## Resistance Temperature Detector

Consider a resistance temperature detector (RTD) is made from platinum. What is the change in resistance of the RTD for a 15°C change in temperature if the RTD’s resistance at reference temperature (0°C) is 50 ohms? Note the resistance temperature coefficient for platinum is 0.004°C^(-1).

Hint
$$R_T=R_0[1+\alpha (T-T_0)]$$$where $$R_T$$ is the RTD’s resistance at temperature $$T$$ , $$R_0$$ is the RTD’s resistance at the reference temperature $$T_0$$ (usually 0°C), and $$\alpha$$ is the resistance temperature coefficient. Hint 2 The problem is asking for $$R_T-R_0=?$$ Resistance Temperature Detector (RTD) is a device used to relate change in resistance to change in temperature. They are typically made from platinum, and have the controlling equation: $$R_T=R_0[1+\alpha (T-T_0)]$$$
where $$R_T$$ is the RTD’s resistance at temperature $$T$$ , $$R_0$$ is the RTD’s resistance at the reference temperature $$T_0$$ (usually 0°C), and $$\alpha$$ is the resistance temperature coefficient.
$$R_T=50\Omega[1+(0.004^{\circ}C^{-1}) (15^{\circ}C)]=50\Omega[1.06]=53\:\Omega$$$To find the change in resistance: $$R_T-R_0=53\Omega-50\Omega=3\:\Omega$$$
$$3\:\Omega$$\$