An analog signal can take a continuous range of values within a specific range, while alternating current (AC) is a type of analog signal that alternates between two extreme values of opposite sign. The mathematical representation of AC, such as i(t) = I sin(2πt), demonstrates its nature by varying continuously between -I and I. Both analog signals and AC share the characteristic of being continuous, but AC specifically refers to the periodic change in direction of current. Understanding these distinctions is essential in fields like electronics and signal processing.