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Electrically exploding foil (EEF) technique offers a unique small-scale device to accelerate thin plastic foils (liner) to high (>10 km) velocities. Besides direct application as a macroparticle accelerator for various applications, such systems can also serve as plasma injectors or pre-accelerators to electromagnetic launchers. Though empirical models for scaling of liner velocity in such devices suggest the important role of burst current density in exploding foil, but behavior of slow and fast (dI/dt≥1012 A/s) systems appear to differ significantly. In this paper, based on some established models and realistic current profiles, it is inferred that higher energy of a capacitor bank may not translate to higher velocity in "optimized" EEF systems, if its rise time is poor. A possible way to overcome this problem could be to use an additional stage of metallic foil as an opening switch. The consequent fast rising current may be expected to enhance the liner velocity by a factor of 2-5 in typical capacitor banks. Analysis and relevant experiments are described to investigate the issues.