The present contribution investigates the physical layer security in a cognitive radio network (CRN). To this end, we consider an underlay uplink CRN consisting of multiple secondary sources, a single-antenna secondary base station, and multiple eavesdroppers. In addition, we assume that the secondary sources transmit their data sequentially and that a jammer is randomly chosen from the remaining source nodes to send a jamming signal to the eavesdroppers. However, in an uplink underlay CRN, a friendly jammer is not always allowed to use its maximal transmit power as the secondary users are required to continuously adapt their power in order to avoid causing interference to the primary users. As a consequence, enhancing the system security using a jammer with low transmit power in the presence of numerous eavesdroppers turns out to be questionable. In this regard, we derive novel analytic expressions that assist in quantifying the achievable security levels and the corresponding limitations. This leads to the development of useful insights on the impact of network parameters on the performance of the system's security. The offered analytic results are corroborated through Monte Carlo simulation. It is shown, that for a low transmit power of the friendly jammer, the system's security can only be enhanced for a small number of eavesdroppers.