excitation of the sample) and frequency (of the microwave driving source). Analysis of the experimental data for different semiconductor materials demonstrates the general applicability of the presented analytical expression here, by retrieving the time dependence of the sample's photo-induced conductivity.