signconventies

Sign conventions are prescribed rules for assigning signs to quantities in mathematical models of physical systems. They specify, for example, which direction is considered positive, which terminal is positive, or whether a quantity is considered to increase or decrease under a given action. The purpose is to remove ambiguity in equations relating quantities such as displacement, velocity, force, current, voltage, power, and energy.

Common examples include: In mechanics and kinematics, choosing a positive axis and using positive signs for quantities that act in that direction; consequently, the signs of velocity, acceleration, and angular quantities follow the chosen convention. In electrical engineering and circuit theory, the passive sign convention designates current entering the positive-labeled terminal as positive, so power P = VI is positive when a component absorbs power; the active sign convention uses opposite assignment, leading to P = -VI for absorbing power. In thermodynamics and related fields, different communities use different conventions for heat and work, which affects energy balance equations; the key rule is to document the chosen convention.

The use of sign conventions requires explicit statement in any analysis or report; changing the convention changes the sign of several quantities but not the underlying physics. Common pitfalls include inconsistent directions, ambiguous nomenclature, and failing to apply the convention consistently across all parts of an equation or model. To avoid errors, researchers verify with simple test cases and ensure clear notation.