The paper deals with electrical impedance tomography, where one utilizes measurements of the voltage and current at the boundary of a body to determine information about the electrical properties inside the body. More precisely, the authors consider a two-phase material with conductivity \(\sigma(x)=\sigma^{(1)}\chi^{(1)}(x) + \sigma^{(2)}\chi^{(2)}(x)\), where \(\chi^{(i)}(x)\) is the characteristic function of phase \(i\), \(i=1,2\), and each phase is assumed to be homogeneous and isotropic. The goal is to use a single measurement of the voltage and current on the boundary to derive lower and upper bounds on the volume fraction of phase 1. The approach, which is a splitting method, is based on the idea to directly derive the bounds by using the positivity of certain variations, is a variational formulation of the relevant PDE, and the null Lagrangians, which are functions of the electric field and current density that can be expressed in terms of the boundary voltage and current data. Particularly, it is found that the bounds are exceedingly tight for a particular two-dimensional geometry consisting of an annulus and surrounding material.