The positivity and asymptotic stability of time-varying discrete-time and continuous-time linear systems and electrical circuits are addressed. Necessary and sufficient conditions for the positivity of the time-varying linear systems and electrical circuits are established. Using the extension to positive fractional systems of the Lyapunov method the asymptotic stability of positive systems and electrical circuits is shown. Conditions for the positivity of descriptor time-varying discrete-time linear systems are established. Examples of positive and asymptotically stable systems and electrical circuits are presented.