limiters (because they present higher initial resistance until the current limiter reaches quiescent temperature), temperature sensors and thermistors. Negative temperature coefficient of resistance of a semiconductor An increase in the temperature of a semiconducting material results in an increase in charge-carrier concentration. This results in a higher number of charge carriers available for recombination, increasing the conductivity of the semiconductor. The increasing conductivity causes the resistivity of the semiconductor material to decrease with the rise in temperature, resulting in a negative temperature coefficient of resistance. Temperature coefficient of elasticity The elastic modulus of elastic materials varies with temperature, typically decreasing with higher temperature. Temperature coefficient of reactivity In nuclear engineering, the temperature coefficient of reactivity is a measure of the change in reactivity (resulting in a change in power), brought about by a change in temperature of the reactor components or the reactor coolant. This may be defined as Where is reactivity and T is temperature. The relationship shows that is the value of the partial differential of reactivity with respect to temperature and is referred to as the "temperature coefficient of reactivity". As a result, the temperature feedback provided by has an intuitive application to passive nuclear safety. A negative is broadly cited as important for reactor safety, but wide temperature variations across real reactors (as opposed to a theoretical homogeneous reactor) limit the usability of a single metric as a marker of reactor safety. In water moderated nuclear reactors, the bulk of reactivity changes with respect to temperature are brought about by changes in the temperature of the water. However each element of the core has a specific temperature coefficient of reactivity (e.g. the fuel or cladding). The mechanisms which drive fuel temperature coefficients of reactivity are different from water temperature coefficients. While water expands as temperature increases, causing longer neutron travel times during moderation, fuel material will not expand appreciably. Changes in reactivity in fuel due to temperature stem from a phenomenon known as doppler broadening, where resonance absorption of fast neutrons in fuel filler material prevents those neutrons from thermalizing (slowing down). Mathematical derivation of temperature coefficient approximation In its more general form, the temperature coefficient differential law is: Where is defined: And is independent of . Integrating the temperature coefficient differential law: Applying the Taylor series approximation at the first order, in the proximity of , leads to: Units The thermal coefficient of electrical circuit