Answer
Yes, it is possible.
Work Step by Step
Use equation 18–3 to find the resistance. The cross-sectional area $A=\pi r^2=\frac{\pi d^2}{4}$.
$$R=\rho\frac{\mathcal{l}}{A}=\rho\frac{4 \mathcal{l}}{\pi d^2}$$
$$R_W=R_{Cu}$$
$$\rho_{W}\frac{4 \mathcal{l}}{\pi d_{W}^2}=\rho_{Cu}\frac{4 \mathcal{l}}{\pi d_{Cu}^2}$$
$$d_W=d_{Cu}\sqrt{\frac{\rho_W}{\rho_{Cu}}}$$
$$d_W=(2.2mm)\sqrt{\frac{5.6\times10^{-8}\Omega \cdot m}{1.68\times10^{-8}\Omega \cdot m }}$$
$$=4.0mm$$
The diameter of the tungsten wire should be 4.0 mm.
