Oxide semiconductor TFTs have attracted considerable attention in the recent past due to their excellent mobility, high optical transparency in the visible region, and most importantly their fabrication process at low-temperature. However, charge trapping formation in the gate dielectric and the interfaces in such oxide TFTs leads to serious issues such as their operational stability and reliability. Understanding the charge trapping mechanism is therefore of utmost importance to identify the root cause of the aforesaid problems. In this report, we present a detailed study on the charge trapping and dynamic charge transport of a-IGZO TFTs by examining microsecond fast IV (FIV), pulse IV (PIV), and transient IV measurements. The a-IGZO TFTs have designed and fabricated with various Ga compositions (0, 0.14 and 0.22). It was observed that the charge trapping in the a-IGZO TFT is reliant on the sweeping time and the carrier mobility measured using the FIV technique was found to be higher than that obtained from the conventional DC IV measurement. Mobility values (mu(m)) was also measured through the PIV technique and are found to be approximately 10%, 16%, and 21% lower than the intrinsic mobility values. Temperature-dependent study reveals that the intrinsic mobility values (18.45, 16.1 and 12.03 cm(2)V(-1) s(-1)) are higher than the pulse mobility values for various Ga compositions (0, 0.14 and 0.22) at higher temperature (175 degrees C) probably due to the formation of free carriers. Suitable optimization of process parameters of a-IGZO TFTs can therefore enhance the device stability and reliability characteristics leading to their potential utilization in flexible and stretchable electronic devices, sensors & detectors and biomedical devices.