The experimental information accumulated by the BABAR, Belle and LHCb experiments have shown disagreement on the measurements of the ratios $R(D)$ and $R(D^{*})$, compared with the SM predictions. In addition, the $D^\ast$ longitudinal polarization $F_L(D^\ast)$ related with the channel $B \to D^\ast \tau \bar{\nu}_\tau$ observed by the Belle Collaboration and the ratio $R(J/\psi)$ measured by the LHCb Collaboration also show discrepancies with their corresponding SM estimations. All these observables are associated with the charged-current transition $b \to c \tau \bar{\nu}_\tau$. We present a model-independent study based on the most general effective Lagrangian that yields a tree-level effective contribution to the transition $b \to c \tau \bar{\nu}_\tau$ induced by a general $W'$ boson and a charged scalar. We present a phenomenological study of parameter space allowed by the new experimental $b \to c \tau \bar{\nu}_\tau$ data. For comparison, we include some of the NP realizations that have already been studied in the literature.