This paper presents a general mathematical technique for studying the response and stability of linear time‐varying circuits that contain parameters whose magnitudes vary in a periodic manner with the time. The method presented reduces the solution of the circuit differential equation to that of computing powers of matrices. For purposes of illustration, the method is used to determine the response of an electric circuit consisting of a constant resistance and inductance in series with a periodically varying capacitance. The cases of square‐wave and saw‐tooth‐wave variations of the variable parameter are considered in detail.