Dissertation (MSc Science in Mathematics)The new exact solutions for the charged anisotropic stellar object were found by using Einstein-Maxwell field equations. In this study, the metric function, linear equation of state, and a new choice of the measure of anisotropy were used to formulate new quark star models. The field equations were transformed by adopting Bannerji and Durgapal transformation variables. The general differential equation governing the model was generated with the help of Einstein field equations, and the form of logarithmic measure of anisotropy. The exact solution for the models was obtained by specifying different values of the parameters used in the models. In this model, anisotropic and isotropic results were regained as a special case. We regained anisotropic models found by Maharaj, and isotropic models performed by Misner and Zapolsky, Harko and Mak, Maharaj and Komathiraj. The plotted graphs and physical analysis revealed that matter variables and the gravitational potentials were behaved well. Therefore the models satisfied the energy conditions, stability condition, and speed of sound that were consistent for quark stars.