Electric network frequency (ENF) is a time-varying signal of the frequency of mains electricity in a power grid. It continuously fluctuates around a nominal value (50/60 Hz) clue to changes in the supply and demand of power over time. Depending on these ENF variations, the luminous intensity of a mains-powered light source also fluctuates. These fluctuations in luminance can he captured by video recordings. Accordingly, the ENF can he estimated from such videos by the analysis of steady content in the video scene. When videos are captured by using a rolling shutter sampling mechanism, as is done mostly with CMOS cameras, there is an idle period between successive frames. Consequently, a number of illumination samples of the scene are effectively lost due to the idle period. These missing samples affect the ENF estimation, in the sense of the frequency shift caused and the power attenuation that results. This paper develops an analytical model for videos captured using a rolling shutter mechanism. This model illustrates how the frequency of the main ENF harmonic varies depending on the idle period length, and how the power of the captured ENF attenuates as idle period increases. Based on this, a novel idle period estimation method for potential use in camera forensics that is able to operate independently of video frame rate is proposed. Finally, a novel time-of-recording verification approach based on the use of multiple ENF components, idle period assumptions, and the interpolation of missing ENF samples is also proposed.