Biological populations of cells show considerable cell-to-cell variability. Study of single cells and analysis of cell heterogeneity are considered to be critical in understanding biological processes such as stem cell differentiation and cancer development. Recent advances in lab-on-a-chip techniques have allowed single-cell capture in microfluidic channels with the possibility of precise environmental control and high throughput of experiments with minimal usage of samples and reagents. In recent years, label-free techniques such as electrical impedance spectroscopy have emerged as a non-invasive approach to studying cell properties. In this study, we have designed and fabricated a microfluidic device that combines hydrodynamic trapping of single cells in pre-defined locations with the capability of running electrical impedance measurements within the same device. We have measured mouse embryonic stem cells (mESCs) at different states during differentiation (t=0h, 24h and 48h) and quantitatively analysed the changes in electrical parameters of cells during differentiation. A marked increase in the magnitude of the cell impedance is found during cell differentiation, which can be attributed to an increase in cell size. The analysis of the measurements shows that the nucleus-to-cytoplasm ratio decreases during this process. The degree of cell heterogeneity is observed to be the highest when the cells are at the transition state (24h), compare with cells at undifferentiated (0h) and fully differentiated (48h) states. The device enables highly efficient single cell trapping and provides sensitive, label-free electrical impedance measurements of individual cells, enabling the possibility of quantitatively analysing their physical state as well as studying the associated heterogeneity of a cell population.