A resistance temperature detector (RTD) provides a resistance output that is related to temperature, Consider an RTD with $$R_o=100Omega$$, $$alpha=004°"C"^-1$$, and $$T_o=0°"C"$$. The change in resistance ($$Omega$$) of the RTD for a 10°C change in temperature is most nearly: 

A.   0.04
B.   0.4
C.   4.0
D.   100.4

The controlling equation for resistance temperature detectors (RTDs) can be found on page 219 of the FE reference handbook, and is as follows:

Since we are interested in finding the change of resistance, $\Delta R_T$, we can manipulate the equation as follows:

$\Delta R_T=\left(R_0\right[1+\alpha (T_2-T_0)\left]\right)-\left(R_0\right[1+\alpha (T_2-T_1)\left]\right) where T_2-T_{1 }=10$

We can arbitrarily assign $T_2=10$ and $T_1=0$ since the temperature difference is 10:

$$\begin{gathered} \Delta R_T=\left(100\right[1+.004(10-0)\left]\right)-\left(100\right[1+.004(0-0)\left]\right) \\ \Delta R_T=\left(100\right(1+.04\left)\right)-\left(100\right(1\left)\right) \\ \Delta R_T=104-100 \\ \Delta R_T=4 \end{gathered}$$

Therefore, the change of resistance is most nearly 4.0$\Omega$, which is answer C.