In virtual synchronous generator (VSG)-related discussions, the inner voltage and current controls are always omitted due to their fast dynamics. However, converters require a lower switching frequency as their power rating increases, which constrains the cascaded controls' bandwidths. Hence, the interactions between the controls at different time-scales should be analyzed. Specifically, the aim is to reveal the effects of inner control loops on the VSG system from the torque perspective. First, this paper derives a linearized model of the internal voltage phase and amplitude, which accurately depicts the VSG system characteristics. Subsequently, based on this linearized model, we derive an equivalent single-input single-output motion-equation- based model. The proposed model can be used to investigate the change in damping and synchronizing torque components under low control bandwidths and weak grid conditions. Finally, simulation results are presented to validate the proposed modeling and effects analysis. Our model is general and can be used for any power ratings, and the study also provides a guide to designing control parameters for VSG systems.