In this paper, we introduce a new elliptic PDE: $${{ abla}{cdot}(frac{|{gamma}^{omega}(r)|^2}{sigma}{ abla}v_{omega}(r))=0,;r{in}{Omega},\v_{omega}(r)=f(r),;r{in}{partial}{Omega},$$ where ${gamma}^{omega}={sigma}+i{omega}{epsilon}$ is the admittivity distribution of the conducting material ${Omega}$ and it is shown that the introduced elliptic PDE can replace the standard elliptic PDE with conductivity coefficient in EIT imaging. Indeed, letting $v_0$ be the solution to the standard elliptic PDE with conductivity coefficient, the solution $v_{omega}$ is quite close to the solution $v_0$ and can show spectroscopic properties of the conducting object ${Omega}$ unlike $v_0$. In particular, the potential $v_{omega}$ can be used in detecting a thin low-conducting anomaly located in ${Omega}$ since the spectroscopic change of the Neumann data of $v_{omega}$ is inversely proportional to thickness of the thin anomaly.