## 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**

**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**

**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:

$$$R_T-R_0=53\Omega-50\Omega=3\:\Omega$$$

$$$3\:\Omega$$$