Hysteresis error in a measurement system is best characterized as:

• A. A random fluctuation around the true value
• B. A linear error proportional to input
• C. A time-based drift without input change
• D. A path-dependent error that depends on input history

Answer: (D)

Hysteresis error arises when the measurement system’s output depends on the path the input took, not just the present input value. In other words, the sensor or instrument “remembers” past inputs, so readings follow different routes for increasing versus decreasing input. This creates a loop-like behavior in the input-output relationship.

This isn’t just random noise (which would fluctuate around a value), nor is it a simple linear offset proportional to the current input. It isn’t a slow drift over time with no input change either; drift would move the reading gradually regardless of the input’s history. Instead, hysteresis shows up as a memory effect: the same input can produce different readings depending on whether the input was previously higher or lower, reflecting the system’s history.

A common mental picture is a loop drawn by plotting output versus input while sweeping the input up and then back down—the darker, offset path on the way up versus down demonstrates the path-dependent nature. This often comes from physical phenomena with memory or friction, such as magnetic materials, mechanical play, or restoring elements that don’t respond identically in opposing directions.

So, the best description is that hysteresis error is a path-dependent error that depends on input history.